Quickly convert between degrees, radians, gradians, minutes, and seconds of arc. Free tool with mathematical formulas, quick reference tables, and unit explanations.
Angle Converter
Common Angle Conversion Formulas
In mathematics, physics, and engineering, angles are often measured in different units depending on the context. While Degrees are common in everyday life, Radians are the standard for calculus and circular motion.
Mathematical Formulas
- Degrees to Radians: rad = deg × (π / 180)
- Radians to Degrees: deg = rad × (180 / π)
- Degrees to Gradians: grad = deg × (10 / 9)
- 1 Degree: 60 Minutes of arc (‘) or 3,600 Seconds of arc (“)
Angle Conversion Quick Reference
Use this table for quick reference to the most common angles used in trigonometry:
| Degrees (°) | Radians (rad) | Gradians (grad) |
|---|---|---|
| 0° | 0 rad | 0 grad |
| 45° | π/4 (0.785) | 50 grad |
| 90° | π/2 (1.571) | 100 grad |
| 180° | π (3.141) | 200 grad |
| 360° | 2π (6.283) | 400 grad |
Units Explained
- Degrees (°): The most familiar unit, where a full circle is divided into 360 parts.
- Radians (rad): The SI unit for angle. It is the ratio between the length of an arc and its radius ($1 \text{ rad} \approx 57.3^\circ$).
- Gradians (grad): Also known as gons, where a right angle is exactly 100 units. Often used in surveying and mining.
- Arcminutes and Arcseconds: Subdivisions of a degree used in astronomy, navigation, and ophthalmology for extremely precise measurements.
Why Use This Converter?
Many scientific calculators default to Radians, which can lead to errors if your input is in Degrees. This tool ensures you have the exact conversion for engineering projects, homework, or CNC machining where precision is paramount.