The radius of a curvature is the radius of a circle drawn through parts of a curve. This radius can be used for a variety of mechanical, physical and optical calculations. Finding the radius requires the use of calculus. The formula for finding the radius of a curvature is:

{[1+(dy/dx)^2]^3/2} / |d^2y/dx^2|

To calculate the radius of a curvature, take the equation of your curve and use the radius of a curvature formula to solve for a variable “x” at a point along the curve.

Step 1

Calculate the derivative, dy/dx, of your curve. Using this result, calculate the second derivative, d^2y/dx,

Step 2

Square the first derivative, dy/dx, and plug the result into the formula for finding the radius of a curvature. Put the result into the formula at (dy/dx)^2.

Step 3

Plug the second derivative of your curve equation into the formula for finding the radius of a curvature. Put the second derivative into the formula at d^2y/dx^2.

Step 4

Solve the equation for a point “x” along your curve by replacing the variable "x" with a numerical value. Use a calculator to speed your calculations.