Radius Caliper gauge with MAGNET no math UNI SIZE

I found that a different gauge is suitable for each type of measurement. That is why I created 3 types of gauges that differ in angle. Mounting 10 mm x 2 neodym magnet. 

The 60 angle is suitable for quick measurements without the need to calculate r = l. The 90 deg angle is suitable for most measurements, but it is necessary to multiply the distance by 2.4142, which is a bit impractical. For special measurements of short radius, I designed the last gauge with an angle of 120 deg, which must be multiplied by 6.4641. This is suitable for measuring short sectors of diameter.

Conversions:

For 60 deg - r = l
For 90 deg - r = l x 2.4142
For 120 deg - r = l x 6.4641

I tried to create a design that is as universal as possible for most of the gauges sold. That is why I used 10x2 mm magnets for mounting.

Keep in mind that the measured values are approximate. There are many variables that make the result inaccurate. 3D printing creates inaccuracies of up to 0.2 mm. Rounding values also creates inaccuracies. However, you can count on an accuracy of +- 0.2 mm depending on the accuracy of the print and the accuracy of the gauge.

The formula for the exact value of the coefficient with the result of the diameter.

k - coefficient for multiplying the measured length
l - measured length
a - vertex angle (for example 90 deg)
d = diameter ?
r = radius ?

k = 2 x sin(a/2) / 1 - sin(a/2)

r = (k x l) / 2
d = k x l