{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"proportion"},"result":{"entity_type":"calculator","id":"proportion","calculator_id":"proportion","canonical_url":"https://tttkmbb.com/math/proportion","name":"Proportion Calculator","title":"Proportion Calculator – Solve a/b = c/x by Cross-Multiplication","category":"math","category_name":"Math","tool_name":"solve_proportion","featured_mcp_tool":false,"description":"Solves the proportion a / b = c / x for the unknown fourth term by cross-multiplication (x = b × c / a) and reports the common scale factor.","use_when":"Three terms of a proportion are known and you need the fourth, e.g. converting a recipe, map scale or unit rate.","do_not_use_when":"You only want to simplify a ratio (use ratio) or the unknown is a percentage (use percentage).","inputs":[{"name":"a","label":"a","type":"number","required":true,"description":"First term (numerator of the known ratio). Must not be 0.","example":2},{"name":"b","label":"b","type":"number","required":true,"description":"Second term (denominator of the known ratio). Must not be 0.","example":3},{"name":"c","label":"c","type":"number","required":true,"description":"Third term: the numerator paired with the unknown x. Must not be 0.","example":4}],"outputs":[{"name":"x","label":"x","type":"number","decimals":6,"description":"The unknown fourth term, b × c / a."},{"name":"scale_factor","label":"Scale factor","type":"number","decimals":6,"description":"c / a = x / b: the multiplier from the first pair to the second."},{"name":"ratio","label":"a ÷ b","type":"number","decimals":6,"description":"The common value of both fractions, a / b = c / x."},{"name":"equation","label":"Solved proportion","type":"string","decimals":4,"description":"The proportion with x filled in, e.g. '2/3 = 4/6'."}],"input_schema":{"type":"object","properties":{"a":{"description":"First term (numerator of the known ratio). Must not be 0.","type":"number","examples":[2]},"b":{"description":"Second term (denominator of the known ratio). Must not be 0.","type":"number","examples":[3]},"c":{"description":"Third term: the numerator paired with the unknown x. Must not be 0.","type":"number","examples":[4]}},"additionalProperties":false,"required":["a","b","c"]},"output_schema":{"type":"object","properties":{"x":{"description":"The unknown fourth term, b × c / a.","type":"number"},"scale_factor":{"description":"c / a = x / b: the multiplier from the first pair to the second.","type":"number"},"ratio":{"description":"The common value of both fractions, a / b = c / x.","type":"number"},"equation":{"description":"The proportion with x filled in, e.g. '2/3 = 4/6'.","type":"string"}}},"formula":"a / b = c / x  ⇒  a × x = b × c  ⇒  x = b × c / a; scale_factor = c / a","sources":[{"name":"Wikipedia – Cross-multiplication","url":"https://en.wikipedia.org/wiki/Cross-multiplication","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wikipedia – Proportionality (mathematics)","url":"https://en.wikipedia.org/wiki/Proportionality_(mathematics)","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":"2/3 = 4/x","inputs":{"a":2,"b":3,"c":4},"expected":{"x":6,"scale_factor":2,"ratio":0.666667,"equation":"2/3 = 4/6"},"url":"https://tttkmbb.com/api/v1/calculate/proportion?a=2&b=3&c=4"},{"name":"5/8 = 12.5/x","inputs":{"a":5,"b":8,"c":12.5},"expected":{"x":20,"scale_factor":2.5,"ratio":0.625},"url":"https://tttkmbb.com/api/v1/calculate/proportion?a=5&b=8&c=12.5"}],"faq":[{"q":"What if the unknown is in a different position?","a":"Rearrange so the unknown is last: a/b = c/x is equivalent to b/a = x/c, c/a = x/b and so on; all give x = b × c / a."},{"q":"Does this handle inverse proportion?","a":"No. For inverse proportion (a × b = c × x) compute x = a × b / c directly."}],"tags":["proportion","solve proportion","cross multiply","a/b = c/x","missing value"],"related":[{"calculator_id":"ratio","reason":"Simplify or scale the ratio a:b."},{"calculator_id":"recipe-scaler","reason":"Proportional scaling of recipe quantities."},{"calculator_id":"percentage","reason":"Proportions with 100 as the base."}],"links":{"html":"https://tttkmbb.com/math/proportion","markdown":"https://tttkmbb.com/math/proportion.md","json":"https://tttkmbb.com/math/proportion.json","api":"https://tttkmbb.com/api/v1/calculate/proportion","schema":"https://tttkmbb.com/api/v1/calculators/proportion","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:22:58Z"}