How to calculate the radius of a curve

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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."

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