To calculate a percentage, divide the part by the whole and multiply by 100. If you got 45 questions right out of 60, that is 45 ÷ 60 = 0.75, and 0.75 × 100 = 75%. To find a percentage of a number, flip it around: 18% of 250 is 0.18 × 250 = 45.
That one relationship, part = whole × percent ÷ 100, covers almost every percentage question you will meet. The trouble is that real problems rarely announce which of the three numbers is missing. A discount sign, a pay rise, a tax receipt and a news headline all hide the same arithmetic in different clothes. This guide walks through each type of question with worked numbers, then covers the traps that catch people out, from reverse percentages to the difference between percent and percentage points.
If you just want an answer, our percentage calculator handles all four classic questions. If you want to understand what it is doing, read on.
What a percentage actually is
“Per cent” means “per hundred”. A percentage is a fraction with 100 as the denominator, written in a form that makes comparisons easy. 3 out of 4 and 75 out of 100 are the same proportion, but 75% is quicker to compare with, say, 68% than 3/4 is with 17/25.
Every percentage problem has three pieces:
- The whole (also called the base or reference value): what you are comparing against.
- The part: the piece of the whole you care about.
- The percentage: the part expressed per 100 of the whole.
You always know two of them and need the third. Once you identify which is missing, the formula picks itself. Converting between forms helps too: 0.75, 3/4 and 75% are the same number. To go from a decimal to a percent, move the decimal point two places right; to go back, move it two places left. The fraction to percent calculator and the decimal to percent converter do this if you would rather not count places.
How to calculate percentage of a number
This is the “what is 18% of 250” question. Convert the percentage to a decimal and multiply.
Formula: part = whole × (percent ÷ 100)
Example: a $250 jacket is 18% off. The discount is 250 × 0.18 = $45, so you pay $205.
Mental shortcuts that actually work
- 10%: move the decimal one place left. 10% of 250 is 25.
- 5%: half of 10%. 5% of 250 is 12.50.
- 1%: move the decimal two places left. 1% of 250 is 2.50.
- Build the rest: 18% = 10% + 5% + 3 × 1%, so 25 + 12.50 + 7.50 = 45.
- Swap the numbers: x% of y always equals y% of x. 8% of 50 looks awkward, but 50% of 8 is obviously 4.
The swap trick works because multiplication does not care about order: 0.08 × 50 and 0.50 × 8 are both 4. It is the single most useful percentage shortcut most people never learned at school.
What percent is one number of another
Here you know the part and the whole and want the percentage. Divide, then multiply by 100.
Formula: percent = part ÷ whole × 100
Example: you scored 45 out of 60 on a test. 45 ÷ 60 = 0.75, so your grade is 75%. Our grade calculator does the same for test scores and shows the letter grade alongside.
The only real risk here is dividing the wrong way round. Ask yourself “45 is what percent of 60?” The number after “of” is the whole and goes on the bottom. If your answer is more than 100% when the part is clearly smaller than the whole, you have flipped them.
Reverse percentages: finding the original number
Reverse percentage questions give you the part and the percentage and ask for the whole. “36 is 15% of what?” or “I paid $107 including 7% sales tax; what was the price before tax?”
Formula: whole = part ÷ (percent ÷ 100)
36 ÷ 0.15 = 240. Check it: 15% of 240 is 36.
The tax example needs one more step of thinking. The $107 is not 7% of anything; it is 107% of the pre-tax price, because it includes the original 100% plus the 7% tax. So the pre-tax price is 107 ÷ 1.07 = $100.
The common mistake is to take 7% off the total: 107 × 0.93 = $99.51. That is wrong by 49 cents, because 7% of $107 is bigger than 7% of $100. The error grows with the rate, which matters when you are backing VAT out of European prices at 20% or more. The sales tax calculator works in both directions and saves you from this one.
Percentage increase and decrease
Percentage change compares a new value with an old one, relative to the old one.
Formula: percent change = (new − old) ÷ old × 100
A positive result is an increase; a negative one is a decrease.
Worked example
Your monthly phone bill goes from $80 to $92. The change is 92 − 80 = $12, and 12 ÷ 80 = 0.15, so the bill rose 15%.
Now suppose it drops back from $92 to $80. The change is −12, but you divide by 92 this time: −12 ÷ 92 = −0.1304, a 13.04% decrease. Same dollar amount, different percentage, because the starting point moved.
This asymmetry is behind one of the oldest traps in finance. If a stock falls 20% and then rises 20%, you have not broken even. $100 falls to $80, and 20% of $80 is only $16, leaving you at $96. To get back to $100 from $80 you need a 25% gain. The percentage change calculator shows the result for any pair of values, and the dedicated percentage increase calculator also works forward: enter a starting value and a rate to get the new value.
Applying an increase or decrease directly
To raise a number by p%, multiply by (1 + p/100). To cut it by p%, multiply by (1 − p/100). A 4% raise on a $52,000 salary is 52,000 × 1.04 = $54,080. A 30%-off sale on a $70 item is 70 × 0.70 = $49. Using a single multiplier is faster than calculating the change and then adding or subtracting it, and it chains neatly when several changes stack.
