Angle Converter

The radian is the SI unit of plane angle, the ratio of arc length to radius, a dimensionless quantity. A full circle is 2π radians ≈ 6.2832 rad. The degree (°) divides a circle into 360 parts, a convention inherited from ancient Babylonian astronomy. Each degree divides into 60 arcminutes ('), each arcminute into 60 arcseconds (''), a base-60 (sexagesimal) system also of Babylonian origin. The gradian divides a circle into 400 parts, making a right angle exactly 100 grad, a feature valued in surveying.

All conversions in this category are computed relative to a single base unit (Degree) using factors sourced from NIST Special Publication 811 and the BIPM SI Brochure. A shared reference unit keeps the conversion relationships consistent. Converting directly from the original measurement avoids the rounding differences that can accumulate when displayed intermediate results are entered again.

This calculator supports 7 units, including Degree, Radian, Milliradian, Gradian, Turn. Choose the unit shown in your source measurement, then the unit needed for your result.

Units may have alternate spellings or abbreviations. You can search using these names too. Examples include Degree (deg, also written as degree or degrees), or Radian (rad, also written as radian or radians), or Milliradian (mrad, also written as milliradian or milliradians).

All angle conversions within the SI family are purely multiplicative: you multiply the source value by a fixed conversion factor derived from the ratio of the two unit definitions. Imperial-to-metric conversions use the exact defined equivalences (e.g., 1 inch = 25.4 mm exactly) rather than approximations.

When precision matters, avoid rounding intermediate calculations. The displayed factors and results are rounded for readability, usually to ten significant digits; very large or small values use scientific notation. Use the original measurement for each conversion and round the final answer to match the accuracy of that measurement.

Keep the unit alongside each angle value when you copy or share it. Check that the source and target units match your task. If two units have similar names, read their definitions before selecting one.

For a second check, use the worked example and formula on the conversion page. Start from your original value rather than a rounded result from another calculator. If you need to report a specific number of decimal places, round once at the end.