Convert between degrees, radians, and gradians.
Free to use, no sign-up required. Angle Converter is one of 198 tools built into Xenition, alongside a chat that can use them for you.
Converts angles between degrees, radians, gradians, arcminutes, arcseconds and full turns. It is used in trigonometry and programming (which work in radians), surveying (gradians) and astronomy or GPS (arcminutes and arcseconds).
Every unit is stored in degrees. A radian is 180/π = 57.29577951308232°, a gradian is 0.9° (a right angle is 100 grad), an arcminute is 1/60°, an arcsecond is 1/3,600°, and a turn is 360°.
45 deg is 0.785398 rad (π/4). A right angle, 90 deg, is exactly 100 grad.
A radian is the angle whose arc equals the radius, so a full circle is 2π radians. That makes formulas in calculus and physics simpler, and it is why Math.sin in most programming languages expects radians.
Convert each part separately and add them, or turn it into decimal degrees first: degrees + minutes/60 + seconds/3,600. 30° 15′ is 30.25°.
Angle Converter converts between 6 units: arcsec, arcmin, grad, deg, rad and turn. Factors are given against deg.
| Unit | In deg | 1 deg equals |
|---|---|---|
| 1 arcsec | 0.0002777778 deg | 3600 arcsec |
| 1 arcmin | 0.0166666667 deg | 60 arcmin |
| 1 grad | 0.9 deg | 1.1111111111 grad |
| 1 rad | 57.2957795131 deg | 0.0174532925 rad |
| 1 turn | 360 deg | 0.0027777778 turn |
Common quantities in deg, converted. Every value is computed from the factors above, so the chart and the converter cannot disagree.
| deg | arcsec | arcmin | grad | rad |
|---|---|---|---|---|
| 1 deg | 3600 | 60 | 1.1111111111 | 0.0174532925 |
| 2 deg | 7200 | 120 | 2.2222222222 | 0.034906585 |
| 5 deg | 18000 | 300 | 5.5555555556 | 0.0872664626 |
| 10 deg | 36000 | 600 | 11.1111111111 | 0.1745329252 |
| 25 deg | 90000 | 1500 | 27.7777777778 | 0.436332313 |
| 100 deg | 360000 | 6000 | 111.1111111111 | 1.745329252 |
1 deg is 3600 arcsec. To convert deg to arcsec, divide by 0.0002777778 — so 10 deg is 36000 arcsec.
1 arcsec is 0.0002777778 deg. To convert arcsec to deg, multiply by 0.0002777778 — so 10 arcsec is 0.0027777778 deg.
1 deg is 60 arcmin. To convert deg to arcmin, divide by 0.0166666667 — so 10 deg is 600 arcmin.
1 arcmin is 0.0166666667 deg. To convert arcmin to deg, multiply by 0.0166666667 — so 10 arcmin is 0.1666666667 deg.
1 deg is 1.1111111111 grad. To convert deg to grad, divide by 0.9 — so 10 deg is 11.1111111111 grad.
1 grad is 0.9 deg. To convert grad to deg, multiply by 0.9 — so 10 grad is 9 deg.
1 deg is 0.0174532925 rad. To convert deg to rad, divide by 57.2957795131 — so 10 deg is 0.1745329252 rad.
1 rad is 57.2957795131 deg. To convert rad to deg, multiply by 57.2957795131 — so 10 rad is 572.9577951308 deg.
You do not have to open Angle Converter to use it. Ask Xenition in plain language and it runs the right tool, then carries the answer into whatever you are working on — a document, a spreadsheet, a deck.