Horizontal Curve Length from Degree of Curve

If one degree of central angle buys 100 ft of arc, then Δ degrees buys 100Δ/D feet — the neatest consequence of the arc definition and the reason highway stationing runs in 100 ft increments in the first place. Chainage was originally measured with Gunter's chain of 66 ft, but American railroad practice standardised on a 100 ft steel tape, and the whole vocabulary of "station 12+50" (1,250 ft from the origin) follows from it. The 100 here is feet, so the printed formula is unit-bound even though this solver converts whatever units you enter.

A worked example: a 4° curve deflecting 60° runs L = 100 × 60/4 = 1,500 ft of arc, or fifteen full stations. If the PC is at station 20+00, the PT lands at 35+00 — and note that the stationing runs along the curve, not along the tangents, which is why the PT station is not simply the PI station plus the tangent length. Chainage discrepancies at the end of a curve are almost always this mistake. Equivalently, L = RΔ with Δ in radians, which is what the brain evaluates internally.