Angle Converter

Written byOleh Soloninupdated 5 October 2026

Value

From

Result

Result1.570796

The conversion every trigonometry function needs

Convert degrees to radians for trigonometry, or into gradians, turns, arcminutes and arcseconds for surveying and astronomy.

The trigonometric functions of programming languages take radians, a scientific calculator works in whichever mode it is set to, and people think in degrees. Hence the classic slip: the sine of 90 taken in radians is 0.894, not 1.

The relationship is fixed: π radians is 180 degrees. So 90° is π/2, about 1.5708 — a number worth recognising on sight.

How to use

Enter an angle.
Choose the unit you are converting from: degrees, radians, gradians, turns, arcminutes or arcseconds.
Choose the unit you are converting to — the result appears straight away.

Degrees to radians

Radians = degrees × π / 180. The values worth recognising: 90° is π/2 ≈ 1.5708, 180° is π ≈ 3.1416, a full turn 2π ≈ 6.2832.

Every row comes from the calculator on this page.
Degrees	Radians	In terms of π
30°	0.5236	π/6
45°	0.7854	π/4
60°	1.0472	π/3
90°	1.5708	π/2
180°	3.1416	π
270°	4.7124	3π/2
360°	6.2832	2π

Gradians, arcminutes and turns

One radian is 57.2958°. A degree splits into 60 arcminutes and each arcminute into 60 arcseconds; a right angle is exactly 100 gradians.

Every row comes from the calculator on this page.
From	To
1 rad	57.2958°
90°	100 grad
1°	60′
1°	3,600″
1′	0.016667°
1 turn	360°

What this calculator shows

Conversion across six angle units
Degrees and radians for everyday trigonometry
Gradians, turns and arcminutes for surveying and astronomy

What to keep in mind

A full turn is 360 degrees, 2π radians or 400 gradians.
Arcminutes and arcseconds subdivide the degree by 60 and 3600.

FAQs

How many degrees is one radian?

57.2958°. A radian is the angle whose arc equals the radius; a full turn holds 2π of them, about 6.2832.

How do I convert degrees to radians by hand?

Multiply by π/180. For example, 45° is 45π/180 = π/4, roughly 0.785.

Why does maths prefer radians?

Because calculus formulas come out clean in them. The derivative of sin(x) is cos(x) only in radians; in degrees an extra factor appears everywhere.

Why does sin(90) give 0.894 instead of 1?

Because the function read 90 as radians. Spreadsheet and programming trig functions expect radians: sin(π/2) = sin(1.5708) = 1.

What is a gradian?

A metric angle unit in which a right angle is exactly 100 gradians and a full turn 400. It is used in surveying.

How many arcseconds are in a degree?

3,600: sixty arcminutes to the degree, sixty arcseconds to the arcminute.

Worked example

A right angle

Input: 90 degrees → radians

Output: 1.5708 rad

Note: That is π/2. If a sine function returns 0.894 instead of 1 for 90, it is reading your number as radians.

Useful links

All tools in Converters for units, temperature, weight, and cooking measures

Angle Converter

Result

Related tools

Triangle Calculator

Unit converter for everyday measurement conversions

Scientific Calculator

Useful links