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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10 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.

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