This spiral curve calculator finds the total spiral angle and the deflection angle for a transition (clothoid) curve used in road and rail alignment. Enter the spiral length and final radius above.
Formulas
Spiral angle θs = Ls ÷ (2 × R) (radians) Deflection to SC ≈ θs ÷ 3
Example
Ls = 100 m, R = 300 m: θs = 100 ÷ 600 = 0.167 rad = 9.55°; deflection to SC ≈ 3.18°.
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Frequently Asked Questions
How do I calculate the spiral curve angle?
Divide the spiral length by twice the final radius to get the spiral angle in radians, then convert to degrees.
What is a spiral (transition) curve?
It is a clothoid that gradually changes curvature between a straight and a circular curve, easing the change for vehicles.
What is the deflection to the SC point?
For a simple spiral it is about one third of the total spiral angle, measured from the tangent.