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How to Find the Radius of a Curve

From building engineers to architects to students, calculating the radius of a curvature has practical and classroom applications. Students use the radius of a curve in geometry, calculus and trigonometry problems while engineers use the radius to design safer turns on railways and roads. Unlike finding the radius of an enclosed shape such as a oval or circle, finding the radius of a curve can be more difficult as the curves become wider and elongated.

Things You'll Need

Calculator
Ruler

Instructions

- 1
  Connect the two end points with a curve by drawing a line from end point to end point with a straight edge ruler.
- 2
  Measure the distance using the ruler. The distance between the end points is called the "chord" length.
- 3
  Find the midpoint of the chord and measure the distance from the midpoint of the chord to the curve directly underneath the chord. Do this by drawing a line from the chord directly to the furthest point of the curve. The line should equal a 90-degree angle from the chord and the line drawn.
- 4
  Use the formula Radius = ((C * C)/(8 * M)) + (M/2) to find the radius of the curve. "C" represents the chord length and "M" represents the distance from the chord's midpoint to the furthest point of the curve. For example, if the chord distance is 5 inches and the distance from the chord's midpoint straight down to the further point of the curve is 10 inches, the radius of the curve would be ((5 * 5)/(8 * 10)) + (10/2) = approximately 5.3 inches

Numerology