Percentages show up everywhere
Sales tags, tips, grades, interest rates, tax, growth charts. You meet a percentage dozens of times a week, and most people do the math in their head or guess. Guessing works until the number matters.
This calculator covers the three questions people ask most. What is X percent of Y? X is what percent of Y? And how much did something change in percent? Each one shows the formula so you can see where the answer came from.
Finding a percent of a number
Turn the percent into a decimal and multiply. 20 percent of 150 is 0.20 x 150, which is 30. That's the discount on a 150 jacket at 20 percent off, so you'd pay 120.
A shortcut for mental math: 10 percent is just moving the decimal one place. 10 percent of 150 is 15. Double it for 20 percent. Half of it gives 5 percent. With those three you can handle most tips and tax in your head.
What percent is one number of another?
Divide the part by the whole and multiply by 100. If you scored 45 on a test out of 60, that's 45 / 60 = 0.75, so 75 percent.
People mix up which number goes on top. The part goes on top and the whole goes underneath. If the answer is above 100 percent, the part is bigger than the whole, which is fine for things like growth but odd for a test score.
Percentage change
Subtract the old value from the new one, divide by the old value and multiply by 100. If rent goes from 1,200 to 1,320, the change is 120, and 120 / 1,200 is 10 percent.
The direction matters, and the base matters most. A drop from 100 to 50 is minus 50 percent. Going back from 50 to 100 is plus 100 percent. That asymmetry trips up investors, who sometimes think a 50 percent loss needs a 50 percent gain to recover. It needs 100.
- Increase and decrease use the old value as the base
- Percentage points and percent are not the same thing. Going from 4 to 6 percent is up 2 points, but up 50 percent
- The tool uses the absolute value of the original, so negative starting values still give a sensible sign
Percentage increase versus difference
Increase compares a new number to an old one. Percentage difference compares two numbers when neither is the starting point, like prices at two stores. It divides by their average. The two answers differ, so pick the one that matches your question.
The calculator keeps a few decimal places so rounding doesn't change the picture. For money, round to cents at the end, not along the way.
Nothing you type leaves your browser.
Real situations, worked out
A jacket is priced at 80 and the sign says 35 percent off. Take 35 percent of 80, which is 28, and subtract it. You pay 52. Many shoppers add the discount to the price by mistake and then wonder why the till disagrees.
A restaurant bill comes to 64 and you want to leave 18 percent. Ten percent is 6.40, eight percent is about 5.12, so the tip is near 11.52. Round it to 11.50 and move on.
Salary raises work the same way. Going from 52,000 to 55,640 is a rise of 3,640, which is 7 percent of the old figure. Always divide by the starting value, not the new one.
Traps worth knowing
A 50 percent drop followed by a 50 percent rise doesn't bring you back. Start at 100, fall to 50, climb 50 percent to 75. You're still down a quarter. Percentages apply to a changing base, so order matters.
Percent and percentage points are different things. If a rate moves from 4 percent to 6 percent, that's up 2 percentage points but up 50 percent in relative terms. News stories mix these up all the time, sometimes on purpose.
Be careful with tiny samples. 'Sales jumped 300 percent' might mean three units became twelve.
Mental shortcuts
Ten percent is the decimal point shifted one place. Five percent is half of that. Twenty is double. Fifteen is ten plus five. With those four you can estimate most tips and discounts in your head.
And it works backwards. If 15 is 10 percent of something, the whole is 150. Use the calculator to confirm when the stakes are higher than a lunch bill.