Degrees to Radians Converter

How to convert degrees to radians

1 degree = 0.0174532925 radians. To convert degrees to radians, divide by 57.29577951 (or multiply by 0.0174532925). A degree is 1/360 of a full turn, exactly π/180 radians (about 0.017453 rad). A radian is the angle at the center of a circle that cuts off an arc as long as the radius; a full turn is 2π rad.

Worked examples

• 30 degrees = 0.523599 rad (30 ÷ 57.29578)
• 90 degrees = 1.5708 rad (90 ÷ 57.29578)
• 180 degrees = 3.14159 rad (180 ÷ 57.29578)

Where this conversion comes up

Degrees are used for maps, navigation, geometry, construction and everyday angles; radians for trigonometry, calculus, physics and programming (sin, cos and tan take radians). Multiply degrees by π/180. The common angles are exact fractions of π: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2 and 180° = π. Trigonometry functions in code expect the decimal radian value, for example 90° = 1.5708 rad.

Quick estimate

Multiply by 0.01745, or by π and divide by 180: 90° = π/2 ≈ 1.5708 rad.

Common mistakes

• Multiplying instead of dividing. A radian is larger than a degree, so the number of radians must come out smaller: 30 degrees = 0.523599 rad.
• Rounding too early. Keep the full factor until the last step; rounding 0.0175 to 0.017 first puts large values noticeably off.

Going the other way? Use the radians to degrees converter.