Civil & Structural Calculation guide Calculate a value

Setting out a horizontal road curve from a deflection angle

Tangent, external distance, middle ordinate and curve length, and which of them you actually stake on site.

The engineering question

You have a deflection angle and a radius. Which of the five curve dimensions does the surveyor actually need, and how are they related?

Worked example

The figures below were produced by running the Horizontal Curve Calculator with the same inputs — during the build, from its authoritative engine.

Results
Tangent length (T)	37.8359 m
Curve length (L)	73.3038 m
External distance (E)	5.8235 m
Middle ordinate (M)	5.554 m
Long chord (C)	72.1694 m
Comfortable speed	52.4039 km/h
Assessment	PI to PC 37.8 m, curve length 73.3 m, middle ordinate 5.6 m — comfortable design speed ≈ 52 km/h.

Tangent length is R·tan(Δ/2) and is set out on each tangent from the point of intersection.
External distance offsets the intersection from the midpoint of the curve.
Entering superelevation and side friction gives the speed the curve will actually hold.

Sanity check

Curve length should always exceed the straight-line distance between the tangent points. A shorter result means the angle or radius has been entered in the wrong units.

Tools for this problem

These are the EngiMetric calculators that compute the numbers in this topic. Each one shows its formula, its units and its limits rather than returning a bare result.

Horizontal Curve Calculator Circular curve geometry from the deflection angle and radius, with a speed check from superelevation and side friction.

References & standards

AASHTO Green Book — geometric design of roads and highways
BS EN 13223 — road geometry