Free tool
Horizontal curve calculator
Enter the radius and one other element of a simple circular curve. Get the rest.
Method and limits
- Formulas for a simple circular arc with radius R and deflection angle D: arc L = R x D (D in radians), chord C = 2R sin(D/2), tangent T = R tan(D/2), mid-ordinate M = R (1 - cos(D/2)), external E = R (sec(D/2) - 1).
- From an arc, chord or tangent, the deflection angle is found first (D = L/R, 2 asin(C/2R), or 2 atan(T/R)), then everything else. The deflection angle must be under 180 degrees.
- Lengths are in whatever unit you use for the radius. Checked against 300 random curves at high precision, including the round trip from arc, chord and tangent back to the angle. Test case: R = 100, D = 60 degrees gives T = 57.735, L = 104.720, C = 100.000.
- Spirals and compound curves are not covered.
- This tool is a convenience, not a survey deliverable. Check results against your own work, and use certified methods for anything you sign off. Provided as is, in line with the terms. Nothing you enter is sent anywhere.