How to Calculate Percentages: A Practical Guide
A percentage tells you how many parts there are out of 100. The word comes from the Latin phrase per centum, meaning “by the hundred.” That makes percentages useful whenever you want to compare values that have different totals. A score of 45 out of 50, for example, is easier to compare with a score of 80 out of 100 once both are expressed as percentages: 90% and 80%.
You probably use percentages more often than you think. They show up on sale signs, restaurant receipts, paychecks, loan statements, school reports, website dashboards, and sports statistics. The math follows a few straightforward rules, but choosing the right rule matters. Finding 20% of a price is not the same calculation as finding how much that price increased.
Our online percentage calculator handles three common questions: What is a given percent of a number? What percentage does one number represent of another? And by what percentage did a value increase or decrease? Each tool displays its formula alongside the answer so you can check the result or repeat the calculation yourself.
The Three Percentage Formulas You Need
Start by identifying which number is the whole, which number is the part, and whether you are comparing an original amount with a new amount. These examples show when to use each formula.
Find a percent of a number
Percent-of-number equation: (Percent ÷ 100) × Number
What is 20% of 500? Convert 20% to 0.20, then multiply by 500. The result is 100. For a $500 item with a 20% discount, you save $100 and pay $400 before tax.
Find what percent one number is of another
Proportion equation: (Part ÷ Whole) × 100
If 75 of 300 people respond to a survey, divide 75 by 300 and multiply by 100. The response rate is 25%. The whole must not be zero.
Calculate percentage increase
Increase equation: ((New − Original) ÷ Original) × 100 for a positive original value
If a product rises from $50 to $65, the change is $15. Divide $15 by $50 and multiply by 100 to get a 30% increase.
Calculate percentage decrease
Decrease equation: ((Original − New) ÷ Original) × 100 for a positive original value
If a laptop drops from $1,200 to $900, the difference is $300. Divide $300 by $1,200 and multiply by 100. That's a 25% decrease.
For an original value below zero, the change calculator uses the absolute value of the original amount as the denominator. That keeps the direction of the change intuitive. If the original value is zero, an ordinary percentage change is undefined, so the calculator asks you to enter a nonzero original value.
Everyday Uses for a Percent Calculator
Shopping and discounts
A jacket costs $120 and the store offers 25% off. Enter 25 and 120 in the first calculator to find a $30 discount. Subtract $30 from the original price to get a sale price of $90. If sales tax applies, calculate it separately using the relevant tax rate.
School and test scores
You answered 42 questions correctly on a 50-question test. Enter 42 as the part and 50 as the whole. The second calculator gives 84%. You can also use the same formula for attendance, assignment completion, or the share of students who passed an exam.
Business and website analytics
Suppose a website received 8,000 visits last month and 9,200 this month. The third calculator shows a 15% increase. You can use the same approach for revenue, order volume, expenses, or newsletter subscribers. For conversion rate, divide conversions by total eligible visits and multiply by 100.
Tips, commissions, and budgets
To calculate an 18% tip on a $60 bill, find 18% of 60: $10.80. For a 5% commission on $2,000 in sales, the same formula gives $100. You can also work out what percentage of a monthly budget goes toward rent, groceries, or transportation.
These examples all use the same basic arithmetic, but the meaning of the result depends on the question. A 15% increase in revenue describes growth relative to the previous revenue figure. A 15% conversion rate describes a share of the total. Keep the original figures nearby so you can explain what your percentage represents.
How to Use the Online Percentage Calculator
- Choose the right calculation. Use the first card to find a percent of a number, the second to find a proportion, or the third to compare an original and a new value.
- Enter your numbers. Whole numbers and decimals are supported. The first calculator also accepts percentages above 100% and negative percentages. The second requires a nonzero whole, while the third requires a nonzero original value.
- Press Calculate. Your result appears beneath the input fields. A visual bar helps illustrate the size of the percentage, capped at 100% for display only; results themselves are not capped.
- Review the formula. Check that you entered the part, whole, original, and new values in the intended order. For money or other figures requiring strict decimal precision, verify the final amount according to your applicable rounding rules.
You can press Enter while typing in an input field instead of clicking the button. Calculations run in your browser, and the tool does not need an account or a server-side calculation request.
Percentages, Decimals, Fractions, and Percentage Points
A percent, decimal, and fraction can express the same proportion. For example, 75% equals 0.75 and three-quarters. To turn a percent into a decimal, divide by 100. To turn a decimal into a percent, multiply by 100. To convert a fraction such as 3/8 into a percentage, divide 3 by 8 and multiply by 100, giving 37.5%.
| Percent | Decimal | Fraction |
|---|---|---|
| 10% | 0.10 | 1/10 |
| 25% | 0.25 | 1/4 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 125% | 1.25 | 5/4 |
Percentage points are different from percent change. If an interest rate moves from 3% to 5%, that's an increase of 2 percentage points. Relative to the original 3% rate, the increase is about 66.67%. Both numbers are correct, but they answer different questions.
Successive percentage changes compound. A $100 item that rises by 20% costs $120. If it rises by another 30%, the new price is $156. The combined increase is 56%, not 50%, because the second increase applies to a larger base. Likewise, a 50% increase followed by a 50% decrease leaves a $100 starting amount at $75.
For a more detailed explanation of the underlying math, see Math Is Fun's illustrated introduction to percentages and its examples comparing percentages with percentage points.
Common Percentage Mistakes to Avoid
Using the wrong base
For a price increase from $80 to $100, divide the $20 change by the original $80, not the new $100. The increase is 25%, not 20%. Reversing the direction produces a different percentage.
Confusing a percent with a percentage point
Moving from 40% to 50% is a 10-percentage-point increase but a 25% relative increase. State which one you mean when discussing polls, interest rates, or conversion rates.
Adding successive changes
A 10% discount followed by another 10% discount does not equal a 20% discount. On a $100 item, the first discount leaves $90, and the second leaves $81: a 19% total reduction.
Rounding too early
Keep extra decimal places during intermediate calculations. Round only the final answer as appropriate. The calculator displays results to two decimal places, so tiny differences may be hidden in the display.
Also remember that percentage change and percentage difference are not interchangeable. Percentage change compares a new value with an identified original value. A symmetric percentage difference between two values commonly divides their absolute difference by the average of their absolute values instead. This tool calculates percentage change, not that symmetric measure.