Angle converters
Degrees, radians, gradians, arcminutes — the angle units for geometry, navigation, astronomy, and engineering.
7 units42 conversions
Angle›° → rad
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1 °=
0.0174533rad
formula1 ° = 0.0174533 rad
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Degrees to Radians
1 ° = 0.0174533 rad
Radians to Degrees
1 rad = 57.2958 °
Degrees to Gradians
1 ° = 1.11111 grad
Degrees to Arcminutes
1 ° = 60 arcmin
Degrees to Arcseconds
1 ° = 3,600 arcsec
Degrees to Turns
1 ° = 0.00277778 turn
Degrees to Milliradians
1 ° = 17.4533 mrad
Radians to Gradians
1 rad = 63.662 grad
Radians to Arcminutes
1 rad = 3,437.75 arcmin
Radians to Arcseconds
1 rad = 206,265 arcsec
All angle conversions
42 pairsEvery unit pair in this category. Tap any cell to open that conversion.
| from \ to | °Degrees | radRadians | gradGradians | arcminArcminutes | arcsecArcseconds | turnTurns | mradMilliradians |
|---|---|---|---|---|---|---|---|
| °Degrees | — | × 0.0174533 | × 1.11111 | × 60 | × 3,600 | × 0.00277778 | × 17.4533 |
| radRadians | × 57.2958 | — | × 63.662 | × 3,437.75 | × 206,265 | × 0.159155 | × 1,000 |
| gradGradians | × 0.9 | × 0.015708 | — | × 54 | × 3,240 | × 0.0025 | × 15.708 |
| arcminArcminutes | × 0.0166667 | × 0.000290888 | × 0.0185185 | — | × 60 | × 4.6296e-5 | × 0.290888 |
| arcsecArcseconds | × 0.000277778 | × 4.8481e-6 | × 0.000308642 | × 0.0166667 | — | × 7.7160e-7 | × 0.00484814 |
| turnTurns | × 360 | × 6.28319 | × 400 | × 21,600 | × 1,296,000 | — | × 6,283.19 |
| mradMilliradians | × 0.0572958 | × 0.001 | × 0.063662 | × 3.43775 | × 206.265 | × 0.000159155 | — |
Each cell shows the multiplier from row → column. e.g. 1 ° × n = result in column units.
About angle units
Common angle units
Degree (°)
A full circle is 360 degrees. The everyday unit for everything from protractors to compass bearings.
Radian (rad)
The SI unit. One radian is the angle where the arc length equals the radius; a full circle is 2π ≈ 6.283 radians.
Gradian (grad / gon)
A right angle is 100 gradians, so a full circle is 400. Used in surveying.
Arcminute / arcsecond
A degree splits into 60 arcminutes, each into 60 arcseconds. Used in astronomy and precise bearings.
Degrees vs radians
Degrees are intuitive for everyday angles; radians are the natural unit for math and physics because they make calculus and circular-motion formulas clean. Convert with degrees = radians × 180/π.
Frequently asked
How many degrees in a radian?
One radian is about 57.2958 degrees (180 ÷ π).
What is a gradian?
A gradian (or gon) divides a right angle into 100 parts, so a full turn is 400 gradians.
How many arcminutes in a degree?
60 arcminutes, and each arcminute is 60 arcseconds.
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