Working out percent change

Divide the change by the starting value, and when both numbers are already percentages, give the gap in percentage points.

Area: InformationFrom age 12Time to learn: 20 minutes

Subtract the old value from the new one, divide the result by the old value and multiply by 100; a positive answer is an increase and a negative answer is a decrease.

Why it matters

Prices, pay and rents are reported as percent changes, measured against where they started, and changes in interest rates are reported in percentage points. The US Bureau of Labor Statistics reports price movements this way because a change in index points depends on how high the index already is, while a percent change does not. In an international assessment of adults aged 16 to 65, the share of US adults at the lowest level in numeracy rose from 29% in 2017 to 34% in 2023.

In 2023, 34% of US adults aged 16 to 65 performed at the lowest level (Level 1 or below) in numeracy on the international PIAAC assessment, up from 29% in 2017.

Source: National Center for Education Statistics, Highlights of the 2023 U.S. PIAAC Results, 2023.Measured

How to do it

Write down the old value (where you started) and the new value (where you ended). The old value is the one you divide by.
Subtract the old value from the new one. A positive result is an increase; a negative result is a decrease.
Divide the result by the old value, then multiply by 100 to get the percent. This is the method the US Bureau of Labor Statistics uses for consumer prices.
Try an increase, using real US prices: the Consumer Price Index was 278.802 in December 2021 and 296.797 in December 2022. 296.797 − 278.802 = 17.995; 17.995 ÷ 278.802 = about 0.065; 0.065 × 100 = a 6.5% increase in a year.
Try a decrease: a jacket goes from $80 to $60 on sale. 60 − 80 = −20; −20 ÷ 80 = −0.25; −0.25 × 100 = −25%, a 25% decrease.
Check the answer by working forward from the old value: 25% of $80 is $20, and $80 − $20 = $60.
When both numbers are already percentages, such as rates, first give the gap in percentage points: subtract one from the other. A rate that goes from 20% to 22% rose 2 percentage points. As a percent change, it rose (22 − 20) ÷ 20 × 100 = 10%.
Practice on a real rate: the share of US adults at the lowest numeracy level went from 29% in 2017 to 34% in 2023. That is a rise of 5 percentage points, and 5 ÷ 29 × 100 = about a 17% increase.
Read inflation figures as percent changes from a year earlier. Statistics Canada reported that prices for food bought in stores rose 1.7% in the year to September 2026, after 2.8% in the year to August. Prices still went up, only more slowly; the rate fell 1.1 percentage points.
For a 12-month change, compare the same month in both years, such as December to December. Do not add up monthly changes to get a yearly one; BLS notes that the 12-month change is not their sum.

Common mistakes

Dividing by the new value instead of the old one. $40 to $50 is a 25% increase, but $50 back to $40 is a 20% decrease.
Calling the gap between two percentages a percent change: 20% to 22% is 2 percentage points, but a 10% increase.
Reading lower inflation as lower prices. Grocery inflation in Canada falling from 2.8% to 1.7% means grocery prices rose more slowly, not that they fell.
Adding up monthly percent changes to get a yearly change.
Reading a rate rise of 1/4 percentage point as a 0.25% increase. When the Federal Reserve raised its target range by 1/4 percentage point in September 2026, to 3-3/4 to 4 percent, the bottom of the range went from 3.5% to 3.75%, an increase of about 7%.

You can do this when …, with a phone calculator, you can show that $40 to $50 is a 25% increase, that $50 back to $40 is a 20% decrease, and that a rate going from 4% to 5% rose 1 percentage point, which is a 25% increase.