Angle Converter

A precise Geometry Hub tool for converting degrees, radians, and other angular units with high-fidelity accuracy.

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3.142Radians
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functionsFormula: rad = deg × (π / 180)

Common Angle Units Reference

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Degrees (°)

The most common unit. A full circle is 360°. Standard for basic geometry and navigation.

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Radians (rad)

Standard unit in calculus and physics. A full circle is 2π radians (approx. 6.28318).

square_foot

Gradians (grad)

Metric unit where a right angle is 100 grads. Used in some surveying and military applications.

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Arcseconds (")

Highly precise units. 1 arcsecond is 1/3600th of a degree. Used in astronomy and precision optics.

Degree to Radian Reference

Degrees (°)Radians (Exact)Radians (Decimal)Gradians
30°π / 60.523633.33
45°π / 40.785450.00
90°π / 21.5708100.00
180°π3.1416200.00
360°6.2832400.00

What is Angle Conversion?

Angle conversion is the process of changing the representation of an angle from one unit to another. This is crucial in trigonometry, physics, and engineering where different systems of measurement are preferred depending on the application.

For example, while degrees are intuitive for daily use, radians are the natural choice for circular motion and wave equations in mathematics.

The Importance of Accuracy

In precise fields like aerospace engineering or long-range surveying, even a tiny error in angle conversion can result in significant deviations. A 1-degree error over a 60-mile flight path results in being 1 mile off target.

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help_outlineAngle FAQ

The 360-degree system likely comes from ancient Babylonian astronomy, which used a base‑60 number system. 360 is highly composite, making it convenient for dividing circles into many equal parts.