Angle converter
Convert degrees, radians, gradians and turns.
How the calculation works
Angles can be measured in different units; the most common is the degree (°), but trigonometry and physics use the radian.
Equivalences
- A full turn = 360° = 2π radians = 400 gradians
- 180° = π rad · 90° = π/2 rad
- 1 rad ≈ 57.2958°
Degree ↔ radian
rad = degrees × π / 180 and degrees = rad × 180 / π
Step-by-step example
90° in radians: 90 × π/180 = π/2 ≈ 1.571 rad.
Examples
- 180° = π ≈ 3.1416 rad.
- 45° = π/4 ≈ 0.785 rad.
Frequently asked questions
How many degrees is 1 radian?
≈ 57.30°. A full turn (360°) is 2π ≈ 6.283 radians.
When to use radians instead of degrees?
In calculus, physics and programming, where formulas assume radians (e.g. most sin() functions).
What is a gradian?
A unit where a full turn is 400 gradians (a right angle = 100). Used in surveying.
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Updated on June 17, 2026 · by Rafael Rossi · Methodology & sources