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To calculate a percentage of a number, turn the percent into a decimal by dividing it by 100, then multiply. 15% of $80 is 0.15 × 80 = $12. To find what percent one number is of another, divide the part by the whole and multiply by 100: $12 out of $80 is 12 ÷ 80 × 100 = 15%.
Almost every percentage question you meet in daily life, from sales tax to a pay raise, is one of those two moves or a small twist on them. Below are the formulas, five worked examples, and the mistakes that trip people up most. To check any answer, use the free percentage calculator, which shows its working step by step.
The three percentage formulas
"Percent" means "per hundred", so 25% is 25 out of 100, or 0.25 as a decimal. Once you can switch between a percent and a decimal, you need only three formulas:
| You want to know | Formula | Answer |
|---|---|---|
| What is 15% of $80? | 0.15 × 80 | $12 |
| $12 is what percent of $80? | 12 ÷ 80 × 100 | 15% |
| $12 is 15% of what? | 12 ÷ 0.15 | $80 |
The same three numbers appear in every row. If you know any two of them, you can find the third.
A fourth formula covers change over time:
The key word is "old". A percent change is always measured from the starting value, and using the wrong starting value is the most common percentage mistake.
Example 1: Sales tax on a purchase
The question: what is a percent of a number?
You buy a $349 laptop where the combined sales tax rate is an illustrative 8.25%.
- 8.25% as a decimal: 8.25 ÷ 100 = 0.0825
- Tax: 0.0825 × $349 = $28.7925, which rounds to $28.79
- Total at the register: $349 + $28.79 = $377.79
You can do it in one step by multiplying by 1 plus the rate: $349 × 1.0825 = $377.79.
A quick sense check helps. 10% of $349 is $34.90 (move the decimal point one place left). 8.25% is a bit less than 10%, so the tax should be a bit under $34.90, and it is. Sales tax rates differ by state, county and city, so use the rate where you shop. The sales tax calculator does the sum for any rate.
Example 2: Rent as a share of your pay
The question: what percent is one number of another?
Your take-home pay is $4,200 a month and your rent is $1,450. What share of your pay goes to rent?
- Part ÷ whole: 1,450 ÷ 4,200 = 0.3452
- Multiply by 100: 34.5%
The order matters. The "whole" is the thing you are taking a share of, here your pay. Put the numbers the wrong way round (4,200 ÷ 1,450) and you get 289.7%, an answer that should make you stop. A share of a whole can't be more than 100%.
Example 3: A sale price, and a discount on a discount
The question: what do you pay after a percent off?
A pair of shoes costs $89.99 and is marked 35% off. The fastest way to the sale price is to multiply by the share you still pay: 100% − 35% = 65%.
- Sale price: $89.99 × 0.65 = $58.4935, so $58.49
- You save: $89.99 − $58.49 = $31.50
At checkout you get an extra 20% off. That 20% comes off the sale price, not the original price:
- $58.49 × 0.80 = $46.792, so $46.79
Adding the two discounts (35% + 20% = 55%) suggests you would pay $40.50. The real price is $46.79, which is $6.29 more. Discounts applied one after another multiply: 0.65 × 0.80 = 0.52, so you pay 52% of the tag price. That is a total discount of 48%, not 55%.
| Discount | Share you pay | Price of a $89.99 item |
|---|---|---|
| 35% off | 65% | $58.49 |
| 35% off, then an extra 20% off | 52% | $46.79 |
| A single 55% off, for comparison | 45% | $40.50 |
The percent off calculator shows the sale price, what you save and the total with sales tax for any discount. For an extra percent off on top of a sale, use the discount calculator.
Example 4: A pay raise and a price rise
The question: by what percent did something change?
Your salary goes from $52,000 to $54,600.
- Change: $54,600 − $52,000 = $2,600
- Divide by the old value: 2,600 ÷ 52,000 = 0.05
- Multiply by 100: a 5% raise
The US Bureau of Labor Statistics uses the same steps for inflation. Its guide to calculating percent changes shows the Consumer Price Index (CPI-U, all items) rising from 278.802 in December 2021 to 296.797 in December 2022. That is 17.995 index points, and 17.995 ÷ 278.802 × 100 = 6.5%, the rise in prices over that year. Our guide to inflation and your savings shows what rates like that do to cash over time.
