How to Calculate Percentage Change (With Examples)

The formula

To find a percentage change, subtract the old value from the new value, divide the result by the old value, and multiply by 100. Written out: change % = (new − old) ÷ old × 100. If the answer is positive, the value went up. If it is negative, the value went down.

The key word is “old”. Percentage change is always measured against the starting point, because the question is “how big is this change compared with what we had before?” Dividing by the new value answers a different question and gives a different number.

Worked examples

A loaf of bread costs 2.00 last year and 2.30 this year. The change is 2.30 − 2.00 = 0.30. Dividing by the old price gives 0.30 ÷ 2.00 = 0.15, and multiplying by 100 gives a 15% increase.

A shop had 1,250 customers in March and 1,000 in April. The change is 1,000 − 1,250 = −250. Then −250 ÷ 1,250 = −0.2, so customers fell by 20%.

Your salary goes from 32,000 to 35,200. The difference is 3,200, and 3,200 ÷ 32,000 × 100 = 10%. If prices rose by 4% over the same period, your pay grew faster than prices, though not by a full 10% in real terms.

Why up and down are not symmetrical

A common surprise is that a rise and a fall of the same percentage do not cancel out. If a share price of 100 rises 50%, it reaches 150. If it then falls 50%, it drops to 75, not back to 100. The second change is measured against 150, a larger base, so 50% of it is a bigger amount.

The same thing works the other way: going from 80 to 100 is a 25% increase, but going from 100 back to 80 is only a 20% decrease. Keeping the base clear in your head avoids most confusion.

Percent versus percentage points

When the numbers you are comparing are already percentages, be careful with wording. If a savings rate rises from 4% to 5%, it has gone up by one percentage point. As a percentage change, though, it has gone up by 25%, because (5 − 4) ÷ 4 × 100 = 25.

News stories and adverts sometimes pick whichever sounds more impressive. When you see a claim, ask whether it is describing points or percent.

When the starting value is zero

If the old value is zero, the formula would divide by zero, so there is no meaningful percentage change. Going from 0 sales to 10 sales is a real improvement, but you cannot express it as a percentage of nothing. In that case it is clearer to state the plain difference.

Common mistakes

Dividing by the new value instead of the old one. Forgetting to multiply by 100, which leaves you with 0.15 instead of 15%. Adding several percentage changes together over several years instead of applying them one after another. And comparing percentages from different bases as though they were the same size.

To check your work quickly, use the Percentage Calculator's percentage change mode. It shows the formula with your numbers filled in, so you can see each step and compare it with your own working.