Angle Converter

Use this tool to convert between different units of angle, such as Degrees, Radians, Gradians, and more.

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Common Angle Conversions

deg to rad ° → rad
rad to deg rad → °
deg to grad ° → grad
arcmin to arcsec ' → "

What is Angle Conversion?

Angle conversion is the process of converting measurements of angular distance or rotation from one unit to another. Our angle converter tool supports all common angular units used in mathematics, engineering, navigation, and astronomy.

Common units include degrees (°), radians (rad), gradians (grad), arcminutes ('), and arcseconds ("). These conversions are essential for trigonometry, engineering surveys, celestial navigation, and mechanical design.

Simply enter your value in the "From" field, select the original unit, choose your target unit in the "To" field, and the converter will instantly display the converted result along with the conversion formula.

Angle Conversion Examples

Mathematics Example

Trigonometric calculations:

  • 180° = π radians = 200 grad
  • 90° = π/2 rad = 100 grad
  • 45° = π/4 rad = 50 grad

Navigation Example

GPS and compass bearings:

  • 1° = 60 arcminutes
  • 1' = 60 arcseconds
  • 360° = full circle

Astronomy Example

Celestial position measurements:

  • 1° = 3600 arcseconds
  • Moon apparent size ≈ 30 arcminutes
  • 1 arcsecond = 1/3600°

Frequently Asked Questions

How many radians in a full circle?

A full circle (360 degrees) equals 2π radians, approximately 6.28318 radians. This is a fundamental constant in trigonometry and calculus.

How do I convert degrees to radians?

To convert degrees to radians, multiply by π/180. For example, 90° × π/180 = π/2 radians ≈ 1.5708 rad.

How many arcseconds in a degree?

One degree equals exactly 3600 arcseconds. This is commonly used in astronomy for precise celestial measurements and telescope adjustments.

What is the difference between grad and degree?

A grad (or gon) divides a right angle into 100 units, so a full circle is 400 grad. One degree equals 10/9 grad. Gradians are used in some surveying applications.

What is the formula for rad to deg conversion?

To convert radians to degrees, multiply by 180/π. For example, 1 rad × 180/π ≈ 57.296°. This is essential for engineering calculations and programming.