Percentage calculator
Three ways to ask the same kind of question. Type numbers, get the answer and the formula that produced it.
Which of the three tools you actually need
Most percentage mistakes are not arithmetic mistakes, they are picking the wrong question. The first tool answers "what is X% of Y", which covers tips, commissions, and deposits. The second answers "what share is this of the whole", which is what you want for test scores, market share, or budget breakdowns. The third compares two values over time, and it is the one people misuse most, because they divide by the new value instead of the old one. The rule to remember: percent change is always measured against where you started.
One trap worth calling out. Going from a 4% rate to a 6% rate is a 2 percentage point increase, but the third tool will correctly tell you it is a 50% increase, because 6 is half again as large as 4. Both statements are true and headlines routinely swap them to make a number sound bigger or smaller. When you read "interest rates jumped 50%", check which kind of percent is being claimed.
Here is the tip that saves people real money: percentages do not run in reverse. If a price rose 25% and you want the original, do not subtract 25%. Use the first tool backwards instead: divide the current price by 1.25. A jacket now at $150 after a 25% markup started at $120, not at $112.50.
Three quick examples, checked by hand
Sales commission: enter 7.5 percent of 2,400 in the first tool. It computes 2400 x 7.5 / 100 and shows 180. Exam score: enter 42 in the second tool, of 168. That is 42 / 168 x 100, which comes out to exactly 25%. Price drop: enter 84 as the old value and 63 as the new value in the third tool. It computes (63 - 84) / 84 x 100 and reports -25%, labeled as a decrease. Notice the asymmetry with the previous example only in appearance: going back up from 63 to 84 would be a 33.3333% increase, because the base changed.
What the calculator is doing under the hood
Each tool applies its formula directly and shows that formula beneath the result, so you can copy the working into homework or a spreadsheet. Percent-of is value x percent / 100. Share-of-whole is part / whole x 100. Percent change is (new - old) / old x 100, with a plus sign added for increases. Results are rounded to at most six decimal places internally, and the two ratio tools display up to four significant decimals, so recurring decimals like 33.3333% are truncated for display rather than shown forever. Division by zero is refused with a message instead of returning a misleading result: you cannot take a share of zero, and percent change from zero is undefined.
Where percentages stop being enough
These are single-step calculations. Chained changes need to be multiplied through, not added: two consecutive 10% increases make 21%, not 20%, and the calculator will not chain steps for you. It also has no notion of compounding over time, so for interest or investment growth use the compound interest calculator instead. Finally, percent change on values near zero produces enormous and mostly meaningless numbers; a metric moving from 0.1 to 0.4 is "up 300%" and that figure tells you almost nothing useful on its own.
Frequently asked questions
How do I calculate X percent of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 80 is 80 x 15 / 100 = 12.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. If 30 of 120 students passed, that is 30 / 120 x 100 = 25%.
How is percent change calculated?
Subtract the old value from the new value, divide by the old value, then multiply by 100. Going from 50 to 65 is (65 - 50) / 50 x 100 = a 30% increase. A negative result means a decrease.
Why is a 50% increase then a 50% decrease not back to the start?
Because the second percentage applies to a bigger base. 100 up 50% is 150; 150 down 50% is 75. Percent changes compound on the current value, not the original.