Radian (rad)

Definition

The SI angle unit — the angle subtending an arc equal to the radius; a full turn is 2π rad.

History

The radian is the natural mathematical measure of angle, the angle that cuts off an arc equal to the radius, so a full turn is 2π radians. The idea dates to the eighteenth century and the name was adopted in the 1870s.

Where it is used

Radians are used in trigonometry, physics and programming, where they make the mathematics of rotation simplest.

Typical uses include trigonometry, physics, programming.

Conversion pages

These pages convert radian to or from another unit in angle.

• Radian to degree

Other Angle units

• Degree (°)
• Gradian (gon)
• Revolution (rev)

Sources

• BIPM SI BIPM SI Brochure (2019); ISO 80000-3 (angle) · Dataset reviewed Nov 11, 2026