Angle Converter
Convert angle units with the factor behind each answer. A radian is the natural unit in formulas, and a degree is the usual unit on drawings and instruments.
1 deg = 0.01745329252 rad
Common conversions
- 1 deg = 0.01745329252 rad
- 1 rad = 57.29577951 deg
- 1 deg = 60 arcmin
- 1 arcsec = 0.0002777777778 deg
- 1 deg = 1.111111111 grad
- 1 turn = 360 deg
Degrees and radians
A full turn is 360 degrees or 2π radians, so one radian is about 57.2958 degrees and one degree is about 0.0174533 radians. Trigonometric functions in spreadsheets and code take radians, so convert first.
Survey and coordinates
Bearings and latitude and longitude are given in degrees, arcminutes and arcseconds. To split an angle into those parts, or to join them, use the degrees minutes seconds converter.
Phase angle in AC work
Power factor angles and phase angles are normally quoted in degrees, while ωt in formulas is in radians. The same angle gives the same cosine in either unit.
Unit factors
Every unit in terms of the base unit shown. To convert, multiply by the factor of the unit you have and divide by the factor of the unit you want.
| Unit | Equals | What it is |
|---|---|---|
| mrad | 0.001 rad | Milliradian, a thousandth of a radian. Sights, optics and beam divergence. |
| rad | 1 rad | Radian, the SI unit of plane angle: the angle at the centre of a circle that cuts an arc equal to the radius. 180 degrees is π radians. |
| deg | 0.01745329252 rad | Degree, 1/360 of a full turn. Bearings, survey and drawings. |
| arcmin | 0.0002908882087 rad | Arcminute, 1/60 of a degree. Written ′ in survey and navigation. |
| arcsec | 4.848136811 × 10⁻⁶ rad | Arcsecond, 1/3600 of a degree. Written ″ in survey and astronomy. |
| grad | 0.01570796327 rad | Gradian (gon), 1/400 of a full turn, so a right angle is 100 grad. Used in some surveying instruments. |
| turn | 6.283185307 rad | A full turn, one complete revolution: 360 degrees or 2π radians. |
Conversion pages
Frequently asked questions
What is the formula to convert deg to rad?
rad = deg × 0.01745329252. For example, 180 deg is 3.141592654 rad.
How do I convert rad back to deg?
deg = rad × 57.29577951. The Swap button above reverses the direction for any pair of units.
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