Percentage Calculator — What Percent, Discounts, Percent Change & Percentage Points
Solve the five percent problems people mix up, all in one tool. Every result shows the working.
How to use
How this percentage calculator works
Percent means “per hundred,” and most everyday percentage questions fall into five types. This percentage calculator has a tab for each: finding X percent of a number, finding what percent one number is of another, working out a sale price or a discount rate, finding the percent change between an old and a new value, and finding the difference between two percentages in percentage points. Choose the tab, fill in two boxes, and press Calculate. The answer appears in large type with the exact calculation underneath, so you can check it, copy it into homework or share it with a link. There are also one-tap shortcuts for common jobs such as 8 percent sales tax, a 20 percent tip, 30 percent off and half price.
The five formulas
- X% of a number: number × percent ÷ 100. Example: 20% of 150 is 150 × 20 ÷ 100 = 30.
- What percent is A of B: A ÷ B × 100. Example: 45 out of 60 is 45 ÷ 60 × 100 = 75%.
- Sale price: price − (price × discount ÷ 100). Example: a $80 jacket at 25% off costs 80 − 20 = $60. To find the discount rate from two prices, use (original − sale) ÷ original × 100.
- Percent change: (new − old) ÷ old × 100. Example: going from 200 to 260 is a 30% increase; going from 260 back to 200 is a 23.1% decrease.
- Percentage points: later % − earlier %. Example: from 40% to 50% is a 10-point increase.
Common mistakes and how to avoid them
Percent change is not symmetrical. A price that rises 50 percent and then falls 50 percent does not return to where it started: 100 becomes 150, and half of 150 is 75. To undo a 50 percent increase you need a 33.3 percent decrease. The percent change tab always measures against the old value, so swapping old and new gives a different answer.
Discounts do not add up. Taking 30 percent off and then another 20 percent off is not 50 percent off. The second discount applies to the already reduced price, so the total is 1 − 0.7 × 0.8 = 44 percent off. Use the discount tab twice, feeding the sale price from the first step into the second.
Percent versus percentage points. If an interest rate moves from 4 percent to 5 percent, it rose by one percentage point but by 25 percent in relative terms. News reports, polls and bank rates mix these up constantly, which is why the last tab exists.
Everyday uses in the United States
- Sales tax: add tax by multiplying the price by (1 + rate). At 8 percent, $50 becomes 50 × 1.08 = $54. State and local rates vary across the country, from none in a few states to over 9 percent in some cities, so use your local rate.
- Tipping: in sit-down restaurants a tip of 15 to 20 percent of the pre-tax bill is customary. On a $64 bill, 20 percent is $12.80.
- Reverse percentages: if the price after a 25 percent discount is $60, the original price is 60 ÷ 0.75 = $80. The “discount and sale price” tab handles this when you enter the original price and sale price to find the rate.
- Grades and scores: a score of 42 out of 50 is 84 percent. Use the “what percent” tab.
- Raises and inflation: a raise from $52,000 to $55,640 is a 7 percent increase; use the percent change tab.
Percentages, decimals and fractions
It helps to move between the three forms in your head. 50 percent is 0.5 or one half, 25 percent is 0.25 or one quarter, 10 percent is 0.1 or one tenth, 75 percent is 0.75 or three quarters, and 1 percent is 0.01. A quick way to find 10 percent of any number is to move the decimal point one place to the left, which also makes tips easy: find 10 percent, double it for 20 percent, or add half of it for 15 percent.
Markup, margin and growth
Business owners often confuse markup and margin. If you buy an item for $60 and sell it for $80, your markup is (80 − 60) ÷ 60 = 33.3 percent of cost, but your margin is (80 − 60) ÷ 80 = 25 percent of the selling price. Use the percent change tab for markup (old value is your cost) and the “what percent” tab for margin (the part is your profit, the whole is the price). The same idea applies to growth rates: a company that grows from 40 to 50 customers has grown 25 percent, while its share of a market that moved from 40 to 50 percent has grown by 10 percentage points.
Rounding and precision
Results are rounded to two decimal places, and trailing zeros are dropped. For money, you will usually want to round to the nearest cent. When a calculation involves several steps, avoid rounding in the middle, because small errors can add up; enter the exact values and round only the final answer. If you need more detail on how an answer was reached, read the calculation line under the result.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15 percent of 80 is 80 × 15 ÷ 100 = 12. In the calculator, use the first tab and enter 80 and 15.
How do I find the percent increase between two numbers?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 40 to 50 the increase is (50 − 40) ÷ 40 × 100 = 25 percent.
What is the difference between percent and percentage points?
A percentage point is the arithmetic difference between two percentages. If a rate goes from 4 to 5 percent, that is a one-point rise but a 25 percent relative increase.
How do I calculate a discount?
Multiply the price by the discount percentage, divide by 100 and subtract the result from the price. A 30 percent discount on $50 saves $15, so the sale price is $35. Enter the price and the rate in the discount tab.
Can I find the original price from the sale price?
Yes. Divide the sale price by (1 minus the discount as a decimal). If $35 is the price after 30 percent off, then 35 ÷ 0.7 = $50. You can also use the discount tab to check the rate when you know both prices.
Why do I get a different answer when I swap the numbers?
Percent change always measures against the starting value, so the same pair of numbers gives a different percentage depending on which is the old value.
Are my numbers saved or sent anywhere?
No. Everything is calculated in your browser, and the share link only encodes your inputs in the web address, which you choose whether to copy.