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. Anchoring every conversion to one reference unit guarantees mathematical consistency: converting from A → B → C always yields the same result as converting directly from A → C.

Among the 7 supported units, the most frequently used include Degree, Radian, Milliradian, Gradian, Turn. These appear across household tasks, professional environments, and academic study.

Many units carry aliases and regional abbreviations that appear in product specs, recipes, and technical documents. We index common synonyms so searches for alternate spellings still reach the right converter — for example, 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 — machining tolerances, pharmaceutical compounding, scientific reporting — avoid intermediate rounding. Each converter page shows the full unrounded factor so you can carry maximum precision through multi-step calculations and only round the final result.

In daily practice, choosing the right angle unit saves time and prevents costly errors. Commercial shipping, construction, and scientific research all depend on correct unit handling to maintain safety, compliance, and reproducibility across borders and disciplines.

Consumer products, regulations, and international standards often specify values in different unit systems — a drug dosage in micrograms, a fuel efficiency in L/100 km, a tyre pressure in PSI. Each domain has a dominant unit, and cross-domain work requires reliable conversion. This converter is built for exactly those situations: results traceable to internationally defined constants, displayed with full precision.