How to calculate a percentage increase

The short answer: percentage increase = (new − old) ÷ old × 100. If your rent goes from £950 to £1,025, that is (1,025 − 950) ÷ 950 × 100 = 7.9%. If the answer is negative, it is a decrease. To add a percentage to a number, multiply by 1 plus the percentage as a decimal: £32,000 × 1.05 = £33,600.

Step by step

1. Take the old value from the new value: 1,025 − 950 = 75.
2. Divide by the old value: 75 ÷ 950 = 0.0789.
3. Multiply by 100: 7.89%.

Always divide by the starting value. Dividing by the new value is the most common mistake and gives a smaller answer (7.3% here).

Everyday examples

Going the other way

• Increase a number by a percentage: multiply by (1 + % ÷ 100). £950 up 8% = 950 × 1.08 = £1,026.
• Decrease a number by a percentage: multiply by (1 − % ÷ 100). £80 down 25% = 80 × 0.75 = £60.
• Find the original before an increase: divide by (1 + % ÷ 100). If £1,026 is after an 8% rise, the original was 1,026 ÷ 1.08 = £950. This is how you remove VAT; see how to remove VAT.

Percent vs percentage points

When rates change, the two get mixed up. A mortgage rate going from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate. Headlines about interest rates, inflation and tax rates usually mean percentage points.

Increases don't add up simply

Two 10% rises are not a 20% rise. £100 up 10% is £110, and up another 10% is £121: a 21% rise overall. And a 20% fall followed by a 20% rise leaves you below where you started: £100 becomes £80, then £96. This is compounding; see what is compound interest.

Pay rises and inflation

To see whether a pay rise beats inflation, compare the percentage rise with the inflation rate over the same period. A 4% rise with 3% inflation is roughly a 1% real increase. But tax takes a share of any rise, so the take-home increase is smaller in pounds. See is a 5% pay rise good? and the pay rise calculator.

Real-life examples

• Pay rise: from £32,000 to £34,000 is (34,000 − 32,000) ÷ 32,000 × 100 = 6.25%. After tax and National Insurance, take-home rises by less in pounds, but by a similar percentage.
• Rent rise: a landlord raising rent from £1,100 to £1,200 a month is asking for 9.1% more, or £1,200 a year.
• Energy price cap: if a typical bill moves from £1,690 to £1,758, that is a 4.0% rise.
• Shop price: a £2.50 item now £2.85 has gone up 14%, even though it is only 35p.
• Shrinkflation: a pack shrinking from 200g to 180g at the same price is a price rise per gram of 11.1%, because you now pay for 180g what 200g used to cost.

Common mistakes

• Dividing by the new number. From £80 to £100 is a 25% rise (20 ÷ 80), not 20% (20 ÷ 100).
• Reversing a percentage by applying the same one. A price that rose 25% to £100 was £80 before, not £75. Divide by 1.25; don't take 25% off.
• Adding percentages from different starting points. A 10% rise in one year and 5% the next is 15.5% in total, not 15%.
• Mixing up the base. "Sales up 50% on last month" and "up 50% on last year" are very different claims.
• Treating a small base as a big change. Going from 2 to 4 complaints is a 100% rise, but only two more complaints.

Percentage increase over several years

To compare growth over different periods, use the average yearly rate. If rent went from £800 to £1,000 over 4 years, the total rise is 25%, but the average yearly rise is (1,000 ÷ 800)^1/4 − 1 = 5.7% a year, not 6.25%. On a phone calculator: 1,000 ÷ 800, then the x^y button with 0.25, then minus 1.

This is why steady inflation of 3% a year raises prices by over a third in ten years.

Spreadsheets

In Excel or Google Sheets, with the old value in A1 and the new in B1, use =(B1-A1)/A1 and format the cell as a percentage.

For discounts, see how to work out 20% off.