Percentage calculator
Calculate a percent of a number, express one number as a percent of another, or find the whole from a known part and percentage.
Percentage change calculator: increase, decrease and points
Compare a new value with a clearly identified old value. The calculator reports the signed difference, change relative to the old value, the multiplier and the change needed to return to the old value.
Free to use, with no sign-in. Inputs and results stay in this page and are not sent with the form. Download a result before leaving; this tool does not save your work.
Worked result
80 → 100 is a 25% increase; returning to 80 is a 20% decrease.
- Subtract the old value from the new value.
- Divide the difference by the old value, 80.
- For the return calculation, the baseline is now 100.
Why a 25% rise reverses with a 20% fall
Start at 80 and increase to 100. The outward and return calculations use different denominators.
Difference = 100 − 80 = 20
Forward change = 20/80 × 100 = 25%
Multiplier = 100/80 = 1.25
Return change = (80 − 100)/100 × 100 = −20%If the inputs represent rates, such as 20% and 25%, the numeric difference is 5 percentage points, while the relative increase is 25%. The labels answer different questions.
Baseline choice determines relative change
Relative change divides the difference by the original baseline. For nonnegative values, a positive result means growth and a negative result means decline. A multiplier of 1.25 means the new value is 125% of the old one, not 125% larger.
The return percentage uses the new value as its baseline. Percentage changes do not generally cancel when added, and successive changes combine by multiplying their factors.
relative change (%) = (new − old) / old × 100
multiplier = new / old
return change (%) = (old − new) / new × 100Input limits and common mistakes
This tool uses nonnegative old and new values so increase/decrease labels have their usual meaning. A zero old baseline has undefined relative change. A zero new value has no finite relative return from zero. Absolute change is still defined.
The tool does not annualize growth, infer time intervals or adjust for inflation. Enter percentages as ordinary numeric rate values only when you also interpret their difference as percentage points.
Questions about percentage change
What is the percentage increase from 80 to 100?
It is (100 − 80)/80 × 100 = 25%.
Is a rise from 20% to 25% a 5% increase?
The increase is 5 percentage points and 25% relative to the old 20% rate.
Why is change from zero undefined?
The usual relative-change formula divides by the old value. Division by zero has no finite result; report the absolute change instead.
Sources and verification
These references explain the formulas or formats. The worked examples above were created for this tool and checked against independent calculations or format round trips. AI-assisted development does not imply a named human expert review.
- OpenStax: understanding percent — Percent as a quantity per hundred and interpreting a chosen whole.
Published 2026-10-23. Examples are illustrations, not measurements of a service or claims about search rankings.
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Further reading
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