Why Frames Tilt Forward

Asked and Answered: 3.1

There is a ten-foot long alcove in our lower-level hallway — we call it the gallery.  This is the one place in our house I can hang whatever I want (i.e., my own art) and switch it out whenever I want. To facilitate this, I installed a hanging system — basically a slotted rail mounted near the ceiling, with sliding wires and height-adjustable hooks.  These systems cost more than you think they should (just search hanging systems to see which company is currently paying Google the most money to promote their wares).

Frame Tilt - Gallery Rail SystemI was a bit surprised when I hung my first piece and saw how far forward it tilted (photo at right). It was not intuitive to me why hanging a fairly light 12″ x 16″ frame on a long wire should cause it to tilt so much. So naturally I googled it.

Unlike the latest Netflix binge-watch, the topic of tilted picture frames is not discussed much on the web. When it is mentioned, some surprisingly bad and/or misleading advice is often given. For example, consider this article in the San Fransisco Chronicle, “How to Keep Heavy Paintings Flush Against the Wall.” Written by a crafter, the author asserts: “A heavy painting tends to lean forward under its own weight, which isn’t attractive and can cause wall damage if it pulls its hanger from the wall.”

The second part of that sentence is true enough, but the notion that only heavy items lean forward is false, as my experience shows. Furthermore, the solution offered by the author may be well-intentioned but is half-baked at best. She instructs the reader to cut a piece of wire slightly wider than the frame, thread it through eye hooks on the sides of the frame, then “ensure the wire is taut to minimize the chances of the picture leaning forward.” Sounds reasonable until you consider the stress this would put on the frame.

The diagram at left shows how the wire tension increases markedly when a wire is strung taut. A 7-lb frame would generate exactly 7 pounds of tension when hung from a single vertical wire. But if you were to string the wire tightly across the frame and hang it on a hook, the 7-lb frame could produce 40 pounds of tension in the wire, pulling inward on each side of the frame and possibly damaging the art.

Stretching a wire tightly across a frame is about the worst thing you can do, especially with a heavy piece of art, says The Fine Art Trade Guild.  This has not prevented people — even decorators and sellers of gallery systems — from recommending the practice. It is much better for the integrity of the frame, and the art, to leave some slack in the wire and hang the item from two widely-spaced hooks at 45-degree angles, as shown later.

All well and good, but it does not really answer my question: why do frames tilt forward? Having failed to find a good explanation on the internet, I decided to answer this myself. Bear with me, fascinated readers.

This side-view (click to enlarge) may help you understand what is going on. Figure A shows a frame hung from a wire attached to an eyelet at its top-center. Now this is a really bad idea, because the eyelet would probably be pulled right out of the frame. But I show this to illustrate that there would be no cause for this frame to tilt. The real reason that a frame tilts forward (see Figure B) is because the wire is attached to the back of the frame, and the center-of-mass of the frame is in front of that point. This produces a torque that makes the frame tilt forward — it swivels at the attachment point until the center-of-mass is at its lowest possible position, denoted by the dot on the frame in Figure B.

Why Frames Tilt Forward -- Animation by CHCollins Most people in the Northern Hemisphere hang their pictures on a wall — I know I do. A wall pushes back against the bottom of the frame and affects its equilibrium position, such that it does not tilt forward as much a free-hanging frame would. The animation at left shows how a frame reaches its equilibrium position when hung on a wall in the traditional way.

Where one attaches the wire makes a difference in how much the frame tilts. The online world offers conflicting guidance on this. Most sites advise that you attach the wire to the frame one-third of the way down. Others say, one-quarter of the way down, or a certain number of inches from the top. Is there a definite answer here or only opinions? Or as Mitch Hedberg asked, with respect to belts and belt loops, who is the real hero?

The hero in this case is geometry, along with a small dose of physics and calculus. We are going to solve the frame-tilt problem for the benefit of man-and-womankind. Don’t worry, there are no equations involved — until the Appendix.

My Findings

Here is the setup (click to enlarge). A frame of length F is hung on a wall by a wire. The slack in the wire (the maximum distance one can pull the wire away from the back of the frame) is W. The wire is attached to the frame B inches from the bottom of the frame and C inches from the center of the frame, and it pivots freely at the wall and the frame. The center-of-mass (denoted by a red dot) is halfway down the frame and distance D from the back of the frame, where I assume the glass is mounted. We know F, B, C, D and W and we want to find g, the gap between the top of the frame and the wall, when the frame is at equilibrium — i.e., the lowest possible location of the center-of-mass. In other words, we want an expression for the maximum value of y (= y1 + y2 + y3) and the corresponding value of g.

