Percentage calculator
A €80 jacket at 15% off: 15% of 80 is 12, so you pay 68. The second row shows that remaining 68 without a second sum.
A percentage is a count out of a hundred. X% of Y is Y multiplied by X and divided by 100: 15% of 80 is 12. Asking what percentage 12 is of 80 reverses that, dividing 12 by 80 and multiplying by 100. Adding 15% multiplies by 1.15 and removing 15% multiplies by 0.85, which is why doing both in turn does not return you to where you began.
How to use it
Two properties of this arithmetic save real time. X% of Y always equals Y% of X, because both come to XY ÷ 100, so 4% of 75 and 75% of 4 are both 3 and you get to pick the easier sum. And taking a percentage off is not the inverse of putting it on: add 21% to 100 and you have 121, take 21% off 121 and you have 95.59. To strip a percentage that is already inside a figure you divide rather than subtract, 121 ÷ 1.21, which is the step the "add or take off" mode does not do for you.
What people use it for
- Working out a discount and the price left to pay in one step
- Turning a mark out of an awkward total into a percentage
- Putting a percentage onto a figure and taking the same one off it
- Applying a second discount to what the first one left
- Checking a share quoted in a report against the two numbers behind it
Questions
Yes, and the second is usually the easier sum. Both are 15 × 80 ÷ 100 = 12. Swapping the two numbers never changes the answer, which is worth knowing when one of them is a round figure.
Divide rather than subtract. A price including 21% VAT is divided by 1.21 to get the net figure. Subtracting 21% gives a different, wrong answer.
The half you did not ask for. On "X% of Y" it is the remainder, so a 15% discount on 80 shows the 12 off and the 68 to pay together; on "X is what % of Y" it is the share you did not take.
Yes, one at a time. Thirty per cent off then a further twenty per cent off is not fifty per cent off: it leaves 56% of the original price. Run the first, then feed the answer back in.
Use "X is what % of Y". Thirty-seven out of forty-three is 86.047%, and the row beneath gives the 13.953% you dropped.