Angle Converter Calculator

Angles can be expressed in degrees (°) or radians (rad). A radian is defined as the arc length divided by the radius, and radians are mainly used in trigonometric functions and physics formulas.

Enter a value and choose the unit (degrees or radians) to instantly convert to the other unit.

For example, 180 degrees equals π radians (about 3.1416 rad).

Angle Converter Calculation Method

radians = degrees × (π / 180), degrees = radians × (180 / π)

Value

Unit

Degrees (°): 0

Radians (rad): 0

About This Calculator

Degrees and radians are two units for measuring angles. A full turn is 360° or 2π radians, so 180° equals π radians and 1 radian is about 57.3 degrees.

Enter an angle in degrees or radians to convert it to the other unit.

Useful reference values: 90° = π/2 ≈ 1.5708 rad, 180° = π rad and 1 rad = 57.2958°. On roads and in sport the gradient matters more than the angle: a 12% slope is arctan(0.12) = 6.84°, and a 100% slope is exactly 45°.

Key Formula:radians = degrees × π / 180 · degrees = radians × 180 / π

Frequently Asked Questions

Why do mathematicians prefer radians?

Radians make the derivatives and series of the trigonometric functions clean — the derivative of sin x is simply cos x only when x is in radians. They are also dimensionless, being a ratio of two lengths.

How do I convert degrees to radians quickly?

Multiply by π/180, or remember the common values: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2 and 180° = π.

What is the difference between a slope in percent and an angle?

The percentage is the tangent of the angle times 100: it compares vertical rise with horizontal run. A 6% climb rises 6 metres for every 100 metres travelled horizontally, which corresponds to 3.43°. Steep alpine roads reach 15% and more.

How many radians is 90 degrees?

90° is π/2, about 1.5708 radians, because a full turn of 360° equals 2π radians. To convert any angle, multiply degrees by π/180, or multiply radians by 180/π to go back.

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Sources & last update

2026-10-19