Chart showing forward tilt of a picture frame varies with frame height and depth of the glassIt took a few hours and some brushing up on my trigonometry to find the right approach, but I got there (see Appendix). The chart at left summarizes how the slack in the wire and the position of the glass affects forward tilt, for frames of various heights. Here, I assumed the wire was attached one-third of the way down from the top of the frame, as most self-styled experts advise.

The solid lines in this chart correspond to 10-inch, 20-inch and 40-inch-high frames with the center-of-mass 1/2-inch from the back of the frame. You may be surprised to see that shorter frames tilt forward more than taller ones, when one follows the “one-third rule” and provides the same slack in the wire in each case.

The dashed lines in the chart show how moving the center-of-mass 1/8-inch to the front or rear of a 20-inch-tall frame impacts forward tilt. It may seem insignificant, but a 1/8-inch increase in the depth of the rabbet would widen the gap at the top of such a frame by 25%. It is simple physics — the farther the center-of-mass from the rear of the frame, the greater the torque and the more the frame tilts.

The next chart Chart showing how the wire attachment point affects the forward tilt of a picture frame(click to zoom) shows how fastening the wire at different points on a 20-inch-tall frame affects the forward tilt. Attaching the wire closer to the top always reduces tilt. Knowing this, one may ask, why not just forget the “one-third rule” and attach the wire one-sixth of the way down or three inches down from the top?

Here is one reason: the closer to the top that the wire is attached, the less slack one can allow without the wire being visible. So the “one-third rule” represents a compromise solution for traditional one-hook installations — some forward tilt is accepted for the sake of having more slack and lower tension in the wire.

Interestingly, the weight of the frame does not enter into the calculation. This means that a sheet of foamboard of the same dimensions and same center-of-mass as a wood frame will tilt the same amount when hung the same way.

So it is not true that “heavy” frames tilt just because they are heavy. Frames tilt forward more when the wire is attached closer to the center, when the slack in the wire increases, and when the frame is front-heavy. In typical hanging situations the forward tilt is usually less than 1/4-inch. But when the frame is suspended on a long wire, as gallery systems do, the tilt can be noticeable — 1 inch or more for a 20-inch-tall frame.

I provide a calculator at the end of this post that allows you to estimate the forward tilt of your own frame. Details below.

The Bottom Line

frame-calc-diagSo what have we learned and what do I recommend? If you want to use hooks and wires and you want to hang pictures close to the wall without undue stress on the wire or frame, I suggest using two hooks and 45° wire angles, as illustrated in the diagram at right. This may look a little complicated but it is do-able.

In the original version of this post, I provided a formula to help you with the installation, but in practice, it didn’t go far enough. So I programmed a two-hook frame hanging calculator and posted it in a companion article titled (what else) The “Hang It with Two Hooks” Calculator. This online calculator suggests where to fasten the D-rings, how to install the wall hooks, and the length of wire to cut. This makes the task much easier.

Yes, two hooks present the added challenge of ensuring they are level, but this post is all about reducing forward tilt without stressing the wire or frame. If you are up to the task of carefully positioning two hooks, you might consider eliminating the wire altogether and hang the frame directly onto the D-rings. One drawback to this method is the visibility of the hardware; the other is the extra precision that is needed in mounting the hardware.

But what about my gallery hanging system with the long cables? Here, since we have to rely on a single hook, I suggest wiring the frame according to the one-third rule, with just enough slack so that the cable hook will engage the wire close to the top rail of the frame. Then attach an offset clip to the top rail,Offset Clip slightly off-center, and tuck the cable behind the clip. For a 20-inch-tall frame hanging 30 inches below a cable track, this will reduce forward tilt from nearly 1-1/4 inches to less than 1/2-inch.

Illustration of using offset clip when hanging frames from a cableBy reader request, I have added a photo (click to enlarge) of how the offset clip, cable, and cable hook are installed. This shows the rear of the frame with the cable threaded behind the offset clip. Here I have used a clear 1/8″ mirror clip instead of a metal clip.

Others have used Velcro strips for this purpose instead of offset clips, which is a nifty idea if you don’t mind attaching something to the dust cover with adhesive.

So now you know and so do I. Asked and answered indeed.

The Forward Tilt Calculator

Several readers asked that I create a calculator to estimate the amount of forward tilt for a particular frame. Because the calculation requires iteration (i.e., the answer cannot be found simply by plugging in the known quantities), I had thought this was impractical. However, I discovered that, with a reasonable starting guess, just one iteration is enough for two-decimal-place accuracy. So I offer the following one-iteration calculator.

The user enters four known quantities: the frame height; the rabbet depth (that is, the estimated depth of the center-of-mass of the frame); the wire-to-frame attachment point, measured from the top of the frame; and the amount of slack in the wire, defined as the distance one can pull the wire away from the back of the frame. The calculator returns the amount of forward tilt one can expect.

