Angle Converter

Converts angle measurements between degrees, radians, and gradians. One full revolution equals 360 degrees, 2π radians, or 400 gradians. The tool applies the standard conversion factors and rounds output to a configurable precision.

Gradians (also called gons) are uncommon in mainstream math but persist in surveying and some European engineering contexts.

The internal representation is radians, the SI-derived unit for plane angle. Inputs in degrees multiply by π/180 on entry; inputs in gradians multiply by π/200. Outputs reverse the factor for the chosen target unit. Storing in radians avoids cumulative rounding error when converting through multiple units in succession, since each conversion is a single floating-point multiplication rather than a chain.

A worked example: 90 degrees corresponds to π/2 radians (about 1.5707963267948966) and 100 gradians. The right angle is the canonical sanity check across all three systems and the reason gradians were introduced in revolutionary France: a quarter turn becomes a clean 100, making percentage-of-quadrant arithmetic trivial. Decimal subdivisions of degrees are the modern norm, but the older degrees-minutes-seconds (DMS) notation, where one degree splits into 60 minutes and one minute into 60 seconds, still appears in geographic coordinates and astronomical catalogs. A toggle converts decimal degrees to DMS and back; 40.7128° becomes 40°42'46.08".

Limitations are mostly about expected use cases. The tool does not reduce angles into a canonical range; an input of 720 degrees converts to 4π radians rather than wrapping to 0. For trigonometric work this is the right behavior, since cosine of 720° equals cosine of 0° anyway, but for a heading or bearing it may surprise. Negative angles pass through with sign preserved. The angular mil (used in artillery, where one mil is 1/6400 of a circle in NATO usage or 1/6000 in Russian/Warsaw Pact usage) is not included by default; mil definitions vary enough that a generic converter would misrepresent the operational unit.

Numerical precision matches double-precision IEEE 754: about 15-17 significant decimal digits. Converting 1 degree to radians and back recovers the exact input bit-for-bit only because the round-trip is two multiplications by reciprocal constants; longer chains accumulate rounding at the last bit. For applications where this matters (long-running orbital simulations, surveying networks), interval arithmetic or symbolic representation is the appropriate tool.