Angle Converter
Degrees, radians, gradians, turns, arcminutes and arcseconds.
Angle Converter
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Units in this category
| Unit | Symbol | Exactly |
|---|---|---|
| degrees (°) | ° | reference unit for this category |
| radians (rad) | rad | 57.29578 ° |
| gradians (grad) | grad | 0.9 ° |
| turns (turn) | turn | 360 ° |
| arcminutes (arcmin) | arcmin | 0.01666667 ° |
| arcseconds (arcsec) | arcsec | 0.0002777778 ° |
Where these factors come from
A full turn is 360°, which is 2π radians exactly. The radian is the SI coherent unit; degrees and gradians are defined fractions of a turn.
All 30 angle pairs
| from → to | ° | rad | grad | turn | arcmin | arcsec |
|---|---|---|---|---|---|---|
| ° (degree) | — | 0.01745329 | 1.111111 | 0.0027777778 | 60 | 3,600 |
| rad (radian) | 57.29578 | — | 63.661977 | 0.15915494 | 3,437.75 | 206,264.81 |
| grad (gradian) | 0.9 | 0.01570796 | — | 0.0025 | 54 | 3,240 |
| turn (turn) | 360 | 6.283185 | 400 | — | 21,600 | 1,296,000 |
| arcmin (arcminute) | 0.01666667 | 0.0002908882 | 0.01851852 | 0.0000462963 | — | 60 |
| arcsec (arcsecond) | 0.0002777778 | 0.0000048481 | 0.000308642 | 0.0000007716 | 0.01666667 | — |
Conversions by starting unit
degrees (°)
° to rad° to grad° to turn° to arcmin° to arcsec
radians (rad)
rad to °rad to gradrad to turnrad to arcminrad to arcsec
gradians (grad)
grad to °grad to radgrad to turngrad to arcmingrad to arcsec
turns (turn)
turn to °turn to radturn to gradturn to arcminturn to arcsec
arcminutes (arcmin)
arcmin to °arcmin to radarcmin to gradarcmin to turnarcmin to arcsec
arcseconds (arcsec)
arcsec to °arcsec to radarcsec to gradarcsec to turnarcsec to arcmin
Common questions
Why does math use radians?
A radian is the angle that subtends an arc equal to the radius, which makes derivatives and series expand without extra constants — sin x ≈ x only works in radians.
What is a gradian for?
Surveying: 400 gradians to a full turn means 100 per right angle, so decimal fractions of a right angle stay tidy. Europe used it for triangulation networks.
How many arcminutes in a degree?
Sixty, and sixty arcseconds in an arcminute — the same base-60 convention as time. One nautical mile is one arcminute of latitude.