Angle Converter — Degrees to Radians
Convert degrees to radians and back — plus gon (gradians), milliradians, arcminutes, arcseconds, turns and degrees-minutes-seconds.
About this tool
Enter an angle, choose the unit you have and the unit you want. You get the exact conversion, the angle in degrees, minutes and seconds (DMS), and the same angle in every unit at once. 180° = π rad, so 1° = 0.0174533 rad and 1 rad = 57.2958°. A full circle is 360°, 2π rad, 400 gon or 21,600 arcminutes. Negative angles work too.
Frequently asked questions
Multiply by π/180 (about 0.0174533), because a half circle is 180° = π rad. So 90° = π/2 = 1.5708 rad, 45° = 0.7854 rad and 30° = 0.5236 rad. To go from radians to degrees, multiply by 180/π (about 57.2958): 1 rad = 57.2958° and 2 rad = 114.59°.
A gon, also called a gradian or grad, is 1/400 of a full circle, so a right angle is exactly 100 gon and 1 gon = 0.9°. It is used mainly in land surveying, where the decimal right angle makes calculations easier. To convert, multiply gon by 0.9 to get degrees: 50 gon = 45°, 250 gon = 225°.
Keep the whole degrees, multiply the decimal part by 60 for minutes, and multiply what is left of the minutes by 60 for seconds. Example: 12.3456° → 12°, 0.3456 × 60 = 20.736′ → 20′, 0.736 × 60 = 44.16″, so 12° 20′ 44.16″. Going back: 12 + 20/60 + 44.16/3,600 = 12.3456°.
One thousandth of a radian: 1 mrad = 0.001 rad = 0.0572958° = 3.4377 arcminutes. A full circle is 2π × 1,000 ≈ 6,283.19 mrad. At a distance of 100 m, an angle of 1 mrad spans about 10 cm (100 m × 0.001), which is why it is handy for estimating sizes and distances.
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