The “Hang It with Two Hooks” Calculator

Asked and Answered 3.2

Click to Use CalculatorTwo years ago, I posted an article here called Why Frames Tilt Forward, explaining why the top of a picture frame tilts away from the wall and what one should and should not do to address this.

The mistake that most people make (and a remedy that even some frame shops prescribe) is to fasten the wire tightly across the frame so that there is almost no slack in it.  But as I pointed out in my article, this can put considerable strain on the wire and the frame when the picture is hung.

If you don’t believe that a professional framer would make such a mistake, let me share a little story.  We recently took a favorite picture of ours to a local frame shop for reframing so that it would better suit our décor.  It was a large frame, about 46″ wide and 34″ high.  When we picked up our frame, I noticed how taut the wire was, and I mentioned this fact to the owner.  I also told her about my blog post on this topic.  She seemed disinterested.

Rather than argue with her, I decided I would rewire it when I got home.  As I was carrying the frame into our bedroom by its wire (the only practical way to carry such a large piece), the wire snapped and the corner of the frame hit the floor.  Luckily, I was carrying it only eight inches or so above the floor and, luckily, the floor was carpeted; otherwise, the frame or the floor or both would have been damaged.   Rest assured, I was not carrying the frame in such a way that it bounced around and tested the wire.

I rewired the frame with my own hardware, my own wire and according to my own rules, and I am confident that it will now not fall, bend or break.

On our next visit to the framer, I told this story to the owner, who remained unconcerned. Her response was that a frame should not be carried by its wire.  Apparently, she was not  familiar with the concept of a safety factor.  I thought her excuse was as flimsy as her wire.

Clearly, this frame shop is winging it.  They are content to string a wire across the frame and call it a day.  They are not mindful of physics — and they will not have a second chance to demonstrate this to me.

So… how do you know whether your frame shop is using their heads?

• • • •

But enough of cautionary tales.  In Why Frames Tilt Forward, I suggested that one way to achieve a low-tilt and low-tension installation is to use two wall hooks and 45° wire angles  (see figure below).  My instructions, however, were not so easy to follow — I know, because I tried to follow them myself.  The main difficulty was figuring out exactly how much wire to cut, something my instructions had not spelled out.Two Hook Frame Hanging Diagram

This is an ideal application for an online calculator — no fancy math, just basic geometry.  So, to help my readers, I have programmed my formulas into the wiring calculator below.  The user enters the outside dimensions of the frame (W and H), the size and position of the D-rings fastened to the frame (D and V), and the desired distance from the top of the frame to the bottom of the wall hook (Z).  The calculator returns the vertical position of the D-rings (Y), the spacing of the wall hooks (X), and the length of wire to cut, which includes three inches at each end for making knots.  To make things easier, some default values are suggested and results are rounded to the eighth-of-an-inch.

Notice that my illustration suggests the use of D-rings as well as double-nail wall hooks.  D-rings are preferable to screw-eyes because D-rings lay flat against the back of the frame, reducing the propensity for the frame to tilt forward.   And the wide base of double-nail wall hooks can help distribute the lateral forces associated with a two-hook installation.  More on this in the final post of this series, The Physics of Hanging Pictures.

In my low-tilt, low-tension scheme, the D-rings are placed one-fifth of the frame height below the wall hook.  The wall hook spacing and the wire length follow directly from this.  However, if the calculated wall hook spacing is less than one-third of the D-ring spacing, the calculator suggests values for a one-hook installation instead.  In the one-hook case, the wire angle varies with frame height, but the angle will be at least 33° above horizontal.

Click CALCULATE after editing your entries to view the installation instructions.

In a two-hook installation, there may be less slack in the wire than you expect.  To avoid frustration, try this: center the frame over the left hook and engage the wire into the hook, then shift the frame all the way to the right and engage the wire into the right hook.

I must end with a disclaimer.  This calculator makes it easy for a person to hang a picture with low forward tilt by using two hooks and 45° wire angles.  But whether this method is suitable in your situation is a judgment only you can make.  You bear full responsibility  for your installation.  I provide this calculator as a convenience but I assume no liability for damage of any kind, even if the suggestions offered in this post are followed exactly.

