Angle Converter
Convert degrees, radians, gradians, arcminutes, arcseconds and turns.
The Angle Converter switches between the units used to measure rotation: degrees, radians, gradians (gons), arcminutes and arcseconds, and full turns. It serves students wrestling with trigonometry, surveyors and astronomers working in arcminutes, and engineers and game developers who think in radians or gradians.
Radians are the mathematician's favorite — a full circle is 2π radians (about 6.2832 rad), and 180° equals exactly π rad — but the conversions are never round numbers, which makes quick mental math unreliable: 45° is π/4 rad, 30° is π/6 rad. Arcminutes and arcseconds divide a degree into 60 and 3,600 parts, the units of precision in astronomy and surveying. A NATO angular mil (1/6,400 of a circle) is included for marksmen and artillery.
Every unit is defined exactly against the degree (1 rad = 57.29578°), conversions run locally in your browser, and the rate line always shows the relationship.
Result
1 ° = 0.0174532925199 rad
1 ° = 0.0174532925199 rad
1 rad = 57.2957795131 °
How to use the Angle Converter
- Type the angle value.
- Choose the source unit (°, rad, grad, arcmin, arcsec, turn, mil).
- Choose the target unit.
- Read the converted value and the exact rate.
- Swap to double-check the other direction.
Frequently asked questions
How do I convert degrees to radians?
Multiply by π/180: 180° = π rad ≈ 3.14159 rad, and 90° = π/2 ≈ 1.5708 rad. The converter reports the decimal value; exact fractions like π/2 are easy to derive by dividing the result by π.
Why do math and physics use radians?
Radian measures make calculus formulas clean — the derivative of sin(x) is cos(x) only when x is in radians — and they relate arc length to angle directly: an angle of 1 radian sweeps an arc equal to the radius.
What are arcminutes and arcseconds used for?
They divide each degree into 60 minutes and each minute into 60 seconds — the units of fine angular measurement. Astronomers use them for star separations (the full Moon spans about 30 arcminutes), and surveyors and optical engineers quote arcsecond-level precision.
Related tools
View all unit converters →Length Converter
Convert between metric and imperial lengths: mm to inches, km to miles and more.
ConvertersWeight Converter
Convert kilograms, pounds, ounces, grams, stones and tons instantly.
ConvertersHeight Converter
Height in cm, meters or feet & inches — with the feet-inches split done for you.
ConvertersTemperature Converter
Convert Celsius, Fahrenheit, Kelvin and Rankine with one click.
ConvertersArea Converter
Convert square meters, square feet, acres, hectares and more.
ConvertersVolume Converter
Convert liters, gallons (US & UK), cups, cubic feet, barrels and more.