How to calculate percentage change
Percentage change compares a new value with where you started. The method is the one the U.S. Bureau of Labor Statistics uses for its index numbers: subtract the earlier value from the later one, divide by the earlier value, and multiply by 100.1
A positive answer is an increase and a negative answer is a decrease. The bars around old mean the size of the old value, ignoring its sign, which only matters when the starting value is negative.
Why the order matters
Going from 80 to 100 is +25%. Going from 100 back to 80 is -20%. Both are correct, because each is measured against a different starting value: 20 is a quarter of 80 but a fifth of 100. This is why a 50% rise followed by a 50% fall does not return you to the start. The table shows several pairs both ways round, with the percentage difference beside them for comparison.
| Values | Percentage change | Percentage difference |
|---|---|---|
| 80 to 100 | +25% | 22.22% |
| 100 to 80 | -20% | 22.22% |
| 50 to 75 | +50% | 40% |
| 75 to 50 | -33.33% | 40% |
| 200 to 100 | -50% | 66.67% |
| 100 to 200 | +100% | 66.67% |
| 1000 to 1100 | +10% | 9.52% |
| 1100 to 1000 | -9.09% | 9.52% |
Percentage change, percentage difference and percentage points
- Percentage change needs a starting point and depends on the order: 80 to 100 is +25%, 100 to 80 is -20%.
- Percentage difference has no starting point. It divides the gap by the average of the two values, so 80 and 100 differ by 22.22% in either order (22.22% the other way). Use it to compare two things side by side, such as two prices from two shops. For 120 and 90 it is 28.57%, against a change of -25%.
- Percentage points are the plain difference between two percentages. A rate moving from 5% to 6% has risen 1 percentage point, which is a +20% change. When a headline says a rate "rose 20%", check which one it means.
Average change per year
When a number changes over several years, the total change divided by the years is misleading, because each year's change is measured on a different base. A value that grows from 100 to 150 in 5 years changed by 50% in total, but not by 10% a year. The steady yearly rate that gets there is (150 ÷ 100) to the power of 1/5, minus 1, which is 8.45% a year. Check: 100 grown by that rate for 5 years is 150. Use the "Average change per year" mode for your own numbers; it needs a start and an end value above zero.
Edge cases
- The old value is 0. The change is undefined, because the formula divides by the old value. Describe it as an absolute change instead.
- The new value is 0. The change is always -100%: from 40 to 0 is -100%.
- The old value is negative. Dividing by the size of the old value keeps the sign meaningful: from -50 to -25 is +50% because the number rose by 25.
- Over 100%. A value that more than doubles has changed by more than 100%. Going from 100 to 250 is +150%.
The U.S. Bureau of Labor Statistics' worked example applies the method to index values: from 277.948 to 278.802 in one month is 0.3%, and from 278.802 to 296.797 over twelve months is 6.5%.1
In Excel or Google Sheets
With the old value in A1 and the new value in B1: change =(B1-A1)/ABS(A1) formatted as Percent; difference (positive values) =ABS(A1-B1)/AVERAGE(A1,B1); average change per year over N years =(B1/A1)^(1/N)-1.
Frequently asked questions
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value, and multiply by 100. From 120 to 90: (90 − 120) ÷ 120 × 100 = -25%, a 25% decrease.
Is percentage change the same as percentage increase or decrease?
They are the same calculation. A positive result is a percentage increase and a negative result is a percentage decrease. This page reports the direction in words. For increases only, with extra modes, see the percentage increase calculator.
Why is the percentage change different depending on which number comes first?
Because the starting value is the divisor. 80 to 100 is +25% (20 ÷ 80) and 100 to 80 is -20% (20 ÷ 100). If you have no natural starting point, use the percentage difference, which gives the same answer in either order.
What is the difference between percentage change and percentage difference?
Percentage change divides by the starting value and depends on the order. Percentage difference divides by the average of the two values and does not. 80 and 100 differ by 22.22%, but 80 to 100 is a change of +25%.
What is the difference between percentage change and percentage points?
Percentage points subtract one percentage from another: 5% to 6% is 1 point. Percentage change divides that by the starting percentage: (6 − 5) ÷ 5 × 100 = +20%. Reports about interest rates, polls and unemployment mix the two up often, so check which is meant.
How do I calculate the average percentage change per year?
Divide the end value by the start value, take the root that matches the number of years, subtract 1 and multiply by 100. From 100 to 150 over 5 years that is 8.45% a year. Dividing the 50% total by 5 to get 10% would overstate it.
Can a percentage change be more than 100%?
Yes for an increase: a value that more than doubles has grown by more than 100%. A decrease cannot exceed -100%, because that is the value falling to zero.
How do I calculate percentage change with a negative number?
Divide the difference by the size of the old value, ignoring its sign. From -50 to -25 the difference is 25 and the size of -50 is 50, so the change is +50%. Excel users write =(new-old)/ABS(old) for this.
How do I calculate percentage change in Excel?
With the old value in A1 and the new value in B1, enter =(B1-A1)/ABS(A1) and format the cell as Percent. For the average change per year over N years use =(B1/A1)^(1/N)-1.
Is what I type sent anywhere?
No. The calculation runs in your browser and the numbers you enter are not sent to a server. We count page visits with our own analytics on our own server, and those events carry no amounts or inputs.
Sources
- U.S. Bureau of Labor Statistics, Calculating percent changes (last modified February 9, 2023): the method, a one-month example (277.948 to 278.802) and a twelve-month example (278.802 to 296.797).
Every answer and table on this page is calculated by this page's own code, which is checked against an independent implementation in the site's test suite.