Horizontal Curve Calculator

A 300 m radius curve with a 40° deflection has a tangent length of 109.191 m and a curve length of 209.44 m.

Radius R (m):

Deflection angle Δ (°):

Chainage of the point of intersection (m, optional):

Tangent length T =

109.191070279861 m

Precision

Full answer, then cut to fewer decimals (not rounded):

109.191070279861 m
109.19107027986 m
109.1910702798 m
109.191070279 m
109.19107027 m
109.1910702 m
109.191070 m
109.19107 m
109.1910 m
109.191 m
109.19 m
109.1 m

Curve length L = πRΔ/180: 209.4395102 m
Long chord 2R sin(Δ/2): 205.212086 m
External distance R(sec Δ/2 − 1): 19.25333174 m
Mid-ordinate R(1 − cos Δ/2): 18.09221376 m
Degree of curve (30 m arc) 1718.87/R: 5.729577951 °
Chainage of the tangent point PC: 890.8089297 m
Chainage of the end point PT: 1100.24844 m

Step-by-step solution

T = R tan(Δ/2) = 300 × tan 20° = 109.1910703 m
L = πRΔ/180 = 209.4395102 m

Horizontal Curve Formula

T = R tan(Δ/2), L = πRΔ/180

long chord 2R sin(Δ/2); E = R(sec Δ/2 − 1); M = R(1 − cos Δ/2)

Worked Example

A 300 m curve deflecting 40°, with the PI at chainage 1000 m:

T = R tan(Δ/2) = 300 × tan 20° = 109.1910703 m
L = πRΔ/180 = 209.4395102 m

Long chord 2R sin(Δ/2): 205.212086 m · External distance R(sec Δ/2 − 1): 19.25333174 m · Mid-ordinate R(1 − cos Δ/2): 18.09221376 m · Degree of curve (30 m arc) 1718.87/R: 5.729577951 ° · Chainage of the tangent point PC: 890.8089297 m · Chainage of the end point PT: 1100.24844 m

GATE tip

A classic trap: chainage of PT = PI − T + L. Adding T to the PI chainage gives a wrong answer.

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Frequently asked questions

How is the degree of curve defined?

The angle subtended by a 30 m arc (or chord), so D = 1718.87/R degrees for R in metres.

How do I find the chainage of the end of the curve?

Chainage PT = chainage PC + curve length, not PI + tangent: the curve is shorter than two tangents.

Sources

The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

Cite this page

APA

Scientific Converters. (2026, October 15). Horizontal Curve Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/horizontal-curve-calculator/

IEEE

Scientific Converters, "Horizontal Curve Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/horizontal-curve-calculator/