Horizontal Curve External Distance
Worked example: 20 m external at Δ = 100 gon → 48.284 m radius — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
Chords and offsets →
UniversityApplied Field Engineering
Test your skills in the Exam Room: new numbers every attempt — free lessons for students, no sign-up, just pure learning.
share your results
Horizontal Curve External Distance explained
The external distance answers the right-of-way question: how far does the pavement stay from the corner the two tangents would have made? Measured from the PI along the bisector to the midpoint of the arc, E is the gap that has to clear whatever sits at the corner — a rock face, a building, a wetland boundary. Because the centre, the PI and the curve midpoint are collinear, R + E is the hypotenuse of the same half-angle triangle that produced the tangent length, giving the secant form.
A worked example: a 500 ft curve deflecting 60° has E = 500(sec 30° − 1) = 500(1.1547 − 1) = 77.35 ft. If the survey shows a building face 60 ft inside the PI on the bisector, that curve will not fit and either the radius has to shrink or the alignment has to shift. Watch the behaviour at large Δ: as the deflection approaches 180° the secant blows up and E runs away to infinity, which is the geometry's way of saying a hairpin needs a small radius, not a big one.
Horizontal Curve External Distance formula
- = External distance (m)
- = Curve radius (m)
- = Deflection angle (°)
Missing one of these? Work it out first, then come back
- External distance — Fuel Consumption (L/100 km), Distance Formula (3D)
- Curve radius — Horizontal Curve Tangent Length, Horizontal Curve Middle Ordinate
- Deflection angle — Horizontal Curve Tangent Length, Horizontal Curve Middle Ordinate