Radius of Curvature Calculator

How it is calculated

The radius of curvature is the reciprocal of the curvature: R = 1 ÷ κ, where κ (kappa) is in reciprocal metres (1/m) and R comes out in metres. A curvature of 0.02 1/m therefore means a circle of radius 50 m fits the curve at that point. The result is printed with four decimals, followed by your curvature echoed back.

A curvature of exactly 0 is a straight line, whose radius is infinite, so the tool gives no result for it. A negative κ gives a negative radius; this is the sign convention for a curve bending the opposite way, and the size of the radius is the same as for the positive value. The curvature echo is also rounded to four decimals, so a very small κ such as 0.00001 is displayed as 0.0000 although R = 100,000 m is calculated from the exact number.

Common mistakes

• Entering the radius in the curvature field. The input is κ in 1/m, not the radius; typing 50 gives R = 0.02 m, the opposite of what was meant.
• Using other units for κ, such as 1/km, 1/cm or degrees per 100 ft. The result is labelled in metres, so convert the curvature to 1/m first.
• Entering 0 for a straight section and expecting an answer. A straight line has infinite radius, so the tool returns nothing.
• Reading a negative radius as an error. It only reflects a negative curvature (bending the other way); the distance is the same.
• Trusting the rounded curvature echo for very small values. 0.00001 shows as 0.0000, yet the radius of 100,000 m is calculated correctly.