How to calculate percentage increase

The formula

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

1. Subtract. Take the original value away from the new value to get the change.
2. Divide by the original. Always divide by the starting value, never the new one. This is the step people get wrong.
3. Multiply by 100. That turns the fraction into a percentage.

In a spreadsheet, with the original in A1 and the new value in B1, use =(B1-A1)/A1 and format the cell as a percentage.

Worked examples

A negative result means the value fell. The formula is the same, and you can report it as a 20% decrease.

Increasing a number by a percentage

The opposite question, “what is 80 plus 15%?”, uses the same multiplier idea. Add the percentage to 100 and multiply:

80 × 1.15 = 92, which is the same as 80 + (15% of 80 = 12)

For a decrease, take the percentage away from 100 instead: 80 less 15% is 80 × 0.85 = 68. Thinking in multipliers makes the next three traps much easier to spot.

Up and back down are not the same percentage

Going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease. The change is 20 both times, but the starting value is different, so the percentage is too.

This is why losses are hard to recover from. A price that falls by 50% has to rise by 100% to get back to where it was, because the rise starts from the lower number.

Two increases in a row don’t simply add up

Write each change as a multiplier: a 10% increase is × 1.10, a 50% decrease is × 0.50. Then multiply them.

Up 10%, then up 10% again: 1.10 × 1.10 = 1.21, so 21% in total, not 20%

Down 50%, then up 50%: 0.50 × 1.50 = 0.75, so 25% lower than the start

The same logic applies to stacked discounts, such as 20% off and then an extra 10% off at the till. That’s 28% off in total, not 30%. The discount calculator handles the sale-price side.

Working backwards to the original value

If you know the new value and the percentage, divide by the multiplier. Don’t take the percentage off the new value.

A price after an 8% rise is $54.00. Original: 54 ÷ 1.08 = $50.00

Taking 8% off $54.00 gives $49.68, which is wrong, because the 8% was worked out from the original $50, not from $54.

Percentage points versus percent

When the values are themselves percentages, such as interest rates, two different answers are both correct, and they mean different things:

• An interest rate going from 4% to 5% rose by 1 percentage point (5 − 4).
• It also rose by 25%, because 1 ÷ 4 = 0.25.

Say which one you mean. “Rates rose 1%” is ambiguous. “Rates rose 1 percentage point” isn’t.

Percentage difference is something else again

To compare two values where neither is the “before”, such as prices in two shops, people use the percentage difference: the gap divided by the average of the two. For $40 and $50 that’s 10 ÷ 45 ≈ 22.2%. It’s different from both the 25% increase (40 to 50) and the 20% decrease (50 to 40), so only use it when there is no starting point.

Average growth per year

If something grew 50% over 3 years, it didn’t grow 16.67% a year, because each year’s growth builds on the last. Take the root of the total multiplier instead:

(1.50)^(1/3) − 1 ≈ 0.1447, so about 14.47% a year

Check: 1.1447 × 1.1447 × 1.1447 ≈ 1.50.

Starting from zero or a negative number

• From zero there is no percentage increase, because you can’t divide by zero. Going from 0 to 15 sales is “up 15”, not an infinite percentage.
• From a negative number, such as a loss of −$2,000 becoming a profit of $1,000, divide by the size of the starting value (2,000), so the sign shows the direction: +3,000 ÷ 2,000 = +150%. Many people prefer to report the change in money terms here, because the percentage is easy to misread.