A Final Word

This post was updated April 7, 2020, with a cleaner derivation, a gap calculator and an animated illustration of why frames tilt forward. This is Part One of a four-part series on hanging frames with hooks and wires. You may also be interested in the follow-up articles, The “Hang It with Two Hooks” Calculator, The Physics of Hanging Pictures, and The “Hang It on Two Studs” Calculator.

If you have found this post informative or entertaining (as about 1000 people a month do), you might enjoy other posts on my blog. Check out my favorites, and consider exploring and subscribing.  My “cup of coffee” invitations appear only on my articles about the physics of hanging pictures.

[ A NOTE FROM THE AUTHOR ]

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you can buy me a coffee or martini!  Click below to add a tip to my coffee fund.

This takes you to my Buy Me A Coffee page. Thanks! – CHC

 

Appendix: Calculating the Forward Tilt in a Frame Hanging on a Wall

I provide a full derivation of the problem here. If you would rather not delve into that, please refer to the diagram above. We want to find the gap g between the frame and the wall, given the known variables F, B, C, D and W. To get there, we first need to find an expression for y = (y1 + y2 + y3), then use calculus to find the maximum value for y and back-calculate g.

I found it easiest to solve for y in terms of the angle formed by the bottom of the frame and the wall, then replace the sine of that angle with g/F (see the full derivation for details). This ultimately led to the following expression for y:

To find the maximum value of y, and the gap between the top of the frame and the wall at that location, we need to differentiate this equation with respect to g, then set dy/dg = 0 and solve for g by iteration:

This is how I generated the data for the graphs in the body of this report.

Read 56 comments below | Read other posts in Asked & Answered, The Arts

56 responses to Why Frames Tilt Forward

  1. Erica Hyatt says:

    Craig- you are my hero! As a professional painter, ex-framer and recovering perfectionist you have provided exactly information I needed! Thanks to your diligence and gracious sharing of your calculations I can breathe easier when hanging my upcoming exhibition! Thank you from the bottom of my heart!

    Erica

  2. Denise Simpson says:

    Smart – the exhaustive math in this answer is way above my pay grade. I am very grateful for your commitment to finding the solution. I have in the past thought the answer was to shorten the wire so with my most recent atempt to hang a picture without the forward lean, the center of mass would have had grave consequences due to the weight of this peticular frame and the sentimental value I place on It. I just finished repurposing an old frame and im so please with the results I knew I had to search out a better solution for proper hanging. Thank you again. Denise

  3. ANDREW says:

    I have a much easier solution. Buy Quakehold rubber adhesive. Pull some small bits off and roll them into balls. Squeeze them on the top inside of the frame and press to the wall. The frame will hang perfectly straight. Total work time: 10 seconds.

    • Craig says:

      Dear Readers:

      Recommended uses for QuakeHold Museum Putty include: keeping objects on shelves from shifting position, mounting posters (without frames) to a wall, or preventing the bottom of a frame from tilting — which is a problem only if the frame was not hung on center to start with. Nowhere does it state that the putty can be used to hang framed art without wires or hooks. It is possible that the putty is strong enough, when used with a wire and hook, to hold the top of a frame closer to a wall. But the putty is not recommended for painted or porous surfaces. So if you have glass or metal walls, or live in a dorm, this product may be right for you.

  4. Aaron says:

    I love nothing more than the application statics, calculus and geometry to real life problems. You are my hero of the week. Expect your page to show up in a high school calculus class sometime soon.

    • Craig says:

      Aaron, thank you for reading, and for your comment. I keep thinking that this problem may have a simpler solution than my contorted approach to it, but I will leave that to high-school students of the future.

  5. John Drake says:

    I have several old and delicate oil portraits that are in jesso wood frames, large, most are 40″X32″ approximately, some on wood panels, some on canvas, so weight varies. These have had fairly poor care and are in need of conservation work in varying degrees, which is an entirely different subject and set of questions. That said, I’d like to hang some of them and would like some good advice. I found that the screw eyes and wire were in bad shape, small and loose and although they were replaced some 30+ yrs ago, are of generic hardware store variety, zinc plated, not big enough(?), or well mounted. Some have much older fastenings and very fine stranded, heavy gauge copper wire , some finely twisted steel or iron wire, I guess, black and stiff, kinda “crispy”. The “original” holes in the back of the frame probably correspond to the “1/3 rule” but definitely seem to allow for forward tilt. And they are fairly wallowed out, requiring a larger diameter screw. Actually, these were likely originally hung with a vertical wire set up from picture moulding on high walls, as there are ancient holes in the top of the frame but these may have possibly mounted an early electric light or sconce.
    I’d like to place 1 7/16″ brass screw eyes on the back of frame, following your guidelines at 1/5th of ht, “c”, from the top of frame. Then use coated wire, possibly doubled, (not for weight considerations, these paintings don’t weigh much, 12-18lbs.) just mass for the hook and possibly tension relief, don’t know if mass or wire size effects that at all. And finally, what type of hook to use, whether to put two on wall to get the right spread and angle for wire since these paintings are so big or if just one will work. And is it OK to use a much larger hook regardless of true weight but more specific to size of piece and/or wire? Thanks very much

