How to Calculate Percentage Increase (With Examples)

The formula for percentage increase is:

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

The key is to always divide by the old (original) value.

Worked examples

A pay raise: your salary goes from $52,000 to $55,120.

1. Subtract: $55,120 − $52,000 = $3,120.
2. Divide by the old value: $3,120 ÷ $52,000 = 0.06.
3. Multiply by 100: 6%.

A rent increase: rent rises from $1,450 to $1,595. ($1,595 − $1,450) ÷ $1,450 = 0.10, a 10% increase.

A price that doubled: $40 to $80 is ($80 − $40) ÷ $40 = 1.00, a 100% increase. Tripling is a 200% increase.

Adding a percentage to a number

To increase a number by a percentage, multiply by (1 + percentage). A 3% raise on $52,000 is $52,000 × 1.03 = $53,560. This multiplier (1.03 here) is also handy in spreadsheets.

Percentage decrease

Same idea, the other way round: (old − new) ÷ old × 100. A price that falls from $80 to $60 dropped ($80 − $60) ÷ $80 = 25%.

Four common mistakes

1. Dividing by the new number

From $80 to $100 is a 25% increase (20 ÷ 80). Dividing by the new value (20 ÷ 100) gives 20%, which is wrong.

2. Mixing up percent and percentage points

If an interest rate goes from 3% to 4%, it rose by 1 percentage point, but by 33.3 percent ((4 − 3) ÷ 3). News reports often blur the two. When in doubt, say "percentage points" for the difference between two rates.

3. Adding successive increases

Two 10% increases in a row add up to 21%, not 20%, because the second 10% applies to the already-higher number: 1.10 × 1.10 = 1.21. The same goes for annual raises, rent increases and investment growth.

4. Assuming a drop and a rise cancel out

If a price goes up 20% and then down 20%, you don't end where you started: 1.20 × 0.80 = 0.96, a 4% loss overall. Losses need bigger gains to recover:

Did your raise beat inflation?

To compare a raise with inflation, divide rather than subtract: (1 + raise) ÷ (1 + inflation) − 1. A 6% raise in a year with 3% inflation is a real raise of 1.06 ÷ 1.03 − 1 = 2.9%. Simply subtracting (6% − 3% = 3%) is a close enough shortcut when both numbers are small.

Average growth per year

If something grew over several years, the total percentage increase overstates the yearly rate. To find the average annual growth, use: (new ÷ old)^(1 ÷ years) − 1.

A home that rose from $200,000 to $300,000 over 5 years increased 50% in total, which is about 8.4% a year, not 10%, because each year's growth builds on the last.

In a spreadsheet

In Excel or Google Sheets, with the old value in A2 and the new value in B2, use =(B2−A2)/A2 and format the cell as a percentage.

Skip the math

The Percentage Increase Calculator finds the percentage change between two numbers or adds a percentage to a number, and warns you if the change is really a decrease. For falls, use the Percentage Decrease Calculator; for anything else, the Percentage Calculator.