Angle
Angle Converter
Convert degrees, radians, gradians, and more
Editable
Input
Auto-Calculated
Conversion Formula
Target = Value × (From Ratio / To Ratio)
Angle conversions use linear ratios. Target = Value × (Source Ratio / Target Ratio). To convert degrees to radians: multiply by 1 / 57.29578.
Angle conversion is important in mathematics, navigation, engineering, and astronomy. Convert between degrees, radians, gradians, arcminutes, and arcseconds.
Radians are the SI standard for angular measurement. A full circle is 2π radians (≈ 6.283 rad). Arcminutes and arcseconds are used in astronomy and navigation.
All Supported Angle Units
| Unit | Symbol | Definition |
|---|---|---|
| Degree | ° | The most common angular unit, dividing a circle into 360 equal parts. |
| Radian | rad | The SI unit of angle, defined by the radius of a circle. |
| Milliradian | mrad | One-thousandth of a radian, used in targeting and optics. |
| Gradian | grad | A unit dividing a right angle into 100 parts, used in surveying. |
| Arcminute | ' | One-sixtieth of a degree, used in astronomy and navigation. |
| Arcsecond | " | One-sixtieth of an arcminute, used in precision astronomy. |
| Revolution / Turn | rev | A complete 360° rotation, also known as a full turn or cycle. |
Common Angle Conversions
| From | To | Value |
|---|---|---|
| 1° | rad | 0.01745 |
| 1 rad | ° | 57.296 |
| 1° | arcmin | 60 |
| 1 arcmin | arcsec | 60 |
| π rad | ° | 180 |
Frequently Asked Questions
To convert degrees to radians, multiply by π/180 (approximately 0.01745). For example, 90° × π/180 = π/2 ≈ 1.571 radians. This is essential for trigonometry and calculus.
Radians are the natural unit for angular measurement in calculus and trigonometry because they simplify derivative formulas. For example, d/dx sin(x) = cos(x) only works in radians.
A gradian divides a right angle into 100 parts. There are 400 gradians in a full circle. It is used in surveying and some European engineering fields.
There are 360 degrees in a full circle. This dates back to ancient Babylonian mathematics, which used a base-60 number system.
Arcminutes (1/60 of a degree) and arcseconds (1/3600 of a degree) are used in astronomy for measuring celestial object positions and in navigation for precise angular measurements.
There are 2π radians (approximately 6.283 radians) in a full circle. One radian is the angle created when the arc length equals the radius.
A revolution (or full turn) equals 360 degrees, 2π radians, or 400 gradians. It represents one complete rotation and is used in engineering and physics for rotational measurements.
Measurement Knowledge
Angle Reference Guides
Master angle measurements with our comprehensive educational resources.
Popular Angle Conversions
Direct access to the most commonly used conversion tools.
° Degree Conversions
rad Radian Conversions
grad Gradian Conversions
' Arcminute Conversions
" Arcsecond Conversions
mrad Milliradian Conversions
Supported Angle Units
Complete listing of available angle units in our converter.
°
Degree
angular
rad
Radian
angular
grad
Gradian
angular
'
Arcminute
angular
"
Arcsecond
angular
mrad
Milliradian
angular
rev
Revolution / Turn
angular