With that out of the way, happy hanging.  Returning readers may click the calculator icon at the top of this post to go directly to the calculator app.  Your suggestions and feedback are always welcome.

[Update 09-22-2017:  In the calculator, I increased the length of the wire to knot and twist from 2 inches per side to 3 inches per side.  There was no need to be so skimpy.]

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29 Responses to The “Hang It with Two Hooks” Calculator

  1. Eric says:

    Dear Professor Collins –

    This is an ingenious and handy algorithm! I’m wondering, though: will we need to know this for the Final Exam? Asking for a friend . . .

  2. Joanne says:

    I was so excited to try out your calculator, but alas, my paintings are larger than you will allow for (50×62, and 62×50). What is an arithmetically challenged artist to do?

    • Craig says:

      Hi Joanne, thanks for visiting the site. I will increase the calculator’s limits on the frame dimensions to 72 inches in height and/or length. The original limits of 50 inches were based on my concern that very large frames may also be very heavy, in which case wall-hooks and wires may not be the best solution. One should always consider whether a piece should be hung directly onto nails/screws that are driven into wall studs, in which case the stud spacing will play a big part in how the piece is hung.

  3. Stephen says:

    Well done. I’m looking forward to your The Physics of Picture Hanging post.

  4. Jenn says:

    I’ve got lathe and plaster walls and so must use picture railing hooks and wire. As you can imagine, I face the problem of pictures protruding wildly from the top of the frame. I would like to adapt your formula to this scenario but don’t know how. Any quick advice?

    • Craig says:

      Not knowing how thick your picture rail is, here is one idea that might lead you to a solution: take a hat hook or towel hook and screw it onto the picture-rail backwards so that the hook end is underneath the rail. Then loop your frame wire over this hook. Perhaps something like this:

      Obviously, the frame wire would have to extend above the top of the frame for this to work, but at least the frame will be closer to the wall. The only other idea (which I’m sure you have considered) is to mount something behind the bottom of the frame so that the entire frame floats out from the wall. Good luck.

  5. Derrick Shelton says:

    Great calculator. What also would be extremely helpful for those that have existing frames with wires and D-rings in place would be to input all the details and have the calculator determine the optimal distance X to install the hooks that would result in the least amount of tilt AND to show what that tilt amount would be. It would help to determine if we could use our picture as-is or if we would need to replace the D rings and wires.

  6. Craig says:

    Derrick — thank you for reading the article and for your suggestion for the calculator. Your idea would be nice. Unfortunately (as I noted in the earlier article “Why Frames Tilt Forward”) the forward tilt at equilibrium cannot be calculated algebraically — instead it involves a “zeroing in” algorithm. I cannot program this kind of algorithm using this WordPress calculator plug-in. So the best I can do for now is refer you to the charts in the article mentioned above.

    I could write a stand-alone program to calculate the answer, but then I would have to design a custom user interface for entering data and reporting results. That alone would be a lot of work, at least for me, as I have only hobbyist-level web programming skills.

    I don’t envision tackling that programming challenge (I would rather be painting!) but I do appreciate your interest. — Craig

  7. Derrick Shelton says:

    I completely understand. Thanks for the response.

  8. Andy says:

    This is awesome! I’m sorry to ask before reading the whole series of your posts. I’m not sure I’ll be able to understand it in the first place. Is there a reason why Z has to be 2.5 or less?

    • Craig says:

      Hi Andy, thanks for reading and for your question. One of the “reasonable entry” checks in the calculator is the 10-inch minimum frame height (H). The top-of-frame to bottom-of-hook check (Z) is based on this. While you could increase Z beyond 2.5 — and increase Y by the same amount — this would only make the frame tilt forward more. Since the focus of this article is to minimize forward-tilt, I chose to limit Z so that it was just enough to hide the hooks and wire. Hope this helps.

  9. christi says:

    This is a handy calculator however it needs wider variables with measurements to say suspend or hand something unusual.

