Work out horizontal curve elements instantly with clear inputs, formula shown and shareable results.
All the elements of a simple circular curve follow from the radius and the deflection angle. Tangent length is R tan(Δ/2), curve length is R times Δ in radians, external distance from the intersection point to the curve is R(sec(Δ/2) - 1), and the middle ordinate from the long chord to the curve is R(1 - cos(Δ/2)).
Curve elements
T = R tan(Δ/2); L = R Δ in radians; E = R(sec(Δ/2) - 1); M = R(1 - cos(Δ/2))
Preliminary estimate only. Horizontal alignment must satisfy the design speed, superelevation and sight distance requirements of the applicable standard.
T = R tan(Δ/2); L = R Δ in radians; E = R(sec(Δ/2) - 1); M = R(1 - cos(Δ/2)). All the elements of a simple circular curve follow from the radius and the deflection angle.
Tangent length locates the curve start and end from the intersection point. Deflection angles from the tangent, or coordinates from a total station, then set out points along the curve itself.
This calculator takes 2 inputs: Curve radius, Deflection angle. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.