  6. Craig says:

    Mr. Drake, thanks for reading. Please be aware that I am not a professional framer, rather a hobbyist and former engineer. That said, my biggest concern, based on what you described here, is the condition of the wood. If the wood has seen moisture or high humidity and is very crumbly, then I would worry about the screw threads pulling out of the back of the frame — in that case I would reinforce the back of the frame or take the frames to a professional framer for advice. But if the wood is in good shape, I would recommend:

    (1) Use D-rings instead of screw-eyes. D-rings lay flat against the back of the frame, so there is less forward-tilt. Screw-eyes create more torque at the wire-attachment point, putting more force on the threads and acting to pull the threads out of the wood — throw those screw-eyes away.

    (2) Drill new holes, slightly smaller than the diameter of the screw for the D-ring. Don’t use the old holes. Don’t worry about whether you are exactly 1/5 the way down.

    (3) I like to use #5 coated wire. This site — https://www.usaoncanvas.com/include/guide_picture_framing_wire.php — shows the breaking strength for wires of various gauges. Looks like #5 coated wire would be good for you. It is not necessary to double the wire — that would only be needed if you were forced to use a light-gauge wire for some reason. Doubling the wire reduces the tension in each individual wire, but does not change the overall force where the wire(s) attach to the frame. For attaching the wire onto the D-ring, a good technique is shown here — http://painting.about.com/od/howtoframepaintings/ss/hang-painting.htm#step3

    (4) I tend to use the smallest wall hooks I can get away with (with safety factor of course) so that they are easier to hide and make a smaller impact on the wall. Using two hooks, positioned as shown in the figure, means you can use smaller hooks, because the total weight will be shared by two of them. Two hooks are also better than one, with respect to reducing the stress on the frame, as my post describes. When placing your second hook, it helps (important) to use a level.

    I can understand why you might want to use larger hooks — a larger hook is easier to “find” with the wire, when hanging the picture. You may need to move your D-rings a little further down on the frame, to make sure those large hooks are concealed by the frame. In any case, be careful that the hook is not so large that it touches the back of your artwork/canvas (if the canvas is exposed in the back).

    Good luck!

  7. That’s helpful of you to post a graph about the frame size and how it correlates to certain angles. I have a few big pictures to hang up, I feel like I need an accurate hanging tool to make it work out.

  8. jsinger says:

    You had a problem and, with no general solutions at hand, you found a solution using a combination of mathematics and trial & error. It seems that your solution is just that; “your solution.” A general solution would include weight(s) (via ‘mass’) to determine COG, friction forces, torque, pre-equilibrium moment of inertia. In short, the solution side-steps Newton’s 3rd Law of Motion with ‘rules of thumb’. Also, it seems we are to assume that all frames have a uniform material-density which is negligible to their structural integrity. You mock the “1/3 rule” in lieu of a “1/5 rule” which is merely trading one problem for another. Wouldn’t it be worth the extra hardware to reinforce the entire frame and maintain precise control of the tension and location of the hanger area(s)?

    It’s nice that your problem is solved and that you even shared your results. However, others may benefit more from the “1/3 rule” that applies glass-supporting tension on the frame’s sides and relief for the frame’s bottom. Maybe the “so-called” experts are actually speaking from a position of experience and expertise.

    • Craig says:

      With all due respect, jsinger, mass and coefficient of friction appear nowhere in this analysis, nor should they. This is equilibrium mechanics, not dynamics. The center-of-mass of the frame “wants” to be as low as it can be, and that’s really the only important factor here — the rest is geometry. If the picture has not been hung “at rest”, it will get there sooner or later, with any little vibration in the wall that allows it to find its equilibrium.

      With respect to my assumption of uniform back-to-front weight distribution of art frames… of course there isn’t. It’s a simplification that most people tackling such a problem would make. The glass, if it is present, makes up most of the weight of a frame, and so its contribution to the center of mass should be given the most “weight” so to speak. The variable “d” in my equations represents the back-to-front location of the center-of-mass, wherever it is, but is most likely (for the purposes of most readers) to be where the glass is.

      Jsinger, you suggest there was some kind of trial-and-error involved here. No, there wasn’t. I provided the justifications for my recommendations and you are free to dispense with them. If you think mass is important with respect to forward tilt, you are free to do the experiment that I suggested, which was to hang a sheet of foam-board on the wall and see if it tilts forward the same as a heavy frame does.

