TontonTools

Angle Converter

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

100% Free No signup Privacy-friendly Unit Converters
Updated Sep 2026

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How to use Angle Converter

  1. Enter the angle in the “From” field — for example 45 for 45 degrees.
  2. Choose its unit in the first dropdown (Degree, Radian, Gradian, Arcminute…).
  3. Choose the target unit in the second dropdown — the converted angle appears instantly.
  4. Press the swap button to flip the conversion, e.g. degrees → radians into radians → degrees.

What is Angle Converter?

An angle converter translates angular measurements between units — degrees to radians, gradians to degrees, or arcseconds to degrees. The degree (360 to a full circle) is Babylonian heritage; the radian is the mathematician's unit, defined so a full circle is 2π radians, which makes calculus formulas clean — every programming language's trig functions expect radians.

The supporting cast: gradians (400 to a circle, used in surveying), arcminutes and arcseconds (1/60 and 1/3600 of a degree, the currency of astronomy, optics and GPS coordinates), and the turn — one full rotation, the most intuitive unit of all.

About the Angle Converter

This converter covers six units — degree, radian, gradian, arcminute, arcsecond and turn — converting between any pair instantly as you type.

The everyday case is degrees ↔ radians: code calling sin() needs radians, so 45° must become 0.7854 (π/4) before it goes in. Surveyors meet gradians on European instruments (a right angle = 100 grad); astronomers describe the Moon as 31 arcminutes wide; GPS coordinates use degrees-minutes-seconds where one arcsecond of latitude is about 31 meters on the ground.

Anchors: 180° = π rad ≈ 3.1416 rad, 1 rad ≈ 57.2958°, 90° = 100 grad = 0.25 turn. Conversions are exact and instant, computed in your browser.

Frequently Asked Questions

Multiply by π/180 (≈ 0.017453). Common values: 30° = π/6, 45° = π/4, 90° = π/2 ≈ 1.5708, 180° = π. Going back, multiply radians by 57.2958.
Because calculus identities (like the derivative of sin being cos) only hold in radians. Math.sin(90) in JavaScript is NOT sin of 90° — convert with degrees × π/180 first.
A unit with 400 to the full circle, so a right angle is exactly 100 grad. It was designed for decimal convenience and survives in European surveying instruments and some calculators (the “GRAD” mode).
Subdividing degrees: 1° = 60 arcmin = 3,600 arcsec. Astronomy (the full Moon spans ~31 arcmin), optometry (visual acuity), and GPS coordinates all rely on them; 1 arcsecond of latitude ≈ 31 m.
About 57.2958° — exactly 180/π. It is the angle where the arc length along a circle equals the circle's radius.

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