How to calculate the radius of a curve

Updated March 23, 2017

Finding the radius of a curve has several practical applications. Architects and building engineers use it to build along curved surfaces. Road and railway engineers use it to design safer turns. You can even use it to design shelving for curved walls. To find the radius, you take two measurements and plug them into a simple formula. However, you can only find the radius of a curve that is constant, meaning that it is part of a perfect circle. Curves that get wider or sharper do not have a radius.

Find the distance in a straight line between the two end points of the curve. This distance is the "chord" length.

Find the midpoint, or the halfway point, of the chord length you just measured.

Find the distance between the midpoint of the chord and the line of the curve. Measure straight up from the chord, at a 90-degree angle. This distance is the "middle ordinate" length.

Calculate the radius of the curve using this formula: Radius = ((C * C)/(8 * M)) + (M/2). Substitute the chord length for "C" and the middle ordinate length for "M."

bibliography-icon icon for annotation tool Cite this Article

About the Author

Alan Sembera began writing for local newspapers in Texas and Louisiana. His professional career includes stints as a computer tech, information editor and income tax preparer. Sembera now writes full time about business and technology. He holds a Bachelor of Arts in journalism from Texas A&M University.