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Percentage Change Calculator
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.
When to use
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).
Formula
change_percent = (new_value − old_value) / |old_value| × 100; percent_difference = |new_value − old_value| / ((|new_value| + |old_value|) / 2) × 100
Dividing by |old_value| keeps the sign of the change meaningful when the old value is negative (−10 → −5 is a 50% increase).
Inputs
| Parameter | Type | Unit | Required | Description |
|---|---|---|---|---|
old_value | number | yes | Starting (reference) value. Must not be 0. | |
new_value | number | yes | Ending value. |
Outputs
| Output | Type | Unit | Description |
|---|---|---|---|
change_percent | number | % | (new − old) / |old| × 100; negative for a decrease. |
absolute_change | number | new_value − old_value (signed). | |
direction | string | 'increase', 'decrease' or 'no change'. | |
ratio | number | new_value / old_value (1.3 means a 30% increase). | |
percent_difference | number | % | |new − old| / ((|new| + |old|) / 2) × 100; the same whichever value is called 'old'. |
Example
50 → 65: {"old_value":50,"new_value":65} → {"change_percent":30,"absolute_change":15,"direction":"increase","ratio":1.3,"percent_difference":26.09}
80 → 60: {"old_value":80,"new_value":60} → {"change_percent":-25,"absolute_change":-20,"direction":"decrease","ratio":0.75,"percent_difference":28.57}
GET https://tttkmbb.com/api/v1/calculate/percentage-change?old_value=50&new_value=65
Machine access
- API:
GET https://tttkmbb.com/api/v1/calculate/percentage-change(query parameters) orPOSTwith a JSON body{"inputs": {...}} - Schema: https://tttkmbb.com/api/v1/calculators/percentage-change · Markdown: https://tttkmbb.com/math/percentage-change.md · JSON definition: https://tttkmbb.com/math/percentage-change.json
- MCP: server
https://tttkmbb.com/mcp, toolcalculate_percentage_change - OpenAPI operationId:
calculate_percentage_change - Freshness:
static. Authentication: none. Rate limit: fair use (see rate limits).
Sources
- Wikipedia – Relative change (reference)
- Wikipedia – Percentage (reference)
FAQ
Why is a 25% decrease not undone by a 25% increase?
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.
What if the old value is 0?
The percentage change is undefined (division by zero) and the calculator returns an error; report the absolute change instead.
Related calculators
- Percentage Calculator — Plain percent-of and what-percent questions.
- CAGR Calculator — Average yearly growth rate over a period.
- ROI Calculator — Return on an investment as a percentage of cost.