I am wanting to know how do you calculate the curvature distance a fold line may produce based on paper thickness?

For instance I am wanting to do artwork on a thick paper stock and I want to make sure my artwork is within the folds instead of perhaps very close to it. As what I am doing is on small thick boxes, it is critical that I can work this out.

Many thanks.


Length of a perfect circular fold for 180 degree turn is π × W:

         corner fold

Image 1 Corner shift

In practice thus you have some slack to the inner side, so W is actually width of paper plus how much inner radius you use. So W is somewhere between 1-2 times the width of the card stock. and the amount of paper that the corner eats is:

         π × 1-2 × w × a/180

where a is the angle of your corner, and w is the width of your cardstock. A value 2 might be pushing it i have never needed to measure card stock this accurately so i allays used a value of 1, but i do regularly accurate sheet metal work which is similar tech. So this is the theoretical underpinning.

Ultimately: Ask your printer.

  • Thanks for the reply however I am a bit confused. What it 'TT' symbol? And what is 'a', this is the radius of the angle? Could you give me an example and your calculation so I can see how you calculate it so I can replicate it as its easier to see it in example since geometry is not my strongsuit since I finished it at school 20 years ago :( Thanks again. – Ninjab Mar 26 '15 at 14:19
  • It's not "TT" it's a π symbol which = Pi – SaturnsEye Mar 26 '15 at 14:27
  • @Ninjab the "TT" is the greek letter pi which is a mathematical constant. a is the angle of your fold if you have a full fold it would br 180 degrees if its the side of a box it would most likely be 90. w is the width of your cardstock – joojaa Mar 26 '15 at 15:20
  • Heh yeh I realied after I posted it cause I recognised pi with the curves. Thanks. However how do I work out this calculation. For instance could you show me an example you would use to work it out. I am not that mathematically gifted. Thanks. – Ninjab Mar 27 '15 at 8:20
  • @Ninjab NP, assume you want to fold a 90 degree turn then you would calculate 3.14159*1.1* Width of card*90/180 this is the amount of paper you loose in the fold. Im allowing for not a operfect fold hece 1.1 . – joojaa Mar 27 '15 at 8:31

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