      By the way, glass can break if there is too much tension on the wire pulling inward on the frame. The point of this article was to help people resist the temptation to string a taut wire across the frame, in the hope of making their pictures hang flush against the wall. There is enough bad advice about this to go around. I stand by the physics presented. I hope you have a great day.

  9. Nick says:

    Excellent post.

    Question: I’m attempting to hang a heavy, wood-framed mirror from an AS Hanging wall mounted track system. I’m worried about the forward tilt. I plan on using two cables, each going down to its own D-ring mounted on the frame.

    Is there anything about the following application that you think could be improved upon: 1) position the d-rings 1/5 from the top of the frame, 2) add the offset hardware to the top of frame so that the cables (each running from its own D-ring) will form 45 degree angles with the vertical sides of the frame, and 3) install those little bumpers.

    Would that be the best approach for minimizing forward tilt?

  10. Craig says:

    Hi Nick, if I understand correctly, you are going to use (for weight purposes I assume) two cables, each of which will run vertically from the track to individual D-rings on either side of the frame. In this case, yes, I would suggest attaching the D-rings 1/5 of the way down, but you could go even higher. The 1/5 (or 1/3 or whatever) rule and the 45-degree angle is meant to cover applications where there is a wire strung from one side of the frame to the other. You are not going to have a wire running from side-to-side so those comments do not apply to you. So, you could go ahead and attach your D-rings 1/5 the way down — but to minimize forward-tilt, you are still going to have to tuck each of the cables behind an offset clip that you attach to the back of the top member of the frame. If that amount of tilt is still too much, you would have to fasten offset clips (or equivalent) to the wall somewhat above the frame, and run the cables behind those clips also, but that might be unsightly. Just some thoughts. Good luck.

  11. Craig says:

    Nick, one more thought — if your frame has very heavy glass installed, you might also consider attaching two D-rings to the bottom member of the frame, maybe 1/5 of the way in from each side, and run each cable from the track down through the D-ring on the side and finally hooked onto the bottom D-ring. And then consider attaching corner braces to strengthen the joints between the bottom and side memberrs.

    • Nick says:

      Thank you for your helpful comments! Yes it’s very heavy glass. I’m doing a cable system (secured to the ceiling) because I don’t want to drill into the brick wall the mirror will be hanging in front of. I think I’ll just attach the cables high up on the frame (maybe running down to the bottom member), try your offset clip trick, and cross my fingers.

  12. Craig says:

    Nick, with due respect, don’t cross your fingers with respect to the weight of the mirror. Please measure the weight of your mirror and give yourself plenty of safety-factor when it comes to the cables and hooks. And do make sure your attachment points are secure. Good luck.

  13. Mike says:

    I found your post after finding the same issue with a cable hanging system and had the following questions.

    1. One of the suggestions on the AS Hanging site was to put 3/4″ bumpers on the bottom of the frame, propping it out from the wall. I assume this moves the hinge point, but does it affect the gap at the top of the frame?

    2. The track at the top positions the cable center at 1/4″ from the wall. Does this affect the gap?

    3. One reason to use a cable is to hang multiple pieces on each cable. Does the weight of subsequent pieces affect the gap.

    4. Does clipping the cable to the top of the frame or using a hook at the top of the frame, e.g. a saw tooth hanger, simplify the equations?

    It would be very helpful to have a spreadsheet with the equation and be able to type in the variables, frame height, cable length, etc. and read out the gap. For example I might test how far down the wall I could move the track to shorten the cable and reduce the gap. My maths are a bit rusty!

    Many thanks for your efforts.

    • Craig says:

      Hi Mike, thank you for reading and for your questions. My answers are as follows:

      (1) The effect of bumpers placed at the bottom of the frame — well, I would have to re-solve the problem to quantify this, but allow me to share with you the results of the “live” experiment that I just did. I have a 24″ tall painting hanging in my gallery. The combination of cable and slack in the wire is 29-1/2″. The ceiling cable track is about 3/16″ from the wall. The anchor point of the wire is 5″ from the top of the frame (a little more than 1/5 the way down). I do not have an offset clip at the top to hold the cable against the painting. There is no glass. The gap at the top is 1-1/4″. Now, here is the interesting part. I placed a 3/4″ thick shim on the wall at the base of the painting to simulate the effect of the bumpers you mentioned. The gap at the top of the painting increased to 1-1/2″. So bumpers would make the whole painting float out from the wall, and the gap at the top would be larger than before.

      (2) Does the distance of the track from the wall affect the gap? Again, I would have to re-solve the problem for this geometry, but I offer this thought-experiment. Hold the frame by its wire in mid-air, as I illustrated in Figure B in the blog post. This configuration has the greatest-possible forward-tilt — nothing is constraining it. Now, as you move the frame closer to the wall, eventually the bottom of the frame will touch the wall — the wall will “push back” on the bottom of the frame, pivoting the bottom of the frame forward and the top of the frame backward. The minimum possible gap at the top will occur when the wire is attached to the wall. So the answer to your question is, yes, the farther that the ceiling track is from the wall (all other things being equal), the more that your frame will tilt forward.

