Angle Converter
Convert between degrees, radians, gradians, turns, arcminutes and arcseconds.
How to use this calculator
- 1Enter the value you want to convert.
- 2Pick the unit you are converting from and the one you want.
- 3The table below shows the same value in every other supported unit.
How the calculation works
result = (value × factor(from) ) / factor(to)- factor
- How many degrees one unit represents
Every value is converted to degrees first, then out to the target unit. This means n units need n factors rather than n² conversion pairs.
Radians are the natural unit for mathematics: one radian is the angle subtending an arc equal to the radius, which is why calculus formulas for sine and cosine only work cleanly in radians.
Gradians divide a right angle into 100 rather than 90, so a full turn is 400 gon. They survive mainly in surveying and on some calculators.
Arcminutes and arcseconds subdivide the degree by 60 twice over, inherited from Babylonian base-60 arithmetic — the same lineage as minutes and seconds of time.
Worked example
90 degree to radian
- 1.One degree is 1 degrees, so 90 ° is 90 degrees.
- 2.One radian is 57.29578 degrees, so divide: 90 ÷ 57.29578 = 1.5707963.
- 3.Put another way, 1 ° = 0.0174533 rad.
Result: 1.5707963 rad
What this assumes, and where it stops
Assumptions
- Conversion factors follow the internationally agreed definitions of each unit.
Limitations
- Results are computed in double-precision floating point, which is exact to about 15 significant figures.
- Very large or very small values are displayed in scientific notation to avoid misleading precision.
Common questions
Why do trigonometric formulas require radians?
Because the derivative of sin(x) is cos(x) only when x is in radians. In degrees an extra factor of π/180 appears throughout, which is why calculus, physics and every programming language's trig functions use radians by default. Degrees are a human convenience, radians are the mathematically natural unit.
What is a milliradian used for?
Chiefly optics and shooting. At 1,000 metres, one milliradian subtends almost exactly 1 metre, which makes range and adjustment arithmetic trivial — a target 2 mrad wide at 500 m is 1 m across. That small-angle convenience is the whole reason the unit is used.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
Related calculators
Tools people commonly use alongside the angle converter.