Horizontal circular curve
No transition spiral.
Method
T = R tan(Δ/2), L = RΔ in radians. Worked case: 200 m radius, 40° deflection, tangent 72.79 m, arc 139.63 m.
What to write beside the result
A review can only check this figure if the inputs sit next to it. Write the value, the unit and the assumption the form used. A diameter in millimetres and a diameter in metres are not the same reading. A force in kilonewtons divided as if it were newtons is a thousand-fold error.
The result is the arithmetic on this page. It is not a utilisation, not a selected product, and not a clause from a standard. If the number is going into a shared container, name the page, the date and the inputs. The file-name checker does not read the calculation.
Logic: how this figure is built.
How to read a horizontal curve
This page answers the setting-out question for a simple circular curve: how long is the tangent from the intersection point to the tangent point, and how long is the arc. It is not a superelevation design and not a visibility check.
Tangent length is R tan(Δ/2). Arc length is R times the deflection in radians. A 200 m radius and a 40° deflection give a tangent of 72.79 m and an arc of 139.63 m. The deflection is the intersection angle, not the bearing of one straights only.
Radius is to the centre-line you are setting out. A kerb radius and a carriageway centre-line radius are different if the offset is not zero. The formula assumes a simple circular curve with two equal tangents. A transition, a compound curve or a broken-back curve is not this page.
Use it to check a chainage before it is written into a setting-out table. The page does not give the coordinates of the tangent points. Those need the intersection point and the two bearings. It also does not apply a design speed or a stopping-sight distance.
- Related: slope
- setting-out logic
Last checked 3 October 2026. See the disclaimer.