Home › Unit Conversion › Angle Converter

Angle Converter

Converts plane angles between degrees, radians, milliradians, gradians (gon), arcminutes, arcseconds and turns (revolutions) using π rad = 180° = 200 gon = 0.5 turn.

When to use

You need an angle in another unit, e.g. degrees to radians for trigonometry, arcseconds for astronomy or turns for rotation counts.

Do not use when: You need an angle from a slope or triangle (use slope, right-triangle or triangle-solver) or a rotational speed (use frequency for rpm and rad/s).

Formula

result = value × factor, factor = (1 from_unit in rad) / (1 to_unit in rad)

Inputs

Parameter	Type	Required	Description
`value`	number	yes	Amount to convert, expressed in from_unit.
`from_unit`	enum: deg \| rad \| mrad \| grad \| arcmin \| arcsec \| turn	yes	Unit of the input value. Accepted symbols: deg, rad, mrad, grad, arcmin, arcsec, turn; spelled-out names and common abbreviations are accepted too.
`to_unit`	enum: deg \| rad \| mrad \| grad \| arcmin \| arcsec \| turn	yes	Unit to convert into (same symbols as from_unit).

Outputs

Output	Type	Description
`result`	number	Converted value expressed in to_unit (rounded to 6 decimals; see result_text for very small or very large values).
`result_text`	string	The conversion as text with 6 significant figures, e.g. "5 mi = 8.04672 km".
`formula`	string	Relation used, e.g. "1 mi = 1.609344 km".
`factor`	number	Multiplier from from_unit to to_unit (result = value × factor); absent for non-linear conversions.
`conversion_table`	object	The input value expressed in every supported angle unit (6 significant figures), keyed by unit symbol.

Example

180 degrees to radians: {"value":180,"from_unit":"deg","to_unit":"rad"} → {"result":3.141593,"factor":0.0174532925,"formula":"1 ° = 0.01745329252 rad","conversion_table":{"grad":200,"turn":0.5,"arcmin":10800}}

1 radian to degrees: {"value":1,"from_unit":"rad","to_unit":"deg"} → {"result":57.29578,"conversion_table":{"grad":63.662,"arcsec":206265}}

GET https://tttkmbb.com/api/v1/calculate/angle?value=180&from_unit=deg&to_unit=rad

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/angle (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/angle · Markdown: https://tttkmbb.com/conversion/angle.md · JSON definition: https://tttkmbb.com/conversion/angle.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="angle"
OpenAPI operationId: convert_angle
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

FAQ

How many degrees is one radian?

180/π = 57.29578°; a full turn is 2π rad = 360° = 400 gon.

What is a milliradian?

1/1000 of a radian (0.0573°), used in optics and ballistics. The NATO 'mil' (1/6400 turn = 0.98175 mrad) is a different unit and is not included.

Related calculators

Right Triangle Calculator — Angles from triangle sides.
Slope Calculator — Angle of a line from its gradient.
Frequency Converter — Rotational speed in rpm or rad/s.