Circular Curve Elements Calculator
A free, browser-based tool. Runs entirely in your browser — no sign up, nothing stored.
Curve inputs
Curve elements
T = R·tan(Δ/2), L = R·Δ(rad), C = 2R·sin(Δ/2), M = R(1−cos(Δ/2)), E = R(sec(Δ/2)−1). A study aid — not for final road design.
How to use this calculator
- Enter the deflection angle (Δ) in your chosen format and the radius R.
- Read the tangent, curve length, long chord, mid-ordinate, external distance and degree of curve.
How it works
From Δ and R: tangent T = R·tan(Δ/2), length L = R·Δ (Δ in radians), long chord C = 2R·sin(Δ/2), mid-ordinate M = R(1−cos(Δ/2)) and external E = R(sec(Δ/2)−1).
Degree of curve here is the angle subtended by a 100 m arc.
Worked example
R = 200 m, Δ = 60°. T ≈ 115.470 m, L ≈ 209.440 m, long chord = 200.000 m (since 2R·sin30° = R).
Frequently asked questions
Is this for designing a road curve?
It's a study aid for the geometry. Final road design must follow the relevant design standards (sight distance, superelevation, transitions, etc.).
Is this official course material?
No. It is free study support mapped to surveying course levels — not official North Metropolitan TAFE content or advice. Always follow your lecturer and the official assessment brief, and check your own working.
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Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.