Percentage Calculator
Find a percentage of a number, what percent one number is of another, or the result of adding or subtracting a percentage. Each answer comes with the working.
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Result
The formula
To find what percentage X is of Y, divide X by Y and multiply by 100.
Worked example
- Divide 25 by 200 → 0.125
- Multiply by 100 → 12.5%
Result: 12.5%
How percentages work
A percent is “parts per hundred.” Keeping the base (the whole) clear is the main way to avoid mistakes.
Part and whole
The basic form is (part ÷ whole) × 100. If the part exceeds the whole, the result is over 100%, which can be valid (for example, beating a sales target).
Increase and decrease
Percent increase = (new − old) ÷ old × 100. Percent decrease = (old − new) ÷ old × 100. The denominator is always the starting value.
Change vs. difference
Percentage change treats one value as the starting point: (new − old) ÷ old × 100. Percentage difference has no starting point — it divides the gap by the average of the two values, so swapping them gives the same answer.
Percentage points vs. percent
If a rate moves from 3% to 4%, that is a 1 percentage-point rise, but a relative increase of about 33%. Saying “it rose 1%” is ambiguous and often wrong.
Common pitfalls
Stacking discounts is not additive (20% off then 10% off is not 30% off). Reversing a percent change also fails: +20% followed by −20% does not return to the start.
Interesting facts
From Latin
“Percent” comes from per centum — “by the hundred” in Latin.
Percentage points are not percents
A tax rising from 5% to 6% is a 1 percentage-point increase, not a 1% increase. News and finance writing often blur the two.
100% is the whole, not a ceiling
Growth, error rates, and performance vs. target can exceed 100%. That simply means the part is larger than the chosen base.
Discounts do not add cleanly
A 25% markdown then an extra 10% off leaves 67.5% of the original price — not 65%. Always apply each percent to the current amount.
Frequently asked questions
Subtract the old value from the new, divide by the old value, and multiply by 100.
Multiply the number by X/100. Example: 18% of 85 is 85 × 0.18 = 15.3.
Percent is a relative change against a base. Percentage points measure the arithmetic gap between two percent figures (4% − 3% = 1 point).
Yes. If the part is larger than the whole, or if you measure growth above a baseline, results above 100% are mathematically fine.
Divide the part by the whole, then multiply by 100. Example: 25 is what percent of 200? 25 ÷ 200 = 0.125 → 12.5%. Use this page’s modes for “X% of Y” and percent change as well.
Take 20% of the original price (price × 0.20) and subtract it, or multiply the price by 0.80 for the sale amount. A $50 item at 20% off costs $40. Stacked discounts compound — they are not simply added.
References
- Percent — definition Percent as parts per hundred in measurement and commerce.
- Fractions, decimals, and percents Converting among percent, decimal, and fraction forms.