Angle Unit Converter

Convert between degrees, radians, gradians, and turns with visual angle representation.

Tested tool guide Tested browser tools Checked August 16, 2026

What Angle Unit Converter does, with a checked example

This tool converts a single angle value across degrees, radians, gradians, and turns at once, updating every field as soon as one changes, and draws the angle as an arc on a circle so you can see its size rather than just read a number. Radians are shown as a decimal, not as a multiple of pi, which is the detail people most often trip over: 1.5708 rad looks unfamiliar until you recognize it as pi/2, i.e. 90 degrees.

Worked example

A concrete input and expected output from the current implementation.

Input

90 degrees

Expected output

1.5708 radians, 100 gradians, 0.25 turns

One full turn equals 360 degrees, 2*pi radians (about 6.2832), and 400 gradians, so 90 degrees is exactly one quarter of that: pi/2 rad, 100 gon, 0.25 turn.

How the result is produced

Radian as the pivot unit

Whatever unit you enter is first converted internally to radians, then radians are converted out to the other three: degrees = radians x 180/pi, gradians = radians x 200/pi (400 gradians per full turn), and turns = radians / (2*pi). Routing every conversion through one common unit keeps all four displayed values mutually consistent even though you only ever edit one field directly.

Visual arc display

Alongside the numeric fields, the tool draws the angle as an arc swept from a reference line on a circle, giving an immediate sense of whether the value is acute, obtuse, reflex, or past a full turn. This is useful for sanity-checking a converted value, such as confirming that 270 degrees points where you expect, without working through the trigonometry yourself.

Good uses

Converting a bearing or survey angle given in gradians (gon) from European surveying instruments into degrees for a US-standard drawing.
Turning a radian value returned by a trig function like atan2 or acos in code into degrees for a log message or UI label.
Checking a CSS rotate() or SVG angle given in turns against a design spec written in degrees.

Limits and checks

Radian output is a decimal approximation of an irrational multiple of pi (pi/2 displays as 1.5708...), so copying it into another calculation carries small rounding error rather than the exact symbolic value.
Gradians (gon) divide a circle into 400 units, not 360 - a value of 100 gradians is 90 degrees, not 100 degrees, which is easy to misread if you weren't expecting that unit.
It isn't documented how the tool handles angles outside one full turn, such as 450 degrees or -90 degrees - whether it normalizes them or shows the raw value - so check that behavior directly before relying on it for wrap-around logic.

Common questions

Why isn't 90 degrees exactly 1.5708 radians?

It is exactly pi/2 radians; 1.5708 is a rounded decimal display of that irrational value, accurate to four places. The conversion itself (radians = degrees x pi/180) is exact - only the on-screen decimal is truncated, so treat trailing digits as approximate.

What's a turn, and when would I actually use it?

One turn is a full 360-degree rotation, equal to 2*pi radians or 400 gradians. It's the unit CSS rotate() and some animation or game engines accept directly, so this field is mainly useful for matching a design spec to code, e.g. confirming rotate(0.25turn) equals 90 degrees.

References and verification

The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.