Common percentage formulas at a glance
| Question | Formula | Example | Answer |
|---|---|---|---|
| What is p% of x? | x × p ÷ 100 | 18% of 250 | 45 |
| x is what % of y? | x ÷ y × 100 | 45 out of 60 | 75% |
| x is p% of what? | x ÷ (p ÷ 100) | 36 is 15% of ? | 240 |
| Percent change | (new − old) ÷ old × 100 | $80 to $92 | +15% |
| Increase by p% | x × (1 + p ÷ 100) | $52,000 + 4% | $54,080 |
| Decrease by p% | x × (1 − p ÷ 100) | $70 − 30% | $49 |
| Remove tax already included | total ÷ (1 + rate) | $107 with 7% tax | $100 |
Stacked percentages and discounts
Percentages applied one after another multiply; they do not add. A store that offers 20% off and then an extra 10% off at the register is not giving you 30% off. The first discount takes $100 to $80, and the second takes 10% off $80, leaving $72. The total discount is 1 − (0.80 × 0.90) = 0.28, or 28%.
The same logic applies to anything that compounds: interest, inflation, population growth and investment returns. Three years of 5% inflation is 1.05 × 1.05 × 1.05 = 1.1576, a 15.76% rise in prices, not 15%. The US Bureau of Labor Statistics publishes Consumer Price Index changes as 12-month percentage changes for exactly this reason: each month builds on the last. If you want to check a sale, the double discount calculator gives the combined rate, and the percent off calculator handles single discounts.
Compounding is also why the order does not matter for multiplication but does matter for wording. “20% off, then 10% off” and “10% off, then 20% off” both end at $72. But “a 10% raise followed by a 10% pay cut” leaves you 1% worse off than where you started (1.10 × 0.90 = 0.99).
Percent vs percentage points
This is the distinction that most often goes wrong in news reports. When a rate moves from 4% to 5%, it has risen by 1 percentage point, but by 25 percent in relative terms (1 ÷ 4 = 0.25). Both statements are true. They just answer different questions.
Percentage points describe the simple gap between two percentages. Percent describes the relative change. The Federal Reserve announces changes to its target rate in percentage points (a “quarter-point” cut is 0.25 percentage points), and that is the clearest way to talk about rates. A headline saying “unemployment jumped 20%” when it went from 5% to 6% is technically correct but sounds far more alarming than “unemployment rose 1 point”. The percentage point calculator shows both numbers side by side so you can pick the honest one.
Common mistakes and quick tips
- Dividing by the wrong base. Percent change always divides by the old value. Percent of always divides by the whole. When two values are on equal footing, such as two shops’ prices, use percentage difference instead; our guide to percent error vs percent difference explains when each applies.
- Adding stacked percentages. Multiply the factors instead: 0.80 × 0.90, not 20% + 10%.
- Taking tax off the total. Divide by 1.07; do not multiply by 0.93.
- Expecting a fall and a rise to cancel. −20% then +20% leaves you 4% down.
- Averaging percentages blindly. If one class of 10 students scored 90% and another of 40 scored 70%, the overall average is (10 × 90 + 40 × 70) ÷ 50 = 74%, not 80%. Weight by the size of each group.
- Mixing up percent and percentage points. Say “points” whenever you subtract one percentage from another.
Percentages in everyday money
Most of the percentage maths people do in a typical week involves money. A few patterns come up again and again.
Tips. An 18% tip on a $64 dinner is 64 × 0.18 = $11.52. A 20% tip is easier: find 10% ($6.40) and double it ($12.80). Our guide on how to calculate a tip covers whether to tip on the pre-tax or post-tax total, and the tip calculator splits the bill too.
Margins and markups. A shop that buys a lamp for $40 and sells it for $60 has a 50% markup (20 ÷ 40) but a 33.3% profit margin (20 ÷ 60). Same $20 profit, different base. The difference trips up plenty of small-business owners, which is why we wrote a separate guide on profit margin vs markup.
Interest rates. A credit card at 24% APR charges roughly 2% per month, but because unpaid interest compounds, the effective yearly cost is higher. That is the APR vs APY story, and it is percentage compounding again.
This guide is general maths help, not personal financial advice; for decisions about loans or investments, check the exact terms with your lender or a qualified adviser.
Frequently asked questions
What is the formula to calculate a percentage?
Percentage = part ÷ whole × 100. For example, 30 out of 120 is 30 ÷ 120 × 100 = 25%.
How do I calculate a percentage of a total in my head?
Start from 10% (move the decimal one place left) and 1% (two places left), then combine. For 15% of 80, take 10% (8) plus half of that (4) to get 12.
How do I find the original price before a discount?
Divide the sale price by (1 − discount rate). If a coat costs $63 after 30% off, the original price was 63 ÷ 0.70 = $90.
Can a percentage be more than 100%?
Yes. A part can exceed the whole when you compare growth: a price that goes from $50 to $150 has risen 200%. A decrease, however, can never be more than 100%, because you cannot lose more than everything.
What is the difference between percent and percentage?
In practice they mean the same thing. “Percent” usually follows a number (25 percent), while “percentage” is used without one (a large percentage of voters).
How do I calculate a percentage in Excel or Google Sheets?
Type =A1/B1 and format the cell as a percentage, or use =A1/B1*100 for a plain number. For percent change, use =(B1-A1)/A1.
Once you can spot which of the three numbers is missing, every percentage problem collapses into one multiplication or one division. Keep the base in mind, multiply rather than add when changes stack, and say “points” when you subtract one rate from another. When the numbers get messy, the calculators linked above will check your work in a second.
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