How to Use the Angle Unit Converter
Type a value into any of the three fields (degrees, radians, or gradians) and the other two are updated instantly. This tool supports the three most common angle units used in mathematics, physics, and surveying.
Angle Conversion Formulas
- To radians: rad = deg × π/180
- To gradians: grad = deg × 10/9
- Reference: 1 right angle = 90° = π/2 rad = 100 grad
- Full circle: 360° = 2π rad = 400 grad
Frequently Asked Questions
Why are radians preferred in calculus?
With radians, d/dx[sin(x)] = cos(x) with no extra constant. Using degrees would require multiplying by π/180, complicating every derivative.
What are gradians used for?
Gradians (gons) are used mainly in surveying and civil engineering, where a right angle equals exactly 100 grad — convenient for grid-based calculations.
What is 45° in radians?
45° × π/180 = π/4 ≈ 0.785398 rad. Key angles: 30°=π/6, 45°=π/4, 60°=π/3, 90°=π/2, 180°=π.