How to calculate percentage change, with worked examples

Percentage change is how most of us compare two numbers over time: a price that has gone up, a rent that has been raised, a balance that has fallen, a school roll that has grown. The sum itself is short, but it is easy to get wrong because the answer depends on which number you treat as the starting point. This guide gives you the formula, works through increases and decreases with real numbers, shows how to go backwards from a final figure, and explains the traps that catch out even careful people, such as mixing up percentages and percentage points.

By Valtrinity. Updated 18 October 2026.

The formula

Percentage change is the difference between the new value and the old value, divided by the old value, multiplied by 100. In words: change divided by where you started. If the answer is positive, the value has gone up. If it is negative, it has gone down.

As a formula: percentage change = (new value minus old value) divided by old value, times 100. The old value is the base. Everything depends on getting that right, because the base is the number the change is measured against.

Say a monthly train season ticket rises from £200 to £212. The difference is £12. Divide £12 by the old price of £200 to get 0.06, and multiply by 100 to get 6 per cent. The ticket has gone up by 6 per cent.

Working out an increase step by step

Take a rent of £950 a month that rises to £1,045. First subtract: 1,045 minus 950 is 95. Then divide by the old rent: 95 divided by 950 is 0.1. Then multiply by 100: 10 per cent. The rent has gone up by 10 per cent.

Now take a salary of £28,000 that rises to £29,400. The difference is £1,400. Divided by £28,000 that is 0.05, so the pay rise is 5 per cent. Notice that the same method works whatever the size of the numbers, which is why it is worth learning once.

If you want to apply a known percentage rise to a figure, you can multiply instead. A 5 per cent rise on £28,000 is the same as multiplying by 1.05, which gives £29,400. A 12 per cent rise is a multiplier of 1.12. Adding the percentage to 100 and dividing by 100 gives you the multiplier.

Working out a decrease

The method is identical, but the answer is negative. A sofa marked at £800 is sold for £680. The change is 680 minus 800, which is minus 120. Divide by the old price: minus 120 divided by 800 is minus 0.15. That is a 15 per cent decrease.

To apply a decrease, subtract the percentage from 100 to get the multiplier. A 15 per cent reduction is a multiplier of 0.85, so £800 times 0.85 is £680. A 30 per cent sale discount is a multiplier of 0.70, so an item at £45 costs £31.50.

When people report a fall in a number of customers, they usually quote the percentage as positive and say it fell by that much. If 1,200 customers last month became 1,020 this month, the drop is 180, and 180 divided by 1,200 is 15 per cent.

Why the order matters: up then down is not back to the start

A rise of 25 per cent is not cancelled by a fall of 25 per cent. Start at 80 and add 25 per cent: you get 100. Now take 25 per cent off 100 and you get 75, not 80. To get back from 100 to 80 you need a fall of 20 per cent, because the base is now 100 rather than 80.

The same thing happens with successive changes. If a price goes up 10 per cent and then falls 10 per cent, the result is not the original price. 100 times 1.10 is 110, and 110 times 0.90 is 99. The net result is a 1 per cent fall.

This is why percentage changes should never simply be added or subtracted. To combine two changes, multiply the multipliers. A 20 per cent rise followed by a 10 per cent rise is 1.20 times 1.10, which is 1.32, or a 32 per cent rise overall, not 30.

Going backwards: finding the original value

Sometimes you know the final value and the percentage change, and you want the starting point. This is called a reverse percentage. You divide by the multiplier instead of multiplying.

For example, a price including VAT at 20 per cent is £120. The multiplier for adding 20 per cent is 1.20, so the price before VAT is £120 divided by 1.20, which is £100. A common mistake is to take 20 per cent off £120 and get £96. That is wrong, because the 20 per cent was calculated on the smaller original number, not on £120.

Another case: a jacket costs £63 in a sale after a 30 per cent discount. The multiplier is 0.70, so the original price was £63 divided by 0.70, which is £90. Check by taking 30 per cent off £90: that is £27, and £90 minus £27 is £63.

Percentages versus percentage points

When a rate changes, there are two ways to describe the movement, and they are not the same. If a savings rate rises from 4 per cent to 5 per cent, it has gone up by 1 percentage point. That is the simple difference between the two rates. But it has also gone up by 25 per cent in relative terms, because 1 divided by 4 is 0.25.

News reports and adverts often blur the two. Read carefully. A change from 2 per cent to 4 per cent is a rise of 2 percentage points, and a rise of 100 per cent in relative terms: the rate has doubled. Both statements are true, but they sound very different.

If you are comparing interest rates, loan rates or inflation figures, say which you mean. Percentage points tell people how big the gap is on a fixed scale, and a percentage tells them how large the move is in proportion to where it started.

Common mistakes and a quick check

The biggest mistake is dividing by the wrong number. Always divide by the old value, the starting point, not the new one. If you divide the £12 rise in a £200 ticket by the new price of £212, you get 5.66 per cent, which is not the percentage rise.

Another is forgetting that the percentage can be above 100. If a number triples, it has risen by 200 per cent. If it doubles, it has risen by 100 per cent. A fall, on the other hand, can never be more than 100 per cent, because a number cannot go below zero in this sense.

For a quick sense check, estimate before you calculate. A rise from 40 to 50 should be a quarter, which is 25 per cent. If your answer is nowhere near that, go back and check which number you divided by.

Tools mentioned in this guide

Frequently asked questions