Calculator
Pick a method, enter inputs, and press Calculate.
Example data table
Sample radii from the design-speed method (metric example set).
| Speed (km/h) | Superelevation (%) | Friction (—) | Radius (m) |
|---|---|---|---|
| 25 | 1.5 | 0.13 | 33.94 |
| 30 | 2.0 | 0.13 | 47.24 |
| 35 | 2.0 | 0.15 | 56.74 |
| 40 | 2.5 | 0.15 | 71.99 |
| 45 | 2.5 | 0.17 | 81.77 |
These are illustrative only; use project-specific criteria.
Formula used
Two common approaches are included for flexibility.
Design-speed method
This method links curve radius to speed, superelevation, and side friction:
- R(m) = V² / [127 · (e + f)] where V is in km/h.
- R(ft) = V² / [15 · (e + f)] where V is in mph.
e is superelevation as a decimal (2% → 0.02). f is the side friction factor. These are planning-level checks and should be validated.
Geometry method
When you already know curve elements, radius is computed using the central angle Δ:
- R = L / Δ (Δ in radians) from arc length L.
- R = C / [2·sin(Δ/2)] from chord length C.
- R = T / tan(Δ/2) from tangent length T.
Derived curve elements
- Arc length: L = R·Δ
- Chord: C = 2R·sin(Δ/2)
- Tangent: T = R·tan(Δ/2)
- External: E = R·(sec(Δ/2) − 1)
- Middle ordinate: M = R·(1 − cos(Δ/2))
- Offtracking (approx.): OT ≈ WB² / (2R)
How to use this calculator
- Select a method: design-speed or geometry.
- Choose units that match your drawings and inputs.
- Enter the required inputs. Add the optional values if needed.
- Press Calculate to see results above the form.
- Use Download CSV or Download PDF after a calculation.
- Cross-check the radius and widening against project criteria.