      (3) Your question about multiple pieces hanging on the same cable is interesting and challenging, because it does bring weight into the equation. This problem cannot be answered by geometry alone, but I offer another thought experiment. Start out by hanging a heavy painting on a long cable. Now, halfway up the cable, attach a piece of foamboard. You will see little if any effect. But let’s say you now switch the positions of the two items — you hook the painting halfway up the cable and hook the foamboard to the bottom. You will see that the tension in the cable below the painting is so little that the bottom of the frame will press the cable against the wall, and the foamboard will hang close to the wall. Now, in part three of our thought-experiment, remove the foamboard and hang another heavy painting at the bottom of the cable (we assume the cable is strong enough). The lower painting will create much more tension in the cable than the foamboard did, and depending on the ratio of the weights of the upper and lower paintings, the cable may now be taut enough to keep the bottom of the upper frame from touching the wall. So you see, this gets complicated. Your best bet, if you wanted to double-up on paintings on one cable, would be to tuck the lower half of the cable under an offset clip attached to the wall, concealed behind the base of the upper painting. But this defeats the purpose of the cable system, yes? To minimize tilt, you would be best-off hanging the heavier painting higher on the cable and the lighter painting below.

      (4) Unless you have a very light piece, like a 8×10 document, I would personally not use a sawtooth hanger at the top of the frame. Yes, it solves the forward-tilt problem, because there is no slack, because there is no wire! For heavier pieces, as I mentioned in the blog post, you can also mostly eliminate tilt by hanging the piece from D-rings mounted on each side of the frame.

      Last but not least, the equation I presented cannot be solved analytically. I had to find each of the data points on the graph by iteration (trying a range of values and zeroing in on the solution, using a spreadsheet of course). I could write a php program to do the iteration, but it’s not the highest thing on my list right now… too many other irons in the fire. But thank you for your interest.

    • Nikola says:

      Thankyou so much for writing this article! My husband and I are an engineer & scientist and absolutely loved the explanation and solution. We can also fix the tilt on the pictures we hung today. Thankyou again!!

  14. P Bolton says:

    I was watching an old movie and googled why did they used to hang paintings tilting forward. I must say yours was the most thoughtful and thorough answer. Picture hanger/rocket scientist, you are! Thank you

  15. Anonymous says:

    Thank you. The best post on the internet about hanging pics and wall-tilt.

  16. Rich G says:

    Great post. I found it while I was trying to find out why hanging paintings/pictures at a slant was THE way people did it back in the 1800’s. You almost never see anything hanging flush in the old photos of shops and homes.

  17. Meg K says:

    Can you post a diagram of how the offset clip should be attached to the top rail of the frame, and how the cable is situated to it? I understand the theory but not the actual “how to do it”.

    I hang my work monthly at a gallery and have puzzled over the tilt for years. Thank you for all the figuring!

  18. Jim Williams says:

    I’ve worked as a Preparator in museums for over 30 years, and the first thing we were taught was to never hang from a wire, always hang the D-ring directly on the picture hook or, in this case, to the rods on the picture rail. No math, no geometry, just paintings hung flat to the wall surface, and no chance of wire failure. Seems much simpler.

  19. John says:

    Amazing piece of work Craig! I can’t pretend to understand all your math, being more of ratio and proportion guy, but it’s impressive nontheless. I echo all the sentiments favoring D-rings over screw-eyes. Thanks to Amazon, you can get bags of 100 D-rings, complete with screws, shipped to you for about what you pay for the same number of screw-eyes at a big box store like Lowe’s or Home Depot (or even less).

  20. Mia says:

    Could you offer any ideas why my mirror which is attached with D rings directly on wall anchor screws with no wires involved is tilting away from the wall at the bottom? Husband says use Velcro at the bottom but I think there has to be a reason involving tension it doesn’t want to lay flat.

  21. Craig says:

    It’s possible but very unlikely that the mirror is warped so that it curves outward at the bottom. You have probably also already ruled out anything protruding from the back of the mirror, below the D-rings, that would keep the mirror from laying flat at the bottom. The last thing you might consider is whether your wall is truly vertical, that is, is it possible that your wall bows into the room where you have attached the mirror, but recedes from the interior of the room at the bottom of the mirror. Good luck – Craig

    • Mia says:

      We finally got around to working on the mirror. You were right! I thought to myself “how could a mirror be bowed or warped” but it was the backer board that was slightly bowed and pushing it out from the wall. Seems so obvious now but it is so slight it wasn’t noticeable unless you really looked for it. We put Velcro at the bottom and it held. Thank you so much for your reply and your help.

