Is Angle Converter free to use?

Yes, Angle Converter is completely free. No subscription, no credit card, and no account required — ever.

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Is Angle Converter safe? Does it store my data?

Angle Converter processes your data locally in your browser. Nothing is sent to or stored on our servers.

How do I use Angle Converter?

Open the tool, enter or paste your input, and your result appears instantly. Use the copy button to save it. The whole process takes under a minute.

Angle Converter

Unit Converter enables you to convert different units of angle

Convert Units

From:

To:

Result:

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.[1] Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.

What is Angle Converter?

An angle is a figure formed by two rays sharing a common endpoint called the vertex. Angles are fundamental in geometry, trigonometry, navigation, engineering, and many scientific applications. Different fields use different units to measure angles based on convenience and tradition.

Understanding the Units

Degree (°)

The most common unit of angular measurement. A full circle is divided into 360 degrees.

Common Uses: Navigation, geography, everyday measurements, construction

Radian (rad)

The SI unit for measuring angles. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.

Common Uses: Mathematics, physics, engineering calculations, calculus

Conversion: 2π radians = 360 degrees, 1 radian ≈ 57.2958 degrees

Gradian (gon)

Also called gon or grade. A right angle is 100 gradians, making a full circle 400 gradians.

Common Uses: Surveying, some European countries

Conversion: 400 gradians = 360 degrees

Minute of Arc (arcmin)

One-sixtieth of a degree. Used for precise angular measurements.

Common Uses: Astronomy, navigation, cartography

Conversion: 60 arcminutes = 1 degree

Second of Arc (arcsec)

One-sixtieth of an arcminute, or 1/3600 of a degree.

Common Uses: Astronomy, precision measurements

Conversion: 3600 arcseconds = 1 degree

Common Conversions

Right angle: 90° = π/2 rad = 100 gon
Straight angle: 180° = π rad = 200 gon
Full circle: 360° = 2π rad = 400 gon
One radian: 1 rad = 57.2958° = 63.662 gon

Conversion Formulas

Degrees to Radians: radians = degrees × (π/180)
Radians to Degrees: degrees = radians × (180/π)
Degrees to Gradians: gradians = degrees × (400/360)
Gradians to Degrees: degrees = gradians × (360/400)

Practical Examples

A quarter turn (90°) equals π/2 radians or 100 gradians

The angle of Earth's axial tilt is approximately 23.5 degrees

In navigation, compass bearings are measured in degrees (0-360°)

Trigonometric functions in programming typically use radians

When to Use Each Unit

Degrees: Everyday measurements, navigation, construction, geography

Radians: Mathematical calculations, calculus, physics, programming

Gradians: Surveying, civil engineering (especially in Europe)

Arcminutes/Arcseconds: Astronomy, precise angular measurements

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