Degrees to Radians Converter
Enter a value to instantly convert between angle units.
1 Degree = 0.0175 Radian
Key Formulas
Degree → Radian
rad = ° × 0.0174533Radian → Degree
° = rad × 57.2958Degree → Gradian
grad = ° × 1.11111Gradian → Degree
° = grad × 0.9Formula
radians = degrees × (π ÷ 180)Degrees are intuitive for humans (a full circle = 360°). Radians are the mathematical standard used in calculus, physics, and engineering. One radian is the angle created by an arc equal to the circle's radius. Computers and scientific calculators default to radians, which is why conversion is critical for trigonometry and programming.
Source: ISO 80000-3:2019 (Quantities and units—Space and time)
Frequently Asked Questions
Real-World Examples
Right angle. 90° = π/2 ≈ 1.571 radians. The basis for sine and cosine calculations.
90 ° = 1.571 rad
Straight line. 180° = π ≈ 3.142 radians. Half a rotation.
180 ° = 3.142 rad
Full rotation. 360° = 2π ≈ 6.283 radians. One complete circle.
360 ° = 6.283 rad
Diagonal. 45° = π/4 ≈ 0.785 radians. Common in geometry and engineering.
45 ° = 0.785 rad