Five percentage questions, one page
Most percentage problems come down to one of five questions. What is 20% of 85? What percent of 85 is 17? By how much did a price go up? What do I get if I add 8% to this number? And what was the number before it went up? The calculator above answers all five. Pick the question after “Work out”, type your numbers in the boxes and read the answer. There is no Calculate button: the result changes as you type, and the line underneath shows the formula, so you can redo it on paper if you want to be sure.
X% of Y
To find a percentage of a number, multiply the number by the percentage and divide by 100. 20% of 85 is 85 × 20 ÷ 100 = 17. A quick way to do it in your head: 10% is the number with the decimal point moved one place to the left (8.5), 20% is twice that (17), and 5% is half of 10% (4.25). This is the calculation behind a tip, a deposit, a commission or the share of a budget.
X is what percent of Y
Divide the part by the whole and multiply by 100. If you got 42 questions right out of 50, that is 42 ÷ 50 × 100 = 84%. If $17 of an $85 grocery bill went on coffee, coffee was 20% of the bill. The order matters: the whole (the “of” number) always goes at the bottom of the division.
Percentage change from A to B
The change is the difference divided by the starting value: (B − A) ÷ A × 100. A price going from $80 to $100 is a rise of 20 ÷ 80 × 100 = 25%. The other way round, from $100 down to $80, it is a drop of 20%, not 25%, because you now divide by 100. The calculator shows the difference and the percentage together, with a plus or minus sign. Use it for a rent increase, a pay raise, a share price or the change in a monthly bill.
Add or take off a percentage
To add a percentage, multiply by 1 plus the rate: 100 plus 20% is 100 × 1.2 = 120. To take one off, multiply by 1 minus the rate: 100 minus 20% is 100 × 0.8 = 80. Tap “plus” in the sentence to switch to “minus”. This is also the quickest way to add a US sales tax rate to a price: type the price and your local rate. For a sale price with two discounts in a row, the discount calculator shows the savings too.
The value before a percentage
This is the trickiest of the five. If a price is $120 after a 20% rise, the old price was not $96 (120 minus 20%). It was 120 ÷ 1.2 = $100. To go back, you divide by the same multiplier you used to go forward. After a drop of 20%, a price of $80 was 80 ÷ 0.8 = $100 before. The same logic finds a price before tax: the VAT calculator does it with the rates of each country.
Two traps worth knowing
A rise and a fall of the same percentage do not cancel out
Start at 100, add 20% and you reach 120. Take 20% off 120 and you land on 96, not 100. The second percentage is taken from a bigger number, so it removes more. This is why a share that falls 50% needs to rise 100% to get back to where it was: from 100 down to 50, then 50 has to double to reach 100 again.
Percentage points are not percent
When a rate moves from 3% to 4%, it rose by 1 percentage point, but by 33.33% in relative terms (1 ÷ 3 × 100). News about interest rates, polls and unemployment usually speaks in points. Both figures are correct, they just answer different questions, so check which one you are reading. Use “percentage change” with 3 and 4 to see the relative rise.
Handy extras
- Microphone. Tap the microphone at the top and say “20% of 85” or “from 80 to 100”: the right calculation opens with your numbers in place.
- Keyboard. Enter jumps to the next box, the up and down arrows change a number by 1 (by 10 with Shift), the space bar copies the result and R resets.
- Share. The Share button, at the bottom left, gives an image of the result and a link that opens the same calculation, numbers included.
- Widget. Teachers and bloggers can put this calculator on their own page with the Widget button.
Your numbers are kept in your browser, so they are still there when you come back, and nothing is sent to a server. For problems of the “if 4 gives 10, then 6 gives…” kind, the proportion calculator is a better fit.