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How to Calculate the Radius of Curvature

The radius of curvature is the radius, or half of the diameter, of a circle. The radius of curvature changes as you move along a curve but can be determined at any location along a curve. Radius of curvature is used in a variety of mathematical, mechanical, optical and physical calculations. Derivative calculus is used when calculating the radius of curvature and is equal to 1 plus dy divided by dx squared raised to the 3/2 power divided by d squared times y divided by dx squared.

Calculator

Instructions

- 1
  Calculate the derivative of your curve. The derivative is dx divided by dy.
- 2
  Calculate the second derivative, d squared times y divided by dx, using the result of the first derivative.
- 3
  Square the result of the first derivative, dy divided by dx, and place that answer into the numerator of the radius of curvature formula.
- 4
  Input the result of the second derivative, d squared times y divided by dx, into the denominator of the radius of curvature equation.
- 5
  Solve the equation for a location on your curve. Use a calculator to increase the accuracy and speed of your calculations.

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