How to work out percentages
A percentage is simply a number expressed as a fraction of 100. The word literally means "per hundred." Once you know that, every percentage problem becomes one of three simple patterns. The calculator above covers those three plus increasing or decreasing a number by a percent.
1. Finding a percent of a number
To find X% of Y, convert the percent to a decimal (divide by 100) and multiply. This is how you calculate a tip, a discount, or a tax. For instance, a 15% tip on a $60 bill is 0.15 × 60 = $9.
2. Finding what percent one number is of another
To find what percent A is of B, divide A by B and multiply by 100. This answers questions like "I scored 42 out of 50 — what percent is that?" (42 ÷ 50 × 100 = 84%).
3. Finding a percentage increase or decrease
To find the percentage change between two values, take the difference, divide by the original value, and multiply by 100. This is the go-to calculation for price changes, growth rates, and comparing before-and-after figures.
The formulas at a glance
- X% of Y:
Y × X ÷ 100 - A is what % of B:
A ÷ B × 100 - Percent change:
(new − old) ÷ old × 100 - Increase Y by X%:
Y × (1 + X ÷ 100) - Decrease Y by X%:
Y × (1 − X ÷ 100)
A handy fact: X% of Y always equals Y% of X. So 8% of 50 is the same as 50% of 8, which is 4 — often much easier to do in your head.
Worked examples with real money
- Sales tax: a $240 purchase with an 8.25% sales tax adds 240 × 8.25 ÷ 100 = $19.80, for a total of $259.80.
- A raise: your pay goes from $52,000 to $55,120. The change is (55,120 − 52,000) ÷ 52,000 × 100 = 6%.
- A price drop: a monthly bill falls from $125 to $100. That's (100 − 125) ÷ 125 × 100 = -20% — a 20% cut, even though going from $100 back up to $125 would be a 25% rise.
That last pair shows why the starting value matters so much: the same $25 gap is a different percentage depending on which number you divide by.
Common mistakes
- Dividing by the wrong number. Percent change always divides by the old (starting) value, not the new one.
- Adding percentages that stack. A 20% discount plus an extra 10% off is not 30% off. It's 20% off, then 10% off the lower price: 0.80 × 0.90 = 0.72, or 28% off in total.
- Expecting changes to cancel. Up 50% then down 50% leaves you at 75% of where you began, not 100%.
- Mixing up points and percent. A mortgage rate moving from 6% to 7% is 1 percentage point, but a 16.7% increase in the rate.
Mental-math tips
- Build from 10% and 1%. 10% moves the decimal one place; 1% moves it two. So 12% of 300 is 30 + 3 + 3 = 36.
- Use fractions you know. 25% is a quarter, 50% is half, 75% is three-quarters and about 33% is a third.
- Find the sale price in one step. For 30% off, multiply by 0.70; for a 6% raise, multiply by 1.06.
- Sanity-check the answer. A discount should always leave a smaller number, and anything over 100% of a number is larger than the number itself.
Everyday uses
- Calculating sale discounts and final prices.
- Working out tips and splitting bills.
- Understanding interest rates and returns.
- Comparing statistics, scores, and growth figures.
When simple percentages aren't enough
Percent change compares two points and ignores what happened in between. For growth that builds on itself year after year — savings, investments or loan interest — a single percentage understates the effect, and you need a compounding formula instead. Percent change is also undefined when the starting value is zero, and it can mislead when the starting value is tiny (going from 1 to 3 is a 200% jump).
Related calculators
For restaurant bills, the tip calculator handles the percentage and splits the check. To see how a yearly percentage return snowballs over time, use the compound interest calculator. And if you're weighing a raise, the salary to hourly calculator turns the new salary into an hourly rate.