Angle Converter
Enter an angle and choose your source and target units to convert instantly between degrees, radians, and gradians.
Converted value
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How the Angle Converter formula works
Conversions relative to a full circle (360° = 2π radians = 400 gradians):
Radians = Degrees × (π / 180) Gradians = Degrees × (10 / 9)
Step-by-step calculation
- Convert the entered angle to degrees first, using its unit's relationship to a full 360° circle.
- Convert from degrees to the target unit using the target's own relationship to a full circle.
Worked example
Converting 90° to radians: 90 × (π/180) = π/2 ≈ 1.5708 radians. Converting 90° to gradians: 90 × (10/9) = 100 gradians.
Frequently asked questions
Why do radians use π instead of a round number?
A radian is defined geometrically — the angle where the arc length equals the radius — so a full circle naturally works out to 2π radians rather than a round number like 360 or 400, which are human-chosen conventions instead.
Where are gradians actually used?
Gradians (also called gons) are mainly used in surveying and some European engineering contexts, where dividing a right angle into 100 gradians (instead of 90 degrees) simplifies certain calculations.