Angle Converter
Convert any angle between degrees, radians, gradians and other angular units.
From
To
- 1
Convert to the target unit
1 deg ÷ 57.29577951 = 0.017453 rad
1 deg =
| Radian | 0.017453 rad |
| Gradian | 1.111111 grad |
| Arcminute | 60 ' |
| Arcsecond | 3,600 " |
| Turn | 0.002778 turn |
Formula
How this is calculated
Every angular unit is defined relative to a single base unit — here the degree. Each unit carries a fixed "to-base" factor: 1 radian = 180/pi degrees (about 57.29578), 1 gradian = 0.9 degrees, 1 arcminute = 1/60 degree, 1 arcsecond = 1/3600 degree, and 1 turn = 360 degrees. These factors are exact definitions, not measurements, so there is no rounding in the constants themselves.
Conversion happens in two steps. First the input value is multiplied by its source unit's factor to express it in degrees (the base). Then that degree value is divided by the target unit's factor to express it in the destination unit. Algebraically this is just value_to = value_from x (toBase_from / toBase_to), so converting from a unit back to itself returns the original number exactly.
The only assumption is that pi is irrational, so any conversion touching radians is shown to a finite precision (6 decimals by default) and may carry tiny floating-point rounding. Degree-gradian-arcminute-arcsecond-turn conversions use rational factors and stay exact. Angles are treated as pure magnitudes — values are not wrapped into a 0-360 range, so 450 degrees stays 450 degrees rather than folding to 90.
About this calculator
An angle measures rotation between two rays. Degrees divide a full circle into 360 parts, while radians — the natural unit in mathematics — define a full circle as 2 pi radians. Gradians (or "gons") split a circle into 400 parts, and a turn is one complete revolution.
This converter uses the degree as its base unit. One radian equals 180/pi degrees (about 57.2958 deg), one gradian equals 0.9 degrees, and a full turn equals 360 degrees. Arcminutes and arcseconds are fine subdivisions of a degree used in astronomy and surveying.
Frequently asked questions
One radian equals 180/pi degrees, approximately 57.2958 degrees.
Multiply degrees by pi/180 (about 0.0174533) to get radians.
A gradian divides a right angle into 100 parts, so a full circle is 400 gradians and one gradian equals 0.9 degrees.
Also known as
TG we-Calculate Editorial Team. (2026). Angle Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/angle-converter
TG we-Calculate Editorial Team. "Angle Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/angle-converter.
TG we-Calculate Editorial Team, "Angle Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/angle-converter
@misc{wecalculate_angle_converter, title = {Angle Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/angle-converter}}, year = {2026}, note = {TG we-Calculate} }
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