{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"percentage-change"},"result":{"entity_type":"calculator","id":"percentage-change","calculator_id":"percentage-change","canonical_url":"https://tttkmbb.com/math/percentage-change","name":"Percentage Change Calculator","title":"Percentage Change Calculator – Increase or Decrease Between Two Values, Percent Difference","category":"math","category_name":"Math","tool_name":"calculate_percentage_change","featured_mcp_tool":true,"description":"Computes the relative change from an old value to a new value as a percentage, the signed absolute change, the new/old ratio and the symmetric percent difference.","use_when":"You have a starting and an ending value and need the percentage increase or decrease, or a symmetric percent difference between two comparable values.","do_not_use_when":"You need a percentage of a number (use percentage), an annualised growth rate over several years (use cagr) or an investment return (use roi).","inputs":[{"name":"old_value","label":"Old value","type":"number","required":true,"description":"Starting (reference) value. Must not be 0.","example":50},{"name":"new_value","label":"New value","type":"number","required":true,"description":"Ending value.","example":65}],"outputs":[{"name":"change_percent","label":"Percentage change","type":"number","unit":"%","decimals":2,"description":"(new − old) / |old| × 100; negative for a decrease."},{"name":"absolute_change","label":"Absolute change","type":"number","decimals":4,"description":"new_value − old_value (signed)."},{"name":"direction","label":"Direction","type":"string","decimals":4,"description":"'increase', 'decrease' or 'no change'."},{"name":"ratio","label":"Ratio new / old","type":"number","decimals":4,"description":"new_value / old_value (1.3 means a 30% increase)."},{"name":"percent_difference","label":"Percent difference (symmetric)","type":"number","unit":"%","decimals":2,"description":"|new − old| / ((|new| + |old|) / 2) × 100; the same whichever value is called 'old'."}],"input_schema":{"type":"object","properties":{"old_value":{"description":"Starting (reference) value. Must not be 0.","type":"number","examples":[50]},"new_value":{"description":"Ending value.","type":"number","examples":[65]}},"additionalProperties":false,"required":["old_value","new_value"]},"output_schema":{"type":"object","properties":{"change_percent":{"description":"(new − old) / |old| × 100; negative for a decrease. Unit: %.","type":"number","x-unit":"%"},"absolute_change":{"description":"new_value − old_value (signed).","type":"number"},"direction":{"description":"'increase', 'decrease' or 'no change'.","type":"string"},"ratio":{"description":"new_value / old_value (1.3 means a 30% increase).","type":"number"},"percent_difference":{"description":"|new − old| / ((|new| + |old|) / 2) × 100; the same whichever value is called 'old'. Unit: %.","type":"number","x-unit":"%"}}},"formula":"change_percent = (new_value − old_value) / |old_value| × 100; percent_difference = |new_value − old_value| / ((|new_value| + |old_value|) / 2) × 100","method":"Dividing by |old_value| keeps the sign of the change meaningful when the old value is negative (−10 → −5 is a 50% increase).","sources":[{"name":"Wikipedia – Relative change","url":"https://en.wikipedia.org/wiki/Relative_change","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wikipedia – Percentage","url":"https://en.wikipedia.org/wiki/Percentage","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":"50 → 65","inputs":{"old_value":50,"new_value":65},"expected":{"change_percent":30,"absolute_change":15,"direction":"increase","ratio":1.3,"percent_difference":26.09},"url":"https://tttkmbb.com/api/v1/calculate/percentage-change?old_value=50&new_value=65"},{"name":"80 → 60","inputs":{"old_value":80,"new_value":60},"expected":{"change_percent":-25,"absolute_change":-20,"direction":"decrease","ratio":0.75,"percent_difference":28.57},"url":"https://tttkmbb.com/api/v1/calculate/percentage-change?old_value=80&new_value=60"}],"faq":[{"q":"Why is a 25% decrease not undone by a 25% increase?","a":"Percent changes are relative to the starting value: 80 → 60 is −25%, but 60 → 80 is +33.33%. The symmetric percent_difference (28.57% here) is the same in both directions."},{"q":"What if the old value is 0?","a":"The percentage change is undefined (division by zero) and the calculator returns an error; report the absolute change instead."}],"tags":["percentage change","percent increase","percent decrease","percent difference","relative change"],"related":[{"calculator_id":"percentage","reason":"Plain percent-of and what-percent questions."},{"calculator_id":"cagr","reason":"Average yearly growth rate over a period."},{"calculator_id":"roi","reason":"Return on an investment as a percentage of cost."}],"links":{"html":"https://tttkmbb.com/math/percentage-change","markdown":"https://tttkmbb.com/math/percentage-change.md","json":"https://tttkmbb.com/math/percentage-change.json","api":"https://tttkmbb.com/api/v1/calculate/percentage-change","schema":"https://tttkmbb.com/api/v1/calculators/percentage-change","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:30:39Z","next_actions":[{"tool":"calculate_percentage_change","calculator_id":"percentage-change","reason":"Run Percentage Change Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/math/percentage-change.md"}}