How to Calculate Percentages: Increase, Decrease, Difference and Percent Of

By the SAA Tool editor, an IT support engineer · Last reviewed 1 October 2026 · 6 min read

Percent means "per hundred". 15% is 15 out of every 100, which is the same as the decimal 0.15. The US National Institute of Standards and Technology puts it simply: the symbol % stands for the number 0.01. Almost every everyday percentage sum, from a shop discount to a pay rise, is one of six questions. Once you know which one you're asking, the maths is a single line.

The six sums at a glance

To turn a percentage into a decimal, divide by 100 (15% becomes 0.15). To turn a decimal into a percentage, multiply by 100 (0.7 becomes 70%).

Finding a percentage of a number

Multiply the number by the percentage as a decimal: 15% of 200 is 0.15 × 200 = 30.

For mental maths, build it from easy pieces. 10% is the number with the decimal point moved one place left, 5% is half of that, and 1% moves the point two places. So 17.5% of 80 is 8 + 4 + 2 = 14 (10% plus 5% plus 2.5%).

There's also a handy swap: X% of Y always equals Y% of X. 8% of 50 is awkward, but 50% of 8 is obviously 4, and it's the same answer.

What percentage one number is of another

Divide the part by the whole and multiply by 100. Scoring 42 out of 60 in a test is 42 ÷ 60 = 0.7, or 70%. If 18 of a company's 72 staff work remotely, that's 18 ÷ 72 × 100 = 25%.

The only difficulty is deciding which number is the whole. The word "of" usually points to it: "what percentage of the staff" means the staff total goes on the bottom.

Working backwards to the original number

If you know the result and the percentage, divide. 45 is 30% of 45 ÷ 0.30 = 150.

This is where most everyday mistakes happen. Say a jacket costs 64 after a 20% discount. The original price is 64 ÷ 0.80 = 80. Adding 20% to 64 gives 76.80, which is wrong, because the 20% was taken off the bigger, original price.

Tax works the same way. If a price of 120 includes a 20% sales tax or VAT, the price before tax is 120 ÷ 1.20 = 100 and the tax is 20. Taking 20% of 120 gives 24, which overstates the tax. Rates differ from country to country, and our guide to VAT and sales tax explains how adding and removing tax works.

Percentage increase and decrease

Percentage change is the difference divided by the starting value:

Change % = (New − Old) ÷ Old × 100

From 80 to 100 is (100 − 80) ÷ 80 = +25%. From 100 back to 80 is (80 − 100) ÷ 100 = −20%. The gap is 20 both times, but the starting value differs, so the percentages do too.

To increase a number by a percentage, multiply by 1 plus the rate; to decrease it, multiply by 1 minus the rate. 250 increased by 10% is 250 × 1.10 = 275, and decreased by 10% it's 250 × 0.90 = 225. Three consequences are worth knowing:

• Up and down don't cancel. 100 up 10% is 110, and 110 down 10% is 99, not 100.
• Stacked discounts multiply. 25% off, then an extra 10% off, is 0.75 × 0.90 = 0.675 of the price, a total of 32.5% off rather than 35%. On a price of 120, you pay 90 after the first discount and 81 after the second.
• Repeated rises compound. A rent of 1,500 a month rising 4% a year becomes 1,560, then 1,622.40, then 1,687.30. After three years it's up 12.49%, not 12%. Our guides to rent increases and compound interest go further.

Percentage points and percentage difference

When a rate itself changes, there are two ways to describe the move. If an interest rate goes from 10% to 12%, it has risen by 2 percentage points, the term Eurostat's glossary gives for comparing two percentages. In relative terms, the rate is 20% higher, because 2 is 20% of 10. A rise from 2.5% to 3% is 0.5 percentage points, or a 20% increase in the rate. Headlines sometimes blur the two, so check which one is meant.

Percentage difference is for comparing two values when neither is the "before", such as prices in two shops. Divide the gap by the average of the two: for 40 and 50, that's 10 ÷ 45 × 100 = 22.22%. The order doesn't matter. Some fields use other conventions, such as dividing by the larger value, so say which formula you used when it matters.

Doing the sums with our calculators

1. Open the Percentage Calculator and find the box that matches your question: What is X% of Y?, X is what percent of Y?, Percentage change from X to Y, X is Y% of what?, Increase or decrease X by Y% or Percentage difference between X and Y.
2. Type your two numbers. There's no button to press: the answer appears under the box as you type, with up to six decimal places. The percentage change box also shows the difference in units, such as +20.
3. For a sale price, use the Discount Calculator. Enter the Original price and the Discount (%), or set Discount type to Amount off. Add an Extra discount % (optional) to see the real combined saving, and a Sales tax / VAT % (optional) if tax is added at the till. It shows what you pay, what you save and the total discount.
4. For tax, the VAT Calculator has two modes: Add VAT to my price and Remove VAT from my price. Enter the amount and your country's rate.
5. For rent, the Rent Increase Calculator works either way round: set I know to the increase in % or the new rent. Show years projects the same rise over 3, 5 or 10 years, and you can enter a legal or contract limit to compare against.

This guide is general information, not financial, tax or legal advice. Tax rates and rent rules change and differ by country and region, so check official sources before you rely on a figure. For example, the EU's Your Europe VAT page lists each member state's rates; elsewhere, your national tax authority publishes the current rate, and your local housing authority or tenancy law sets any limit on rent rises.

Common mistakes

• Dividing by the wrong number. Percentage change always divides by the starting value, not the new one.
• Reversing with the same percentage. To undo a 20% discount, divide by 0.80. Adding 20% back doesn't work.
• Adding percentages that apply one after another. Two discounts or two rises multiply; they don't add.
• Mixing up percent and percentage points. 10% to 12% is +2 points but +20%.
• Averaging percentages. If one shop's sales grow from 1,000 to 1,100 (+10%) and another's from 100 to 130 (+30%), the combined growth is 1,100 to 1,230, or 11.82%, not 20%. Add the totals first, then work out the percentage.
• Rounding too early. Keep the full figures through each step and round only the final answer.
• Doubting results over 100%. An increase can be more than 100% (doubling is +100%), but a part can never be more than 100% of the whole it belongs to.

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