Horizontal Curve Layout Calculator

Every curve element here — Tangent, Arc Length, Long Chord, External, and Middle Ordinate — is Radius multiplied by a trigonometric factor of the Central Angle, so Radius and Central Angle carry equal structural weight: in Input Method 1 (Radius + Delta Angle), where Radius is set directly, a 10% change in either one moves Arc Length by roughly the same 10%, since Arc Length is literally Radius times the angle in radians with nothing else in the formula. That symmetry breaks in Input Method 2 (Tangent + Delta Angle): there, Radius is back-solved from Tangent and Central Angle, so changing Central Angle also changes the Radius it derives — Arc Length is no longer simply proportional to Central Angle in that mode. Where they diverge is Tangent, Long Chord, External, and Middle Ordinate, which run through tan, sin, and cos of the half-angle — these grow faster than linearly as Central Angle approaches large values, since tangent in particular climbs steeply once the half-angle nears 90°.

Input Method lets you supply either Radius directly or a Tangent Length instead, in which case the engine back-solves Radius from Tangent and Central Angle using R = T / tan(Δ/2) before running the same downstream formulas — so switching Input Method changes which field drives the calculation but not the underlying geometry. PC and PT Station are simple offsets from PI Station using Tangent and Arc Length, so raising PI Station shifts both station outputs by the same amount. Degree of Curve uses the arc definition (100-ft arc basis) rather than the chord definition some older references use, which can differ slightly for very sharp curves.