Angle Converter — Degrees, Radians, Gradians, Arcminutes & More
Convert between degrees, radians, gradians, arcminutes, arcseconds, milliradians, and turns. Free online angle unit converter for geometry, navigation, and surveying.
Angle Converter
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The Formula
Angle conversion uses linear factors relative to the degree (°). Radians use the mathematical constant π (1 rad ≈ 57.296°). Gradians divide a right angle into 100 units (100 grad = 90°), used primarily in surveying and European engineering. Compass points divide the circle into 32 equal parts of 11.25° each for navigation.
Variable Definitions
Angle (theta)
The figure formed by two rays sharing a common endpoint, measured in degrees, radians, or gradians.
One Degree
1/360 of a full rotation. The most common unit for everyday angle measurement.
Angular SI and Metric Units (Radian & Gradian)
Radian (≈57.296°): the SI unit for angular measurement, essential for calculus and physics. Gradian (1/400 of a circle): used in surveying and some European engineering, 100 grad = 90°.
How to Use This Calculator
- 1
Enter the angle value you want to convert in the "Value" field.
- 2
Select the current angle unit from the "From" dropdown.
- 3
Select the desired angle unit from the "To" dropdown.
- 4
The converted value is displayed instantly with the formula. Use this for math homework, navigation, machining, or surveying work.
- 5
Check the quick reference for common angle equivalents like 90° in radians, gradians, and arcminutes.
Quick Reference
| From | To |
|---|---|
| 180° | π rad / 200 grad / ½ turn |
| 90° | π/2 rad / 100 grad / ¼ turn |
| 1 rad | 57.296° / 63.662 grad |
| 1° | 0.01745 rad / 1.111 grad |
| 1° | 60 arcminutes / 3,600 arcseconds |
| 1 arcmin | 1/60° / 0.0167° |
| 1 mrad | 0.0573° / 3.438 arcmin |
| 1 compass point | 11.25° |
Common Applications
- Navigation: 90° is east, 180° is south, 270° is west (compass bearings)
- Roof pitch: a 6/12 roof has a 26.6° slope
- Rifle scope: 1 mrad ≈ 3.6 inches at 100 yards / 10 cm at 100 m
- Astronomy: Moon diameter ≈ 0.5° (30 arcminutes)
- Surveying: theodolites measure to sub-arcsecond precision
- Machining: CNC rotary tables use degrees, gradians, or decimal degrees
A full circle = 360° = 2π rad = 400 grad = 1 turn
Understanding the Concept
Angles are measured in several units depending on the field and region. Degrees (360° per circle) are the everyday standard — used in navigation (compass bearings), construction (roof pitch), and education. Radians are the mathematical standard — 2π radians equals a full circle — and are essential for calculus, trigonometry, and physics because radian measure simplifies derivative and integral formulas. Gradians (400 per circle) divide the right angle into 100 parts, making decimal calculations easier in surveying and some European engineering fields. Milliradians (mrad) are used in rifle scopes and artillery for range estimation — 1 mrad subtends approximately 1 meter at 1,000 meters distance. Arcminutes (60 per degree) and arcseconds (3,600 per degree) are used in astronomy and optics for measuring extremely small angles — the angular diameter of the Moon is about 30 arcminutes (0.5°). Compass points (32 per circle) were the standard for maritime navigation before modern instruments.
Frequently Asked Questions
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