  22. JP Watkins says:

    I also like the more slack wire hanging from two hooks because its easy to hang. You can reach behind the picture and use your hand to place the wire on the hooks one side at a time. And ddjusting level is simple with slight slide left or right.
    Also a few kerfed 1×4 boards of various standard lengths can be used to accurately measure the distance from the top of the frame to the hooks (for that standard length/distance between hooks) so frames can be accurately hung at the desired height, no matter the wire length. You just use the appropriate length of board for the frame, place it kerf out on the back of the frame, put the wire in the kerf, and lift up on the board. Measure down from the top of the frame to the wire to see how far the hooks should be below the top of the frame. In the gallery I worked in the kerfs were all made two inches down from the top edge so you could just measure to the top of the board and add 2″ The same boards were used when wiring the frames to make the wires standard, more or less.

  23. Ronnie says:

    I was so pleased to find this analysis. Permanent bookmark.
    Well done! Thank you!

  24. Chris Grant says:

    The center of mass wants to be *directly below* the hanging point, vertically, as opposed to what you’re saying which is the lowest possible point. That may amount to same thing (dunno) but it’s easier to understand if you just think of verticalness.

    The more the hanging point is directly above center of mass, the better. Therefore if it possible, for a given piece of art, to attach the wires to the inside surface of the frame, (closer to the front of the piece), there will be less tilt.

    The principle is like your item A in your second figure — a hook attached to the center top, which is the same as directly above the center of gravity.

    • Craig says:

      Maybe you are saying the same thing as I did, but I think it is much clearer (and more accurate) to say that the center of mass “wants” to be as close as possible to the center of the earth, given the constraints of the wire and the wall.

  25. Thanks so much for the idea of adding a clip at the top of the frame to solve the lean that occurs on cable hanging systems. I will definitely be trying this, perhaps installing a discreet wire hook of sorts. I have on occasion used a piece of the “Tacky” putty (sold in different strengths at craft stores) placing it on the back of the hanging clip itself and holding that to the wall. This only works on my small lightweight pieces and it also works only if the space is temperature controlled and not susceptible to sunlight warming.

  26. Patrick says:

    Thanks for all your effort here Craig, judging by the comments it looks like you’ve helped many people solve this issue over the last several years, and this article is still the best solution available. Now, lets talk about how to light a wall of art hung salon style. 🙂

  27. Jeffrey S. says:

    Spending my Covid-19 sabbatical making art and then a frame as I’m lucky enough to have an onsite workshop. I was looking for guidance on hanging and your two sites were most useful and a bit entertaining as well. Thanks.

  28. Anonymous says:

    I just tried to hang a tv like one might a piece of art – its a distinct example of these forces at play.

    THANK YOU for such a thorough explanation.

  29. Mr Mysterio says:

    Thank you for working this out and putting this on the internet! The great thing about the internet is that people take the time to do things like this. My solution after reading the comments was to use (in lieu of museum putty) blu-tack which is a common product here in England, I found that is is available in the USA under the name “Elmer’s poster tack. My paintings still have the wire holding them up, the blu-tack just holds the wayward edge to the wall.

  30. I just hung a picture on my wall and this happened. We love in an old Victorian house with picture rails. I love your diagrams explain and including the math. I’m off to rehang my pictures now!

  31. Frankie says:

    Hi Craig,

    If I understand correctly the two hooks are attached directly to the wall (which could make leveling harder for clients).
    Would it be possible to attach the hooks directly in the frame (like : http://chcollins.com/100Billion/wp-content/uploads/frame-calc-diag.jpg), then use a simple hook in the wall to support the whole thing ?

    Sure this hook need to be solid for supporting total weight of the frame but it should be easier for the customers to hang.

    What are you opinion on this ?

    Very great article by the way, good work !

    Best,
    Frankie

    • Craig says:

      You raise an interesting physics question. But at first glance, I am guessing that this would create high tension in the section of wire between the two hooks (or better, D-rings) that you propose to attach to the back of the frame instead of the wall. I think your proposal would also create a significant force acting to pull those D-rings on the top of frame downward and toward the middle. You would essentially be transferring a large portion of the total load from the sides of the frame to the top member of the frame, which is generally not a good idea. Thank you for reading and for your idea.

  32. Denise says:

    Thank you for this post. I was so proud of myself when I attached the D-rings and wire to my art pieces. Then when I hung the art on the wall and saw the massive gap I hung my head down in shame. I had a sneaky suspicion there was more math involved to achieve success and your blog proved it.

  33. Allie says:

    I actually had the opposite problem. I wanted to hang a mirror over my stove tilted so I can see into a pot or pan–I like to sit when I cook. You helped me figure out how to get the correct angle. Thank you!

