Converter Tools
Angle Converter
Convert angles between degrees, radians, gradians, turns, arcminutes, arcseconds, and milliradians. Also parses DMS (degrees, minutes, seconds).
Quick conversions
From unit
Decimal places
Headline
Decimal degrees
180 deg
Everyday geometry, navigation, and engineering.
Radians
3.1416 rad
SI base. Required by trig functions in most programming languages.
Degrees, minutes, seconds (DMS)
180° 0' 0"
Standard format for surveying, astronomy, and aviation.
All units
The source unit is highlighted. Every other row is derived from the same radian value.
Converted
Radians
3.1416 rad
SI base unit. One radian is the angle subtended by an arc equal in length to the radius. A full circle is 2π rad.
Example: 1.5708 rad is a right angle
Converted
Milliradians
3141.5927 mrad
One thousandth of a radian. Used in optics, military range estimation, and laser beam divergence. A full circle is 6283.185 mrad.
Example: 0.291 mrad ~ 1 minute of arc
Source
Degrees
180 deg
Decimal degrees. 360 degrees in a full circle. The everyday unit for navigation, geometry, and most engineering drawings.
Example: 90° is a right angle
Converted
Gradians
200 grad
Also called gon. 400 gradians in a full circle so each quadrant is a clean 100. Common in surveying, French engineering, and some calculators.
Example: 100 grad is a right angle
Converted
Turns
0.5 turn
One full revolution. 0.25 turn is a quarter circle, 1 turn is a complete loop. Sometimes called a cycle or revolution.
Example: 0.25 turn is a right angle
Converted
Arcminutes
10800 arcmin
Also written ' (single prime). One sixtieth of a degree. Used for fine angular measurement in astronomy and optics. 21600 arcmin in a circle.
Example: 60 arcmin = 1°
Converted
Arcseconds
648000 arcsec
Also written " (double prime). One sixtieth of an arcminute, so one 3600th of a degree. The standard for high-precision astronomy. 1296000 arcsec in a circle.
Example: 3600 arcsec = 1°
Conversion factors used
- 1 deg = π / 180 rad ≈ 0.01745329 rad
- 1 rad = 180 / π deg ≈ 57.29578°
- 1 grad (gon) = π / 200 rad = 0.9°
- 1 turn = 2π rad = 360° = 400 grad
- 1 arcmin (') = 1/60 deg = π/10800 rad
- 1 arcsec (") = 1/3600 deg = π/648000 rad
- 1 mrad = 1/1000 rad ≈ 0.05729578°
Reference angles
Tap any reference to load it as radians. Every other unit updates instantly.
How to use
- Pick the source unit you are converting from (degrees, radians, gradians, turns, arcmin, arcsec, or mrad).
- Type your angle value. A bare number is interpreted in the selected source unit; you can also type a suffix like '45 deg', '1.2 rad', '100 grad', or paste a DMS expression like '12° 30' 30"' directly.
- Read the Headline cards for decimal degrees and radians, plus a DMS card with degrees, minutes, and seconds.
- Scan the All units grid to see every other unit derived from the same radian value.
- Adjust Decimal places to control precision from 0 to 8.
- Click any Reference angle (right angle, equilateral triangle interior, Earth's axial tilt, and more) to load it instantly.
- Use Copy buttons to paste a single value or the full summary into your work.
About this tool
Angle Converter turns any single angle into every common unit at once: decimal degrees, radians, gradians (gon), turns (revolutions), arcminutes, arcseconds, and milliradians. Type a number with an optional suffix (45, 45 deg, 45°, 1.2 rad, 100 grad, 0.25 turn, 30 arcmin, 30'), or paste a full degrees-minutes-seconds expression like 12° 30' 30" and the tool parses every common spelling. Internally every value goes through radians (the SI base unit), so the conversion math is exact within IEEE 754 limits and adding a new unit is a one-line change. The standard factors are 1 deg = π/180 rad, 1 grad = π/200 rad, 1 turn = 2π rad, 1 arcmin = 1/60 deg, 1 arcsec = 1/3600 deg, and 1 mrad = 1/1000 rad. A headline panel shows the two units most people actually need (decimal degrees and radians), with a separate DMS card for surveying, astronomy, and aviation use. Useful for trigonometry homework, programming with Math.sin and Math.cos in JavaScript or numpy in Python (both expect radians), CAD and engineering drawings, scope and ballistics calculations in milliradians, and converting GPS coordinates between decimal degrees and degrees-minutes-seconds. Everything runs in your browser; the values you type never leave your device.
Free to use. Works in your browser. No signup, no login.
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