Angle Converter

Convert degrees, radians, gradians, arcminutes and arcseconds.

Popular angle conversions

Angle unit reference chart

What one of each unit is worth in degrees, the base unit used for every conversion in this category.

Angle units expressed in degrees
Unit	Symbol	1 unit in °
degrees	°	1 °
radians	rad	57.29577951 °
gradians	grad	0.9 °
arcminutes	′	0.01666666667 °
arcseconds	″	0.0002777777778 °
revolutions	rev	360 °
milliradians	mrad	0.05729577951 °

Angle units explained

Degrees (°)

A degree is 1/360 of a full turn. The division into 360 comes from ancient Babylonian astronomy.

Radians (rad)

A radian is the angle subtended by an arc equal in length to the radius. A full turn is 2π radians, so 1 rad ≈ 57.2958°.

Gradians (grad)

A gradian divides a right angle into 100 parts, so a full turn is 400 gradians. It is used in surveying.

Arcminutes (′)

An arcminute is one sixtieth of a degree. One arcminute of latitude is one nautical mile, which is where that unit’s definition comes from.

Arcseconds (″)

An arcsecond is one sixtieth of an arcminute, or 1/3600 of a degree. Telescope resolution and stellar parallax are quoted in arcseconds.

Revolutions (rev)

One revolution is a complete turn: 360 degrees, or 2π radians.

Frequently asked questions

What is the base unit of angle?

This converter routes every angle conversion through the degree. Converting from one unit to another means converting to degrees first and then out again, which keeps every pair consistent with every other pair.

How accurate are these angle conversions?

Results are shown to 10 significant digits using exact defined factors wherever a unit has one. No rounding is applied beyond that final display step.

All angle conversions

Every angle conversion page on this site, 36 in total.