Angle Converter
Convert degrees, radians, gradians, and turns.
Conversion sheet
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Degrees are the everyday angle unit, but math and physics run on radians, surveying uses gradians, and rotations are sometimes counted in full turns. This converter pivots every angle through degrees so they all line up.
How it works
Angles convert through degrees as the base unit.
Degrees are the base, with a full circle being 360. Radians are the natural unit for trigonometry: a full circle is 2π radians, so one radian is about 57.296 degrees.
Gradians (or 'gons') split the circle into 400, making a right angle exactly 100 gradians — a tidy decimal system used in some surveying. Turns simply count whole revolutions, where one turn is 360 degrees.
Result = (value × degrees-per-source-unit) ÷ degrees-per-target-unit.
Worked examples
Convert 180 degrees (a straight line) to radians. → 3.1416 radians
180 ÷ 57.29578 degrees per radian = 3.1416 (which is π).
Convert a quarter turn to degrees. → 90 degrees
0.25 × 360 degrees per turn = 90 degrees.
Tips & gotchas
- Key checkpoints: 180° = π radians (≈ 3.1416), 90° = π/2 (≈ 1.5708), and 360° = 2π (≈ 6.2832).
- Calculators have a degrees/radians mode that silently changes trig results. If a sine or cosine looks wrong, that mode is the usual culprit.
- Gradians make a right angle a round 100, which is why some survey instruments prefer them — but most everyday work stays in degrees.
- To convert degrees to radians by hand, multiply by π and divide by 180; reverse it to go back.
FAQ
How many degrees is one radian?
About 57.296 degrees (180 ÷ π). A full circle is 2π radians, equal to 360 degrees.
What's a gradian and where is it used?
A gradian divides a circle into 400 parts, so a right angle is exactly 100 gradians. It appears in some surveying and engineering systems for its decimal convenience.
Why do programming and physics prefer radians?
Radians make calculus and trigonometry simpler — derivatives of sine and cosine come out clean only in radians, and most math libraries expect them.
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