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Angle Converter

Degrees, radians, gradians, arcminutes, mils and turns — with DMS and π.

Converters Reviews Free · no sign-up

Degrees can also be typed as degrees, minutes and seconds — 12° 30′ 45″ or 12 30 45.

Result
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Quick Tool Overview

The Angle Converter handles degrees, radians, gradians, arcminutes, arcseconds, NATO mils, turns and five more, accepts degrees-minutes-seconds input, and shows each angle as a multiple of π, in DMS and normalised to 0–360°.

What it does
Converts angles between 12 units
You give it
An angle as a decimal or in degrees-minutes-seconds
You get back
The result, the π form, DMS and a unit table
Best for
Maths, programming, surveying and navigation
Converters Free, unlimited use No sign-up Runs in your browser

About the Angle Converter

An angle is the same idea in every field that uses one, but each field measures it differently. Maths and programming work in radians, surveyors in gradians or degrees-minutes-seconds, astronomers in arcseconds, the military in mils, and mechanics in turns.

This converter takes a value in any of twelve units — degrees can be typed as 12° 30′ 45″ — and gives it in the unit you choose and in all the others at once. It also shows the angle as a multiple of π when that is exact, writes it out in degrees, minutes and seconds, normalises it into the 0 to 360 degree range and gives its sine, which covers most of what people need an angle converted for.

Key features of the Angle Converter

DMS input

Type 12° 30′ 45″, 12 30 45 or 12:30:45, with N, S, E or W, and it is read as decimal degrees.

Exact multiples of π

135° is shown as 3π/4 rather than only 2.35619, which is the form maths answers need.

Normalised angle

Any angle, including negative ones and several turns, is reduced into the 0 to 360 degree range.

Military and survey units

NATO mils, milliradians, gradians and compass points sit alongside the everyday units.

All units at once

A table lists the angle in every supported unit, each value one click to copy.

How to use the Angle Converter

  1. 1

    Type the angle

    A decimal such as 45 or 0.7854, or degrees-minutes-seconds such as 12° 30′ 45″.

  2. 2

    Pick the units

    Choose the unit you have and the unit you want. DMS input works when degrees are the source.

  3. 3

    Read the result

    The answer appears with the π form, the DMS form and the angle normalised to 0–360°.

  4. 4

    Check the table

    Every unit is listed below the result, each one click to copy.

Frequently asked questions

Multiply by π and divide by 180. So 90° is π/2, about 1.5708 radians. One radian is about 57.2958 degrees.

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