Percentage Calculator

Which percentage calculation do you need?

"Percentage" is one word for seven different sums, and picking the wrong one is the usual mistake. Find your question in the left column and use that mode:

Every answer comes with the formula and your numbers in it, like 15 ÷ 100 × 80 = 12, so you can check it or show someone how you got there.

How do you find the original price before a discount?

Work out what share of the original price you actually paid, then use the X is Y% of what mode. After 20% off you paid 80%, so a sale price of $150 means the original was 150 ÷ 0.8 = $187.50.

The same logic undoes any increase. A salary of $5,500 after a 25% raise is 125% of the old salary, which was $4,400. The common mistake is to take 25% off the new figure, which gives $4,125 and is wrong, because the 25% was measured against the old salary, not the new one.

Is 20% off and then 10% off the same as 30% off?

No, it is 28% off. The second discount applies to the price that is already reduced. On a $100 item, 20% off leaves $80, and 10% off $80 leaves $72, a total saving of $28.

The quick way to combine discounts is to multiply what remains after each one: 0.8 × 0.9 = 0.72, so you pay 72% of the original. To do it here, run Add / subtract % twice, using the first result as the value for the second step. Sales tax, where it applies, is charged on the price after the discounts, so add it last.

What is the difference between percentage points and percent?

Going from 40% to 44% is a rise of 4 percentage points, and it is also a 10% increase. Both are true. Percentage points are the plain gap between two rates, 44 − 40. Percent change divides that gap by where you started, 4 ÷ 40.

The two numbers drift apart whenever the thing measured is already a rate: interest, unemployment, conversion, a tax band. A rate moving from 2% to 3% is 1 point and a 50% increase, which is why the same news can sound small or dramatic. The Percentage points mode shows both side by side.

Is a 50% markup the same as a 50% margin?

No. Markup is measured against the cost and margin against the selling price, so the same profit gives two different percentages. Buy at $100 and sell at $150: the $50 profit is a 50% markup on cost but a 33.3% margin on the price.

To get the margin here, use X is what % of Y with the profit and the selling price: 50 is 33.3% of 150. For the markup, use the profit and the cost: 50 is 50% of 100. Mixing the two up is one of the most common pricing errors, because a 50% markup sounds like half the price is profit when only a third of it is.

Why does a 50% rise and then a 50% fall not bring you back?

Because each percentage is measured against a different number. Start at 100 and add 50%: you get 150. Take 50% off 150 and you get 75, not 100, since the fall is half of the bigger number. To undo a 50% rise you need a 33.3% fall, and a stock that drops 50% needs to gain 100% to recover.

How do you work out percentages in your head, or in a spreadsheet?

In your head, start from 10%: move the decimal point one place to the left. 10% of 80 is 8, so 5% is 4, 15% is 12 and 20% is 16. Two more shortcuts help:

• 25% is a quarter and 50% is a half.
• X% of Y equals Y% of X. 4% of 75 sounds hard, but 75% of 4 is 3, and so is the answer.

In Excel or Google Sheets there is no percentage function, only ordinary formulas:

• Percent of a number: =A1*15%
• Share of a total: =B2/B10, then format the cell as a percentage
• Percent change: =(B2-A2)/A2, formatted as a percentage

This calculator is quicker for a one-off question, and it shows the working, which a spreadsheet cell does not. It does not do compound interest or anything that repeats a percentage over many periods, which needs a different formula.