Angle Converter
Convert angles between degrees, radians, gradians and turns.
Results update as you type.
About this calculator
An angle converter changes an angle between degrees, radians, gradians (gon), arcminutes, arcseconds and full turns. It converts through the degree as a common base and uses π to bridge degrees and radians.
The essential relationships are 360° = 2π radians = 400 gradians = 1 full turn, so 180° = π radians and 90° = π/2. Within a degree the sexagesimal split gives 60 arcminutes, and each arcminute holds 60 arcseconds, mirroring how clocks divide an hour.
Worked example: to convert 90 degrees to radians, multiply by π/180, giving π/2 ≈ 1.5708 radians. To convert 1 radian to degrees, multiply by 180/π, giving about 57.30°. A results table shows the same angle in every unit at once, handy for trigonometry, CAD and surveying.
Frequently asked questions
How do I convert degrees to radians?
Multiply degrees by π/180. A full circle of 360° equals 2π radians, so 180° = π radians ≈ 3.14159 and 90° = π/2 ≈ 1.5708 radians.
What is a gradian?
A gradian (gon) divides a right angle into 100 parts, so a full circle is 400 gon. It is used in some surveying and engineering contexts.
How many arcminutes are in a degree?
One degree is 60 arcminutes, and one arcminute is 60 arcseconds — the same sexagesimal split used for time.
How many degrees are in a radian?
One radian is about 57.2958 degrees (180/π). It is the angle at which the arc length equals the radius, which is why radians are the natural unit in calculus and physics.
How do I convert radians to degrees in this angle converter?
This angle converter multiplies radians by 180/π (about 57.2958). So π radians becomes 180° and 2 radians becomes about 114.6°.
What is a turn?
A turn is one full revolution — 360 degrees, 2π radians or 400 gradians. Fractions of a turn describe rotations compactly, so a half turn is 180° and a quarter turn is 90°.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/angle/curl
curl "https://calculator.free/api/v1/angle/?amount=1&from=deg&to=rad"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/angle/?" + new URLSearchParams({
"amount": "1",
"from": "deg",
"to": "rad"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.