Angle Converter
Convert between degrees, radians, gradians and turns — instantly.
Result
Result
1.570796
How it works
Angles come in four common units, all describing the same thing: a fraction of a full turn. One turn is 360 degrees, 2π radians (about 6.283), or 400 gradians. This converter routes any value through that shared reference. Degrees are the everyday unit, inherited from Babylonian astronomy — 360 divides neatly by 2, 3, 4, 5, 6, 8, 9, 10 and 12, which is why it survived. Radians are the mathematician's unit: an angle of 1 radian cuts an arc exactly as long as the radius, which makes calculus formulas clean. Gradians split the right angle into a tidy 100 and survive in surveying. The conversion to remember: multiply degrees by π/180 for radians, or radians by 180/π for degrees. So 90° = π/2 ≈ 1.571 rad, and 180° = π ≈ 3.142 rad. Watch your calculator's mode — most trigonometry errors come from feeding degrees into a function expecting radians.
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Frequently asked questions
How do I convert degrees to radians?
Multiply by π/180. Example: 90° = π/2 ≈ 1.5708 rad.
What is a gradian?
A gradian (grad) splits a full turn into 400 — so 90° = 100 grad.
Why do mathematicians prefer radians?
Because an angle of 1 radian subtends an arc equal to the radius, which makes calculus results clean — the derivative of sin(x) is cos(x) only when x is in radians.
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