Percentage increase tells you how much something has grown compared with where it started. It's used for prices, pay rises, website visits, test scores and much more. The formula is simple, but a few common mistakes trip people up. Here's how to get it right.

The formula

Percentage change = (new value − old value) ÷ old value × 100

If the answer is positive, it's an increase. If it's negative, it's a decrease. The key point is that you always divide by the old (starting) value.

Worked examples

A price rise

A product's price goes from $40 to $50.

(50 − 40) ÷ 40 × 100 = 10 ÷ 40 × 100 = 25% increase

A pay rise

A monthly salary goes from 2,500 to 2,650.

(2,650 − 2,500) ÷ 2,500 × 100 = 150 ÷ 2,500 × 100 = 6% increase

A decrease

Website visitors fall from 1,200 to 900 in a month.

(900 − 1,200) ÷ 1,200 × 100 = −300 ÷ 1,200 × 100 = −25%, a 25% decrease

More than doubling

Sales grow from 30 to 75.

(75 − 30) ÷ 30 × 100 = 150% increase

Doubling something is a 100% increase, and tripling it is a 200% increase. Increases can be larger than 100%. For things that can't go below zero, such as prices or visitor numbers, a decrease can never be more than 100%, because you can't lose more than everything.

Why going up and coming down aren't the same

If a price goes from $40 to $50, that's a 25% increase. If it then drops back from $50 to $40, that's a 20% decrease, not 25%. The change is $10 both times, but the starting value is different.

This works the other way too: after a 50% drop, you need a 100% rise to get back to where you started. 100 falls to 50, and 50 has to double to return to 100.

Percent vs percentage points

When the values are themselves percentages, such as interest rates, be careful with wording. If an interest rate rises from 2% to 3%:

  • it rose by 1 percentage point (3 − 2), and
  • it rose by 50% ((3 − 2) ÷ 2 × 100).

Both statements are true, but they sound very different. Say which one you mean.

Working backwards to the original value

Suppose a price is $60 after a 20% increase, and you want the original price. A common mistake is to take 20% off $60, which gives $48. That's wrong, because the 20% was calculated on the original price, not on $60.

Instead, divide by the growth factor:

Original = 60 ÷ 1.20 = $50

Check: 20% of $50 is $10, and $50 + $10 = $60. ✓ To undo a decrease, divide by (1 − the percentage). For example, after a 25% discount, divide by 0.75.

Back-to-back changes multiply

Two changes in a row don't simply add up. A 10% increase followed by a 10% decrease leaves you slightly below where you started:

100 × 1.10 = 110, then 110 × 0.90 = 99, a 1% decrease overall

Likewise, two 20% discounts in a row are not 40% off. They're 36% off, because 0.8 × 0.8 = 0.64. To combine changes, multiply their factors together.

When the starting value is zero or negative

If the old value is zero, percentage change can't be calculated, because you'd be dividing by zero. Any growth from nothing is, in percentage terms, infinite. In that case, describe the change in plain numbers instead, for example “up from 0 to 25”.

Negative starting values, such as a loss shrinking from −50 to −25, are tricky. Our calculator divides by the size of the starting value, so a move towards positive counts as an increase (here, 50%). Many people find plain numbers clearer in these cases, so consider saying “the loss halved” instead.

Percentage change or percentage difference?

Use percentage change when there's a clear before and after. When you're comparing two values where neither is the starting point, such as two shops' prices, use percentage difference, which compares the gap with the average of the two. The Percentage Calculator can work out both.