Percentage Calculator
Three everyday percentage problems, solved instantly: what is X% of a number, one number as a percentage of another, and the percentage change between two values — the math behind discounts, tips, grades, raises and price rises.
How do you calculate a percentage of a number?
Percentage: A percentage is a share of a whole expressed in hundredths; finding a percent of a number means multiplying that number by the percentage divided by 100. 15% of 240 is 36: multiply 240 × 0.15. So a 15% discount takes 240 down to 204, while a 15% markup or tax takes it up to 276. The calculator below also finds what percent one number is of another, and the percentage change between two numbers.
How to calculate percentages
- Convert the percentage to a decimal by dividing it by 100.
- Multiply the number by that decimal to get the percentage amount.
- Add the amount for an increase (markup, tax, tip) or subtract it for a decrease (discount).
- For percentage change, divide the difference between the two numbers by the original number and multiply by 100.
Source: CFPB — Consumer Tools
1 · What is a percentage of a number?
2 · One number as a percentage of another
3 · Percentage change
The three percentage formulas
Part as a percentage = part ÷ whole × 100
Percentage change = (new − old) ÷ old × 100
Every percentage question you will ever meet is one of these three shapes. A sale discount is shape one: 15% of $240 is $36 off, so you pay $204. A test score is shape two: 30 marks out of 120 is 25% — hmm, that exam went badly, but the math is honest. And a price rising from $80 to $100 is shape three: ($100 − $80) ÷ $80 = a 25% increase. This calculator runs all three at once, so you can paste whichever numbers you have and read off the answer without deciding which formula applies first.
Worked examples from real life
- Discounts and sales tax. A $240 jacket at 15% off saves $36 (shape one); with 8% sales tax on the discounted price, the tax is $16.32 and the total is $220.32. Chain the calculator: first the discount, then tax on the result.
- Tips. 18% of an $86 restaurant bill is $15.48. A fast mental route: 10% is $8.60, half of that is 5% ($4.30), and 18% is 10% + 5% + 3% — but the calculator is faster than pride.
- Pay rises. A salary moving from $52,000 to $55,900 is a 7.5% raise (shape three). Compare that against inflation for the same period to see your real raise: if prices rose 3%, you are about 4.5% ahead.
- Grades and scores. 45 correct out of 60 is 75% (shape two). Weighted finals use shape one repeatedly: each component contributes its percentage of the total.
- Price changes and returns. Stock up from $150 to $172.50 is +15%; rent from $1,450 to $1,595 is +10%. Shape three is also how investment returns, inflation rates and interest rates themselves are expressed.
Percentage points vs. percent — the classic trap
When a rate itself changes, two different statements can both be true. If a loan's APR rises from 4% to 5%, that is an increase of 1 percentage point — but it is also a 25% increase in the rate (1 ÷ 4). News reports exploit this confusion constantly, in both directions. The calculator's change tool always reports relative change ((new − old) ÷ old), so a move from 4 to 5 shows +25%; if you need percentage points, that is simply the subtraction, 5 − 4 = 1 point. Knowing which one a headline is using is most of statistical literacy.
Mental-math shortcuts worth keeping
Ten percent of anything is a decimal shift ($240 → $24). Five percent is half of that. One percent is two decimal shifts. From those three anchors you can build almost any percentage: 15% = 10% + 5%, 35% = 25% (a quarter) + 10%, 19% = 20% minus 1%. And remember the symmetry trick: X% of Y always equals Y% of X — 8% of 50 is awkward, but 50% of 8 is 4, instantly. For everything else, that is what the tool above is for. Percentages also run quietly underneath most of this site: APRs, PMI rates, property-tax rates and investment returns are all percentages with consequences, and the finance hub collects the calculators that use them.
Frequently asked questions
How do I calculate 15% of 240?
Multiply 240 by 15 and divide by 100: 240 × 0.15 = 36. The calculator's first section does this for any pair of numbers, and also shows the number plus and minus that amount — handy for discounts (240 − 36 = 204) and markups or tax (240 + 36 = 276).
How do I work out a percentage increase?
Subtract the old value from the new one, divide by the old value, and multiply by 100. A price rising from $80 to $100: (100 − 80) ÷ 80 × 100 = 25% increase. If the result is negative, it is a decrease. The third section of the calculator does this and shows the absolute change alongside.
What is the difference between percent and percentage points?
Percent is relative; percentage points are the plain difference between two percentages. A rate going from 4% to 5% rose by 1 percentage point, which is a 25% relative increase. Confusing the two is the most common percentage error in news, politics and lending — always check which one is meant.
How do I calculate a percentage of a percentage?
Multiply them as decimals. If 40% of a group are students and 25% of those students cycle to class, then 0.40 × 0.25 = 0.10 — 10% of the whole group cycles. Percentages of percentages appear constantly in surveys, fees on fees, and tax-on-tax calculations.
How do I reverse a percentage — find the original before a 20% increase?
Divide by one plus the rate: if a price after a 20% rise is $120, the original was 120 ÷ 1.20 = $100. The common mistake — subtracting 20% of $120 — gives $96, which is wrong because the increase was calculated on the smaller original amount, and decreases are calculated on the larger new one.
Sources
- CFPB — Consumer Tools — The same percentage math sits behind APR and rate disclosures.