What is the arc definition of degree of curve?

The arc definition states that the degree of curve D is the central angle (in degrees) subtended by a 100-foot arc. It is the standard used in US highway engineering. The radius is then R = 5729.578 / D (feet).

What is the chord definition of degree of curve?

The chord definition uses a 100-foot chord instead of a 100-foot arc. It gives R = 50 / sin(D/2). This definition is used in railway surveying in some countries. This calculator uses the arc definition.

How do I convert the result to meters?

Select "Meters (SI)" in the unit toggle. The calculator divides the 100-ft station length by 3.28084 (giving a 30.48 m arc), so the formula becomes R = 1746.374 / D. You can also multiply a feet result by 0.3048 manually.

What degree of curve corresponds to a 300-foot radius?

D = 5729.578 / 300 ≈ 19.10°. That is a very sharp curve, typically only seen on low-speed roads or industrial railway spurs.

Is there a minimum radius for highway design?

Yes. AASHTO sets minimum radii based on design speed and superelevation. At 60 mph with 6% max superelevation the minimum is roughly 1,145 feet (D ≈ 5°). Always check the applicable design standard for your project.

Horizontal Curve Radius Calculator

Name: Horizontal Curve Radius Calculator
Availability: InStock
Author: Nham Vu

Enter degree of curve to get radius, or enter radius to get degree of curve — using the standard R = 5729.578 / D surveying formula.

Inputs

Unit System

Degree of Curve (D) degrees

Central angle subtended by a 100-ft (or 30.48 m) arc

Radius (R) feet

Center-line radius of the horizontal curve

Results

Radius (R)

—

feet

Degree of Curve (D)

—

degrees

Derived Values

Chord for 1 Station

—

Tangent Length (T)

—

(for 1° arc)

Circumference

—

Arc for 1° Deflection

—

Formula (arc definition): R = 5729.578 / D | D = 5729.578 / R
SI: R = 1746.374 / D | D = 1746.374 / R

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Summary

Enter degree of curve to get radius, or enter radius to get degree of curve — using the standard R = 5729.578 / D surveying formula.

How it works

Enter a degree of curve (D) value to calculate the corresponding radius R using R = 5729.578 / D.
Or enter a known radius (R) to compute the degree of curve D = 5729.578 / R.
Results update instantly as you type in either field.
Use the unit toggle to switch between feet (US customary) and meters (SI).
Copy any result with the Copy button for use in drawings or reports.

Use cases

Convert degree of curve to radius for highway geometric design.
Verify railway curve data from track plans.
Check minimum radius requirements against design speed standards.
Convert legacy degree-of-curve specifications to modern radius notation.
Quick field check during route survey stakeout.
Compare alternate horizontal alignments by radius.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu