Angle converter — degrees, radians and gradians

Trigonometry wants radians, drawings are dimensioned in degrees, surveying instruments read gradians, optics data comes in milliradians. One number, all of them.

How to use it

1
Type into any row — say ° or rad. The results appear immediately, no button needed.
2
Need a combined figure? Fill in two rows, for example ° and grad, and they are added together before converting.
3
Set how many digits you want (4–12) and click a result to copy the plain number.

Exact conversion factors

These are the definitions the calculator uses. Nothing here is rounded for convenience — where a value is exact by definition, it says so.

1 rad = 57.2957795° · 1° = 0.0174532925 rad
90° = 1.57079633 rad = 100 grad · 180° = π = 3.14159265 rad
1 turn = 360° = 6.28318531 rad = 400 grad
1° = 60' = 3600" · 1 mrad = 0.0572957795° = 3.43774677'

Formularad = ° × π/180 · ° = rad × 180/π · grad = ° × 10/9 · arcmin = ° × 60

Angle conversion table — every unit

One of each unit, converted into the three units people ask for most.

Unit	°	rad	grad
1 turn	360 °	6.28319 rad	400 grad
1 °	1 °	0.0174533 rad	1.11111 grad
1 rad	57.2958 °	1 rad	63.662 grad
1 grad	0.9 °	0.015708 rad	1 grad
1 '	0.0166667 °	0.000290888 rad	0.0185185 grad
1 "	0.000277778 °	0.00000484814 rad	0.000308642 grad
1 mrad	0.0572958 °	0.001 rad	0.063662 grad

° → rad, grad — quick values

°	rad	grad
0.5 °	0.00872665 rad	0.555556 grad
1 °	0.0174533 rad	1.11111 grad
2 °	0.0349066 rad	2.22222 grad
3 °	0.0523599 rad	3.33333 grad
5 °	0.0872665 rad	5.55556 grad
10 °	0.174533 rad	11.1111 grad
20 °	0.349066 rad	22.2222 grad
25 °	0.436332 rad	27.7778 grad
50 °	0.872665 rad	55.5556 grad
100 °	1.74533 rad	111.111 grad
250 °	4.36332 rad	277.778 grad
1 000 °	17.4533 rad	1 111.11 grad

How this converter works

The conversion that trips people up in code: most programming languages take radians, not degrees. Math.sin(30) is not the sine of thirty degrees — you need 0.5236 rad. Type 30 in the degree row and the radian row gives you the number to pass.

Arcminutes and arcseconds subdivide the degree by sixty and by thirty-six hundred, and they are still how coordinates, telescope resolution and rifle sights are specified. One MOA at 100 yards is 1.047 inches, which falls out of the arcminute row directly.

Notes and abbreviations

1 turn = 360° = 2π rad = 400 grad
1 rad = 57.2958°; 1° = 0.0174533 rad
1° = 60 arcminutes (') = 3600 arcseconds (")

Questions

What is 90 degrees in radians?

π/2, or 1.5707963 rad.

What is a gradian?

A right angle divided into 100 parts instead of 90, so a full circle is 400 grad. Surveying and some European calculators use it.

How big is one milliradian?

0.0572958°, and it subtends 1 m at 1000 m — which is why scopes are marked in mrad.