Measuring Radius of Arc Formula and Calculator

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Figure 2, Measuring Convex Radii

Measuring Convex Radii

Figure 2, Measuring Concave Radii

An accurate method of finding or checking the radius on a part is illustrated in Figs. 1 and 2. In this method, we may calculate either an inside or an outside radius by the following equations:

Eq. 1
for convex radii,
r = ( L + D )² / ( 8 · D )

Eq. 2
for concave radii,
r = ( L + D )² / [ 8 ( h - D ) ] + h / 2

where

L = length over gage pin or plugs, in (mm)
D = diameter of gage pin or plugs, in (mm)
h = height of concave high point above the gage pin or plugs, in (mm)

For accuracy, the rolls or plugs must be placed on a tool plate or plane table and the distance L across the rolls measured accurately. The diameter D of the rolls or plugs also must be measured precisely and the height h measured with a telescoping gauge or inside micrometers.

Source:

Handbook of Machining and Metal Working Calculations
2001
Ron A. Walsh