Reference definitions and notation for mathematical functions.
Math
Percentage change
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Your result
%
Increase
Formula(new − original) ÷ |original| × 100
- Find the difference.
- Divide by the absolute original value.
- Multiply by 100.
Worked example: 80 to 100 is a 25% increase.
Accuracy notice: The arithmetic follows the displayed formula. Its practical accuracy still depends on valid inputs, appropriate units, and display rounding.
Understand the result before using it
Percentage change uses original value and new value to calculate its result. It applies a defined mathematical relationship to the values you enter and reports the resulting quantity.
Formula, assumptions, and example
Formula
(new − original) ÷ |original| × 100
Assumptions
- The entered original value and new value are complete, valid, and use the units or format shown beside each field.
- Inputs represent ordinary real numbers unless the tool explicitly accepts another format.
- The displayed operation and order of operations match the formula shown on the page.
Worked example
80 to 100 is a 25% increase.
When to use it
Good uses
- Check homework or a hand calculation.
- Explore how changing an input changes the result.
- Create a quick numerical reference without setting up a spreadsheet.
Limitations
Common mistakes to avoid
- An undefined operation, such as division by zero, cannot produce a valid finite result.
- Rounded display values can differ slightly from the full internal result.
- Check the formula, source data, units, and displayed precision before relying on the result.
Sources and further reading
These references explain the underlying standards or provide authoritative context. Your own contract, institution, clinician, product documentation, local code, or governing standard may be the controlling source.
Measurement and numerical-reference guidance from NIST.
Questions about this calculation
What does the Percentage change calculate?
Percentage change uses original value and new value to calculate its result. It applies a defined mathematical relationship to the values you enter and reports the resulting quantity. The formula used is: (new − original) ÷ |original| × 100
Which inputs affect the Percentage change result?
The result uses original value and new value. Changing any of these values can change the output, so enter them using the labels and units shown.
Is the Percentage change result exact?
The arithmetic follows the displayed formula. Its practical accuracy still depends on valid inputs, appropriate units, and display rounding.
When should I verify a Percentage change result?
Verify it whenever the source measurement, unit convention, rounding, or consequences make small differences important.
Clear answers, without the guesswork
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