{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"percent-error"},"result":{"entity_type":"calculator","id":"percent-error","calculator_id":"percent-error","canonical_url":"https://tttkmbb.com/math/percent-error","name":"Percent Error Calculator","title":"Percent Error Calculator – Absolute, Relative and Percentage Error of a Measured vs Accepted Value","category":"math","category_name":"Math","tool_name":"calculate_percent_error","featured_mcp_tool":false,"description":"Compares a measured or estimated value with the accepted (true) value and reports the absolute error, relative error, percent error and whether the measurement over- or underestimates.","use_when":"You have an experimental, estimated or approximated value and a reference value and need the error as a percentage of the reference, e.g. in a physics lab or to judge an approximation.","do_not_use_when":"You want the percentage change between two values over time (use percentage-change) or the symmetric percent difference between two equally valid measurements (also percentage-change).","inputs":[{"name":"measured","label":"Measured (experimental) value","type":"number","required":true,"description":"The observed, estimated or approximate value.","example":9.5},{"name":"accepted","label":"Accepted (true) value","type":"number","required":true,"description":"The reference, theoretical or exact value. 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Unit: %.","type":"number","x-unit":"%"}}},"formula":"absolute_error = |measured − accepted|; relative_error = absolute_error / |accepted|; percent_error = relative_error × 100; signed_percent_error = (measured − accepted) / |accepted| × 100","sources":[{"name":"Wikipedia – Approximation error","url":"https://en.wikipedia.org/wiki/Approximation_error","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wolfram MathWorld – Relative Error","url":"https://mathworld.wolfram.com/RelativeError.html","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wolfram MathWorld – Percentage Error","url":"https://mathworld.wolfram.com/PercentageError.html","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. 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Use percentage-change for the latter."},{"q":"Should percent error be reported with a sign?","a":"Most lab conventions report the absolute (unsigned) value; signed_percent_error is provided when the direction of the bias matters."}],"tags":["percent error","percentage error","relative error","absolute error","experimental error","measurement accuracy"],"related":[{"calculator_id":"percentage-change","reason":"Relative change and symmetric percent difference."},{"calculator_id":"percentage","reason":"General percent-of and what-percent questions."},{"calculator_id":"rounding","reason":"Round the reported error to significant figures."}],"links":{"html":"https://tttkmbb.com/math/percent-error","markdown":"https://tttkmbb.com/math/percent-error.md","json":"https://tttkmbb.com/math/percent-error.json","api":"https://tttkmbb.com/api/v1/calculate/percent-error","schema":"https://tttkmbb.com/api/v1/calculators/percent-error","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:52:03Z","next_actions":[{"tool":"run_calculator","calculator_id":"percent-error","reason":"Run Percent Error Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/math/percent-error.md"}}