{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"angle"},"result":{"entity_type":"calculator","id":"angle","calculator_id":"angle","canonical_url":"https://tttkmbb.com/conversion/angle","name":"Angle Converter","title":"Angle Converter – Degrees, Radians, Gradians, Arcminutes, Arcseconds and Turns","category":"conversion","category_name":"Unit Conversion","tool_name":"convert_angle","featured_mcp_tool":false,"description":"Converts plane angles between degrees, radians, milliradians, gradians (gon), arcminutes, arcseconds and turns (revolutions) using π rad = 180° = 200 gon = 0.5 turn.","use_when":"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).","inputs":[{"name":"value","label":"Value","type":"number","required":true,"description":"Amount to convert, expressed in from_unit.","example":180},{"name":"from_unit","label":"From unit","type":"enum","required":true,"values":[{"value":"deg","label":"Degree (°)","aliases":["°","degree","degrees","degs","arcdeg"]},{"value":"rad","label":"Radian (rad)","aliases":["radian","radians","rads"]},{"value":"mrad","label":"Milliradian (mrad)","aliases":["milliradian","milliradians"]},{"value":"grad","label":"Gradian (grad)","aliases":["gradian","gradians","gon","gons","grade","grads"]},{"value":"arcmin","label":"Arcminute (′)","aliases":["′","arcminute","arcminutes","minute of arc","minute-of-arc","minuteofarc","minute·of·arc","minute_of_arc","minutes of arc","minutes-of-arc","minutesofarc","minutes·of·arc","minutes_of_arc","moa","amin"]},{"value":"arcsec","label":"Arcsecond (″)","aliases":["″","arcsecond","arcseconds","second of arc","second-of-arc","secondofarc","second·of·arc","second_of_arc","seconds of arc","seconds-of-arc","secondsofarc","seconds·of·arc","seconds_of_arc","asec"]},{"value":"turn","label":"Turn (turn)","aliases":["turns","revolution","revolutions","rev","revs","rotation","rotations","cycle","cycles","full circle","full-circle","fullcircle","full·circle","full_circle"]}],"description":"Unit of the input value. 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Accepted symbols: deg, rad, mrad, grad, arcmin, arcsec, turn; spelled-out names and common abbreviations are accepted too.","type":"string","enum":["deg","rad","mrad","grad","arcmin","arcsec","turn"],"examples":["deg"]},"to_unit":{"description":"Unit to convert into (same symbols as from_unit).","type":"string","enum":["deg","rad","mrad","grad","arcmin","arcsec","turn"],"examples":["rad"]}},"additionalProperties":false,"required":["value","from_unit","to_unit"]},"output_schema":{"type":"object","properties":{"result":{"description":"Converted value expressed in to_unit (rounded to 6 decimals; see result_text for very small or very large values).","type":"number"},"result_text":{"description":"The conversion as text with 6 significant figures, e.g. \"5 mi = 8.04672 km\".","type":"string"},"formula":{"description":"Relation used, e.g. \"1 mi = 1.609344 km\".","type":"string"},"factor":{"description":"Multiplier from from_unit to to_unit (result = value × factor); absent for non-linear conversions.","type":"number"},"conversion_table":{"description":"The input value expressed in every supported angle unit (6 significant figures), keyed by unit symbol.","type":"object"}}},"formula":"result = value × factor, factor = (1 from_unit in rad) / (1 to_unit in rad)","sources":[{"name":"NIST Special Publication 811 – Guide for the Use of the International System of Units (SI), Appendix B conversion factors","url":"https://www.nist.gov/pml/special-publication-811","type":"standard","retrieved_at":"2026-09-23"},{"name":"BIPM – The International System of Units (SI Brochure, 9th edition)","url":"https://www.bipm.org/en/publications/si-brochure","type":"standard","retrieved_at":"2026-09-23"},{"name":"Wikipedia – Conversion of units","url":"https://en.wikipedia.org/wiki/Conversion_of_units","type":"reference","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"180 degrees to radians","inputs":{"value":180,"from_unit":"deg","to_unit":"rad"},"expected":{"result":3.141593,"factor":0.0174532925,"formula":"1 ° = 0.01745329252 rad","conversion_table":{"grad":200,"turn":0.5,"arcmin":10800}},"url":"https://tttkmbb.com/api/v1/calculate/angle?value=180&from_unit=deg&to_unit=rad"},{"name":"1 radian to degrees","inputs":{"value":1,"from_unit":"rad","to_unit":"deg"},"expected":{"result":57.29578,"conversion_table":{"grad":63.662,"arcsec":206265}},"url":"https://tttkmbb.com/api/v1/calculate/angle?value=1&from_unit=rad&to_unit=deg"}],"faq":[{"q":"How many degrees is one radian?","a":"180/π = 57.29578°; a full turn is 2π rad = 360° = 400 gon."},{"q":"What is a milliradian?","a":"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."}],"tags":["angle converter","degrees to radians","radians to degrees","gradians","arcseconds","turns"],"related":[{"calculator_id":"right-triangle","reason":"Angles from triangle sides."},{"calculator_id":"slope","reason":"Angle of a line from its gradient."},{"calculator_id":"frequency","reason":"Rotational speed in rpm or rad/s."}],"links":{"html":"https://tttkmbb.com/conversion/angle","markdown":"https://tttkmbb.com/conversion/angle.md","json":"https://tttkmbb.com/conversion/angle.json","api":"https://tttkmbb.com/api/v1/calculate/angle","schema":"https://tttkmbb.com/api/v1/calculators/angle","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:24:36Z","next_actions":[{"tool":"run_calculator","calculator_id":"angle","reason":"Run Angle Converter with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/conversion/angle.md"}}