Angle Converter

Convert between different units of angular measurement.

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Common Angle Conversions

• 1 turn = 360 degrees
• 1 degree = π/180 radians ≈ 0.0174533 rad
• 1 radian = 180/π degrees ≈ 57.2958°
• 1 gradian = 0.9 degrees
• 1 degree = 60 arc minutes
• 1 arc minute = 60 arc seconds
• π radians = 180 degrees
• 2π radians = 360 degrees = 1 turn

Common Angles

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About Angle Measurement

Angles measure the amount of rotation between two lines that meet at a point. Different systems use different units, with degrees being most common in everyday use and radians preferred in mathematics and physics.

Degrees

The degree is the most commonly used unit for measuring angles. A full circle is divided into 360 degrees (360°). This system dates back to ancient Babylonian mathematics.

Radians

Radians are the SI unit for angles and are preferred in mathematics and physics. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle is 2π radians (approximately 6.28318).

Gradians

Also called "gons," gradians divide a right angle into 100 parts, making a full circle 400 gradians. This decimal system was intended to simplify angle calculations but is less commonly used today.

Arc Minutes and Seconds

Arc minutes and arc seconds provide finer angular measurements. They're used in astronomy, navigation, and surveying. One degree equals 60 arc minutes, and one arc minute equals 60 arc seconds.

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