Angle Converter

Convert angles between degrees, radians, gradians and turns.

How the Math Works

The Angle Converter uses a straightforward proportional formula to transform angles between different units. At its core, the calculation follows: result = value × (from in base unit) ÷ (to in base unit). This works by first expressing each angle unit as a proportion of a full rotation (our base unit). For example, since 360 degrees equals 1 full turn, one degree is 1/360 of a turn. Similarly, 2π radians equal 1 turn, making one radian equal to 1/(2π) turns. When converting, we multiply the original value by the fraction representing the source unit relative to the target unit, effectively scaling it appropriately.

Practical Applications

To use this calculator practically, simply enter your angle value and select its current unit from the dropdown menu, then choose your desired output unit. For instance, if you need to convert 45 degrees to radians for a trigonometry problem, enter 45, select 'degrees', and choose 'radians' as your target. The calculator instantly applies the conversion formula and displays the result. This tool is invaluable for students working on homework, engineers verifying calculations, or anyone needing to switch between angular measurements quickly and accurately.

Day-to-Day Use

Angle conversions appear in many everyday situations. When setting up a projector or adjusting a security camera, you might need to convert between degrees and turns to ensure proper positioning. Artists and craftsmen frequently work with different angular measurements when creating geometric designs or patterns. Even in fitness, understanding angular movement can help with exercises involving rotation. The Angle Converter eliminates guesswork and calculation errors, making it easy to bridge the gap between different measurement systems you might encounter in technical manuals, online tutorials, or collaborative projects with people using different conventions.

Worked example

Pick the units and type a value — the result updates instantly.

FAQ