    • Craig says:

      Knowledge is power that can be used in all sorts of ways. Thank you for taking the time to share your application!

  34. Aaron says:

    Craig, thank you very much for this article. I have the exact same setup as described on one of the threads above (two cables (anchored from top track), each of which will run vertically from the track to individual D-rings, the cables are then tucked behind offset clips installed at the top above the D-rings). The forward lean is however still too much, and I prefer not to fasten offset clips to the wall above the frame. I have two questions:

    (1) if I installed two more D-rings at the bottom part of the frame (below the existing two D-rings) and clip them onto the same two vertical cables, and try to pull those clips further down the cables, would that reduce the forward lean of the frame? Given the cables are slack (as they are anchored only to the top track), I am unsure as to whether this is going to help?

    (2) As a follow-up to the first question, I assume that if the cable is NOT slack, then what is suggested above in 1. could reduce forward lean much more? Let’s say I add a track to the bottom of the wall and then anchor two vertical cables to the bottom track, and then clip these two cables onto the two additional D-rings that are installed at the bottom part of the frame. Have you seen that done before? I assume having two cables pulling from the top track and two cables pulling from the bottom track would make the frame have almost no forward tilt? Do you see any issues with this setup?

    • Craig says:

      Hi Aaron, sorry I didn’t answer sooner, but I was visiting family. To answer your questions:

      (1) Your intuition is correct — feeding the cables from above to a second pair of D-rings mounted to the bottom of your frame will make *no* difference in the forward tilt. The tilt will still be determined by the “slack” between the top pair of D-rings and the point where the wire is attached to the wall.

      (2) Yes, you could attach a bottom rail to the wall, and run cables to D-rings attached to the bottom of the picture, and put tension on those cables to make the picture lay flatter. But I have never seen this done.

      The problem seems to be, your picture is front-heavy *and* you have already done as much as you can on the back of the frame to reduce slack *and* you don’t want to attach guide-hooks to the wall (understandably). The only other alternatives I can think of are (a) some kind of putty/adhesive — see previously-contributed comments, or (b) attach a weight to the back of the frame to counterbalance the weight of the front. Here’s how you can tell how much weight you would need:

      * Cut a length of string about 5x the height of the frame, then tie the loose ends together. Put one loop of the string over the left side of the frame, then put the opposite loop over the right side of the frame, which forms a kind of string cradle at the bottom of the frame. You can put an S-hook on the strings at the bottom and then attach various weights to the S-hook (kitchen tools, wrenches, whatever) to see how much weight would be needed to make the frame lay flat. That would at least tell you whether trying to counter-balance the frame is even feasible.

      Good luck!

      • Aaron says:

        Thank you very much Craig. My painting is indeed front heavy. I will give the two alternatives you suggested a try. Many thanks for your kind advise.

    • Craig says:

      Aaron, one last thing — you asked about running the cables to D-rings mounted on the bottom of the frame — this appears to be in reference to a reply I made to a comment by “Nick”. The reason I suggested Nick run his cables to the bottom of his frame was because he said he had a heavy piece, and doing so would take some of the stress off the bottom miter joints. So that was to address weight, not tilt.

  35. Matthew Lee says:

    Fun article. I’m thinking of another option which I don’t see mentioned here or in comments, but perhaps I’ve missed it. That option is to create a triangle with the hanging system, using a traditional picture rail. You install D rings at top right and left corners at back of picture frame, then extend wire or ribbon or string up to a single picture rail hook from each D ring, creating a triangle. Then the picture can easily be made level by adjusting it from side to side. The picture has minimal tilt, only the depth of the d-ring to center of gravity.
    Some may not like the triangle look. As a full-time artist, I’ve used this before, but the only issue is it means putting an extra D ring in each top corner, which is an extra step. Most clients don’t have a picture rail and will just use a traditional nail and hook in the wall- so it’s adds extra labor to my process.

  36. Jonathan says:

    What do you think of this idea to reduce tilt?
    Assume (as shown in your picture) a wire strung between two D-rings on the back of the frame and hung on two hooks.
    To reduce the tilt, attach another D-ring to the picture in the middle of the top, and string the wire thru it. So the wire passes from the left D-ring, to the left hook, to the top D-ring, to the right hook, to the right D-ring.

    • Craig says:

      Assuming that the two hooks are mounted as high as possible without being visible above the frame — which is what I’d recommend — I’m not sure there would be a lot more gained by also threading the wire through a third D-ring at top-center. The bottom of the D-ring wouldn’t be much higher than the bottom of the hooks. Thank you for reading and commenting.

  37. kent gordon says:

    Use an small eye shaped screw hook pried open at the bottom a little bit (to slip the wire inside) instead of an off set clip. The eye shaped hook can be centered easily and its weight is not lop-sided either

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