  10. Thuc Nguyen says:

    How about calculation for an unsymmetrical configuration where the distances form the LHS edge and RHS edge to the hooks are not equal (slightly different due to the position of the studs.
    For example 3 inches on one side and 6 inches on the other. mirror dimension is 24 x 36,
    How do one locate the vertical position of hookers.
    Thank you.

    • Craig says:

      Perhaps that will be the topic of “Asked and Answered 5.4” but right now, I’m working to finish a journal article about bidding strategy on “The Price is Right.” Seriously! But I’ll keep this in mind.

  11. Dante Lanzetta says:

    I used the calculator for two different sizes of picture, with good results but, on my third, the calculator returned only results for ONE hook. I had thought the one-hook results were only there as a collateral benefit, because most users would only be using it to determine correct two-hole dimensions.

    My picture is 24×35.5, with V=3.125 and D=.875. What am I doing wrong?

    • Craig says:

      Dante, you are not doing anything wrong. As the note on the calculator says, if the distance between the two hooks is less than 1/3 the frame-width, the calculator decides that two hooks is too much trouble for too little benefit, and it gives you the answer for one hook instead. In your case, the distance between the hooks in a two-hook installation, assuming that you left Z=1.5, would only be 3.5 inches. The wire-angles are so close to 45 that there is almost no advantage to simply using one hook.

      I did wonder about your value of V = 3.125 (that is a very wide frame molding, but hey) so assuming that value is right, I’d say, just be happy that one hook is good for you. Hope this helps.

  12. Liliane says:

    Thank you for this information. Would this method work for a large, heavy mirror to be hung on drywall where the stud spacing allows for only one of the wall hooks with the 2 little nails to in a wooden stud (the other one would have to be in drywall)? Will the little nails hold being in just the drywall?

    Thank you!

    • Craig says:

      I would not hang anything heavy using only drywall picture hangers — I would make sure at least one hanger was nailed into a stud. If I were doing this, I would: (a) weigh the mirror, (b) get a very large hook that was strong enough to hold the mirror on its own, (c) make sure the nail for that hook (Hook #1) is long enough to go through the drywall and enter the stud, (d) use a regular drywall picture hanger as Hook #2, but make sure this hanger is also strong enough to hold the mirror on its own, (e) use strong wire or hang directly on D-rings. There are many ways to hang heavy items involving off-center studs (in fact, you can google that phrase)… not sure what would be best for your situation. Good luck.

  13. John M says:

    Hi, I am confused about the last field, “Distance from top of frame to bottom of hook” (Z). Which hooks do you mean? The ones in the wall? I am not sure if the illustration indicates to put the double nail hooks in the wall or on the back of the frame. Sorry, can you clarify?

    • Craig says:

      Hi, John M, thanks for your question. The hooks shown on the diagram are the wall hooks. The distance Z represents how far below the top of the frame you want the hooks to be. Normally you want Z to be *at least* the height of the hook and a bit more, otherwise the hooks would show above the top of the frame. You may want to specify a different Z if you want the hooks to be at a particular spot with respect to the artwork. Sorry for any confusion with the diagram… you have to pretend the frame is transparent.

  14. Phil says:

    Many thanks for the calculator as needed to hang a large mural flat against the wall. I’m a professional physicist but too lazy to work it out myself! Your sums worked perfectly & my wife is very happy.

  15. Mark says:

    Being a retired master craftsman, I had the time and good fortune to come across this most excellent article for my personal use – it assuaged my perfectionist insecurities! While having been intuitively close to the mark when occasionally hanging pictures for my clients, your frame hanging calculator is a hopeless perfectionist’s dream.
    Thank you for your efforts.

  16. Jack says:

    The calculator is down. Any chance of it coming back up today?

    • Editor says:

      Jack, thank you — somehow the plug-in had been deactivated, maybe after an update. Sorry for the inconvenience. – Craig

  17. I wanted to use 3 hooks to hang a 15 lb large picture. I can’t get the wire onto all 3 hooks at the same time. Any suggestions?

    • Craig says:

      Without questioning why you would want to do this, the answer is that you would need to place the middle hook slightly higher than the other two, which means the middle hook would carry somewhat more than one-third the load.

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