Why a 20% fall and a 20% rise don't cancel out
Say a price of $100 falls 20% to $80, then rises 20%. The rise is 20% of $80, which is $16, so you end at $96, not $100. To get from $80 back to $100, you need a 25% rise: (100 − 80) ÷ 80 × 100 = 25%. The starting value changed, so the same dollar change is a different percentage.
Example 5: The price before tax or before a discount
The question: what was the whole before a percent was added or taken off?
A receipt shows $86.40 including 8% sales tax, and you need the price before tax for an expense claim.
The tempting shortcut is to take 8% off $86.40. That gives $86.40 − $6.91 = $79.49, which is wrong, because the tax was 8% of the price before tax, not 8% of the total. Divide by 1.08 instead:
- $86.40 ÷ 1.08 = $80.00 before tax
- Check: $80.00 × 0.08 = $6.40 of tax, and $80.00 + $6.40 = $86.40
The same idea finds an original price. If you paid $54 after 40% off, you paid 60% of the original, so the original was $54 ÷ 0.60 = $90.
Percent vs percentage points
When the number that changes is itself a percentage, such as an interest rate, there are two ways to describe the change. A mortgage rate that goes from 6% to 7% has risen by 1 percentage point, but by 16.7% in relative terms (1 ÷ 6 × 100). Both are true; they answer different questions.
Key idea "Points" are a plain subtraction of two percentages. "Percent" compares the change with where you started. When a lender or a news story quotes a change in a rate, check which one they mean.
Our guide to APR vs interest rate explains which rate to compare when you shop for a loan.
Mental math shortcuts
You don't always need a calculator. Start from 10% and build from there:
| Percent | How to find it | Example: percent of $250 |
|---|---|---|
| 1% | Move the decimal point two places left | $2.50 |
| 5% | Half of 10% | $12.50 |
| 10% | Move the decimal point one place left | $25.00 |
| 15% | 10% plus 5% | $37.50 |
| 20% | Double 10% | $50.00 |
| 25% | Divide by 4 | $62.50 |
| 50% | Divide by 2 | $125.00 |
Percentages also work in both directions: 8% of 50 is the same as 50% of 8, which is 4. When one way looks hard, flip it.
Common mistakes
- Dividing by the wrong number. A share is measured against the whole. A change is measured from the old value.
- Adding percentages that apply one after another. Stacked discounts, yearly growth and back-to-back price changes multiply. It is also why money growing at 7% a year doubles in about 10 years, not 14; see the rule of 72.
- Forgetting to divide by 100. 8.25% is 0.0825, not 8.25 and not 0.825.
- Mixing up percent and percentage points, especially with interest rates.
- Rounding too early. Keep the full figure until the last step, then round money to cents.
Frequently asked questions
How do I calculate a percentage of a total?
Divide the part by the total and multiply by 100. If you got 42 questions right out of 50, your score is 42 ÷ 50 × 100 = 84%.
How do I add a percentage to a number?
Multiply by 1 plus the percent as a decimal. Adding 8% tax to $80 is $80 × 1.08 = $86.40. To take 8% off instead, multiply by 0.92.
How do I work out the percentage increase between two numbers?
Subtract the old number from the new one, divide by the old number and multiply by 100. Going from 40 to 50 is a 25% increase, but going from 50 back to 40 is a 20% decrease.
Can a percentage be more than 100%?
Yes, for a change or a comparison. A price that goes from $20 to $50 has risen 150%. A share of a whole, like the share of your pay spent on rent, can't be more than 100%.
A quick checklist
- Decide what you are looking for: a part, a percent, a whole or a change.
- Find the whole, or the starting value, and divide by that.
- Turn percents into decimals by dividing by 100.
- Multiply percentages that apply one after another. Never add them.
- Sense-check the answer against 10% or 50%, then confirm it in the percentage calculator.
This article is for general education and is not financial advice. Rules, rates and products vary by lender and country. See our disclaimer.
