Angle Converter

Convert between all angle units. Select a conversion from the table below.

Degree

The degree (°) is the most common angle unit, with 360 degrees in a full rotation. It is used in navigation, construction, geography, and everyday descriptions of turns and rotations.

1 ° to rad 1 ° to grad 1 ° to ′ 1 ° to ″

Radian

The radian (rad) is the SI unit of angle. One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. A full circle equals 2π radians. It is essential in calculus and physics.

1 rad to ° 1 rad to grad 1 rad to ′ 1 rad to ″

Gradian

The gradian (grad), also called a gon, divides a right angle into 100 parts, making a full circle 400 gradians. It is used in surveying and civil engineering, particularly in Europe.

1 grad to ° 1 grad to rad 1 grad to ′ 1 grad to ″

Arcminute

The arcminute (′) equals 1/60 of a degree. It is used in astronomy for measuring celestial positions, in navigation for coordinates, and in optics for describing visual acuity.

1 ′ to ° 1 ′ to rad 1 ′ to grad 1 ′ to ″

Arcsecond

The arcsecond (″) equals 1/60 of an arcminute or 1/3,600 of a degree. It is used in astronomy for measuring star positions, in geodesy for precise coordinates, and in telescope specifications.

1 ″ to ° 1 ″ to rad 1 ″ to grad 1 ″ to ′

What Is an Angle?

An angle is a figure formed by two rays sharing a common endpoint (vertex). Angles measure the amount of rotation between two directions and are fundamental in geometry, trigonometry, navigation, surveying, astronomy, and computer graphics.

Common Angle Units

The degree (°) is the most widely used angle unit, with a full rotation equal to 360°. A right angle is 90°. Degrees are used in navigation, geography, construction, and everyday descriptions of rotation.

The radian (rad) is the SI unit of angle, where a full rotation equals 2π (approximately 6.283) radians. One radian equals approximately 57.3°. Radians are essential in calculus, physics, and engineering because they simplify mathematical formulas involving trigonometric functions.

The gradian (grad), also called gon, divides a right angle into 100 parts, making a full circle 400 gradians. It is used in surveying and civil engineering, particularly in continental Europe. The arcminute (′) equals 1/60 of a degree and the arcsecond (″) equals 1/60 of an arcminute. Both are used in astronomy, navigation, and precise surveying.