AngleLab

Angles Calculator

Four units, one input.

Degrees

Radians

1.571

Gradians: 100
Turns: 0.25

What you entered

Degrees: 90

1
Radians
90 × π ÷ 180= 1.5708
2
Gradians
90 × 10/9= 100
3
Turns
90 ÷ 360= 0.25

Result

Radians: 1.571

90° equals 1.571 radians, 100 gradians, or 0.25 full turns.

Angle conversions: degrees, radians, gradians and turns

The same angle expressed four ways. A full circle is 360 degrees, 2 pi radians, 400 gradians or 1 turn.

Degrees	Radians	Gradians	Turns
30	0.523599	33.3333	0.0833
45	0.785398	50.0000	0.1250
60	1.047198	66.6667	0.1667
90	1.570796	100.0000	0.2500
180	3.141593	200.0000	0.5000
270	4.712389	300.0000	0.7500
360	6.283185	400.0000	1.0000

The 180 degree row shows radians equal to pi, which is the definition: a radian is the angle subtending an arc equal to the radius, so a half circle is exactly pi of them. Radians are the natural unit for calculus and for any programming language's trig functions, which is why converting from degrees is the first step in most code. Gradians divide the right angle into 100 rather than 90 and survive mainly in surveying. Turns are the most intuitive for rotation - a quarter turn is 0.25.

Why more than one unit exists

Degrees split a circle into 360 parts (an ancient Babylonian convention), radians measure angle by arc length relative to the radius (the natural unit for calculus and physics), and gradians split a right angle into 100 — each suits a different field.

The one worth memorizing

π radians = 180° is the single conversion fact that unlocks all the others — most programming languages' trig functions expect radians, not degrees, which is a frequent source of bugs.

Frequently asked questions

My GPS says a bearing of 1.2 radians — what's that in degrees?

Multiply by 180/π: 1.2 × (180/π) ≈ 1.2 × 57.2958 ≈ 68.75°. That's roughly east-northeast. Enter 1.2 in the radians field above for exact conversion to all units.

What are gradians and who uses them?

Gradians split a right angle into exactly 100 parts (so a full circle = 400 gradians). French surveyors and some European engineering fields use them because they make percentage-grade calculations cleaner — a 1% slope is exactly 1 gradian.

Why do programmers keep getting trig functions wrong?

Most programming languages (JavaScript, Python, C) expect radians, but most humans think in degrees. Passing 45 (degrees) to Math.sin() gives sin(45 radians) ≈ 0.851, not the expected sin(45°) = 0.707. Always multiply by π/180 before calling a trig function in code.