Angle Converter

Convert between degrees, radians, gradians, arcminutes, and turns.

Value

From

Result

1.57079633

Radians (rad)

Common angles

Degrees	Radians (rad)	Gradians (grad)	Arcminutes (′)	Arcseconds (″)	Turns
0°	0	0	0	0	0
30°	0.52359878	33.33333333	1800	108000	0.08333333
45°	0.78539816	50	2700	162000	0.125
90°	1.57079633	100	5400	324000	0.25
180°	3.14159265	200	10800	648000	0.5
360°	6.28318531	400	21600	1296000	1

Angle units in mathematics and engineering

Angles can be expressed in several units. Degrees (°) are the most familiar — a full circle is 360°. Radians are the SI unit used in mathematics and physics: a full circle is 2π rad ≈ 6.2832 rad, and 1 rad ≈ 57.296°. Gradians (grad) divide the full circle into 400 parts, making right angles exactly 100 grad — convenient in surveying. Arcminutes (1/60°) and arcseconds (1/3600°) are used in navigation and astronomy for very precise angular measurements. A turn is simply one full revolution (360°). All conversions route through degrees and run entirely in your browser.

Built and maintained by Meet Shah · Last updated 19 July 2026

What this tool is used for

Converting an angle for a library whose functions take a different unit.
Reading a gradian value from a surveying instrument into degrees.
Converting a rotation expressed in turns for a CSS or animation property.
Comparing two angle specifications quoted differently.
Converting a bearing expressed in turns for an animation that counts full rotations.

Frequently Asked Questions

Why do programming languages use radians?: Because the calculus only works cleanly in them — the derivative of sin is exactly cos, and the series expansions carry no stray constants. Degrees would thread a π/180 factor through every identity, which is why `Math.sin` in every mainstream language takes radians.
Why 360 degrees in a circle?: Babylonian sexagesimal counting, plus the convenient fact that 360 divides evenly by 24 numbers including 2 through 6, 8, 9, 10 and 12. That divisibility is why halves, thirds, quarters, fifths, sixths and eighths of a circle are all whole numbers of degrees.
What are gradians for?: Making a right angle exactly 100, which suits surveying arithmetic. 400 gradians make a full turn, and they survive in some European surveying practice and as the third mode on scientific calculators — usually discovered by accident when every trigonometric answer is slightly wrong.
How small is an arcsecond?: 1/3600 of a degree — the angle a coin subtends from about four kilometres away. Astronomy works in them routinely, and milliarcseconds below that: Gaia measures stellar positions to tens of microarcseconds, which is a coin on the Moon.
Why is a turn sometimes a useful unit?: Because rotational quantities are naturally counted in whole revolutions, and CSS accepts `turn` directly — `rotate(0.5turn)` is more legible than `rotate(180deg)` when the intent is half a rotation. It removes the arbitrary 360 from expressions that never needed it.

Common errors and gotchas

Passing degrees where radians are expected, which is the classic trigonometry bug.
Confusing gradians with degrees, where a right angle is 100 in one and 90 in the other.
Converting an angle past a full turn and losing the winding count, which matters for a rotation but not a direction.
Losing the direction convention, where one system measures clockwise and another anticlockwise.
Assuming a CSS angle defaults to radians, when it defaults to degrees.