How to Calculate a Percentage Increase (With Examples)

A percentage increase tells you how much something has grown compared with where it started. It is the number behind pay-rise announcements, rent increases, price rises and exam-score improvements, and it is surprisingly easy to get wrong: use the wrong starting value and the same change can come out as 13% or 15% depending on how you divide. This guide walks through the formula once, slowly, then works three real examples so you can reuse the method on any pair of numbers. If you would rather skip the arithmetic, the Percentage Calculator has a percentage-change mode that does exactly this calculation and shows its working.

The formula

Percentage increase has two steps. First, find the increase itself: subtract the old value from the new value. Second, divide that increase by the old value - the starting point, never the new one - and multiply by 100 to turn it into a percentage.

Dividing by the old value is the whole trick. You are asking: the growth is what fraction of what I started with? A rise of 12,000 sounds huge until you learn it started from 80,000, at which point it is a solid but unspectacular 15%. The same logic is why a shop can honestly advertise a large percentage increase on a tiny starting price, and why percentages quoted in news stories are always worth one question: increase relative to what?

Worked example 1: a pay rise

Your salary goes from 80,000 a year to 92,000 a year. Step one: the increase is 92,000 - 80,000 = 12,000. Step two: divide by the old salary, 12,000 / 80,000 = 0.15, and multiply by 100. Your pay rise is 15%. A quick sanity check: 10% of 80,000 is 8,000 and 20% would be 16,000, so an increase of 12,000 sitting between them at 15% makes sense.

Worked example 2: a price jump

A train pass costs 250 one month and 300 the next. The increase is 300 - 250 = 50. Divide by the old price: 50 / 250 = 0.20, so the price has gone up by 20%. Notice that the increase, 50, is 20% of the old price but only about 16.7% of the new one - which is exactly why dividing by the wrong end of the change gives a different, wrong, answer.

When the answer is negative: decreases

The formula does not change when a value falls; the answer simply comes out negative. Say a jacket drops from 500 to 425. The change is 425 - 500 = -75, and -75 / 500 = -0.15, so the result is -15%, which you report as a 15% decrease. Treat the minus sign as information rather than an error, and describe the result in words - "a 15% fall" - so nobody has to decode it. On the Percentage Calculator, the percentage-change mode shows the direction for you, which saves a step when you are checking a whole list of figures.

Three mistakes that give wrong answers

• Dividing by the new value. 12,000 / 92,000 gives about 13%, not 15%. The old value is always the denominator for an increase or decrease.
• Confusing percentage points with percent. If an interest rate moves from 4% to 5%, that is a rise of 1 percentage point, but a 25% increase in the rate itself (1 / 4 = 0.25). Both statements are true; they answer different questions.
• Adding percentages up and down. A price that rises 10% and then falls 10% does not return to its start: 100 becomes 110, then falls by 11 (10% of 110) to 99. Percentages of different bases never simply cancel out.

All three mistakes have the same root cause: forgetting that a percentage is always a percentage of something, and that the "something" changes as the value changes. Keep the base straight and the rest of the calculation looks after itself. For chains of workings - adding tax, then a discount, then a fee - a plain Standard Calculator helps you keep each intermediate step visible.

Percentage increase vs percentage difference

These two get mixed up constantly. Percentage increase (and its sibling, percentage change) compares a value against its own earlier value, so order matters: going from 80 to 100 is +25%, and going back from 100 to 80 is -20%. Percentage difference compares two values that have no before-and-after relationship - two quotes for the same job, say - and divides by their average instead, so the answer is the same whichever way round you put them. Use change when time or sequence is involved, difference when you are comparing two things side by side. Both modes are built into the percentage calculator linked above, alongside our other Calculators.

Common questions

Can I calculate a percentage increase from zero? No. Division by zero is undefined, and any growth from nothing is not meaningfully a percentage - describe it in absolute terms instead ("sales began at 40 units"). In practice, if the old value is zero, there is no percentage answer, and any spreadsheet that shows one is hiding an error.

How do I turn a percentage increase back into the new value? Multiply the old value by 1 plus the percentage as a decimal. A 15% rise on 80,000 is 80,000 x 1.15 = 92,000. For a decrease, subtract instead: a 15% fall is 80,000 x 0.85 = 68,000.

Why does my spreadsheet show a slightly different answer? Usually rounding - the sheet is keeping more decimal places than it displays - or one of the mistakes above, most often dividing by the new value. Recompute by hand with the formula at the top of this page; if the two disagree, the hand calculation is the one to trust.