Angle Converter
Degrees, radians, gradians and turns all measure the same thing — rotation — but different fields default to different units, which is exactly why a CAD drawing in degrees and a physics formula in radians need converting before they'll agree.
Inputs
Result
0.017453 Radian
How it works
- 11 Degree → base = 1
- 2Base → Radian = 0.017453
How the angle converter works
Every unit converts through degrees as the common base: 1 Radian = 57.2957795°, 1 Gradian = 0.9°, 1 Turn = 360°, 1 Arcminute = 1/60°.
To convert, the input is scaled to degrees, then from degrees to the target unit.
Worked example: π radians to degrees
- π ≈ 3.14159 radians.
- 3.14159 × 57.2957795 ≈ 180°.
- This confirms the well-known identity that π radians equals exactly 180°.
Common mistakes to avoid
Leaving a calculator's angle mode on the wrong unit before converting
A scientific calculator's trig functions interpret angle inputs according to its own mode setting (degrees or radians) — converting a value here doesn't change that mode, so it still needs to be set correctly wherever the converted value is actually used.
Assuming 'gradian' is the same as 'degree'
A gradian divides a full circle into 400 parts rather than 360, making 1 gradian = 0.9° exactly — close enough in casual glancing to be confused with degrees, but a meaningfully different unit used mainly in surveying and some European engineering contexts.
Frequently asked questions
Why does a full circle equal 360° but 2π radians?
Degrees are an arbitrary historical division of the circle (360, likely chosen for its many divisors); radians are defined geometrically as the ratio of arc length to radius, making a full circle exactly 2π radians — a definition rooted in the circle's own geometry rather than an arbitrary count.
Where are gradians actually used?
Mainly in surveying and some European engineering and cartography contexts, where a 400-gradian circle offers convenient decimal subdivisions (100 gradians per quarter turn) compared to degrees' less decimal-friendly 90 per quarter turn.
How do I convert directly between radians and turns?
1 turn = 2π radians ≈ 6.2832 radians — so dividing a radian value by roughly 6.2832 gives the equivalent number of full turns.
Why do trigonometric functions in most programming languages expect radians?
Radians make calculus involving trig functions (derivatives, integrals) mathematically clean without extra conversion constants — this mathematical convenience is why radians became the standard internal unit in most programming languages and scientific computing, even though degrees remain more intuitive for everyday human use.
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