Angle Converter

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

How to Use This Converter

Type a value in either box and pick the units. The other box updates instantly. Use the swap button to reverse the direction.

All 6 units are supported in both directions.
Results update live as you type — no button to press.
Values are formatted for readability while staying precise.

Frequently Asked Questions

How many degrees in a radian?

About 57.296°. One full circle is 2π radians = 360°.

What is a gradian?

A unit where a right angle = 100 gradians and a full circle = 400. Used in surveying and some European engineering.

How many arcminutes in a degree?

60 arcminutes in 1 degree, and 60 arcseconds in 1 arcminute.

How do I convert degrees to radians?

Multiply by π/180. 180° = π radians.

Practical Example

Convert 90° to radians. Because a full circle is 360° = 2π radians, one degree equals π/180 ≈ 0.017453 radians. So 90° × 0.017453 = 1.5708 radians — exactly π/2.

Formula: radians = degrees × π/180
90° ÷ 360 = 0.25 turns
90° × 0.9 = 81 gradians
90° × 60 = 5,400 arcminutes

What Your Results Mean

Radians — the angle as arc length divided by radius on a unit circle; 2π rad = 360°.
Turns (rev) — the fraction of a full rotation; 1 turn = 360°.
Gradians (gon) — 100 gradians per right angle and 400 per full circle, used in surveying.
Arcminutes/Arcseconds — finer subdivisions of a degree: 1° = 60 arcminutes = 3,600 arcseconds.