Measure a rise or a fall in percent
Raw numbers do not tell you much on their own. A price that went up by 150 could be a huge jump or barely worth noticing, depending on where it started. Percent change puts every rise and fall on the same scale, so a 12% increase in rent and a 12% increase in sales mean the same size of move.
This calculator does two jobs. Give it an old value and a new value and it tells you the percent increase or decrease. Or give it a number and a percent, and it raises or lowers the number by that much, which is what you need when you are putting your prices up by 8% or working out a new figure after a cut.
How to use it
- Choose Change between two values or Increase or decrease by a percent.
- For a change, enter the old value first and the new value second. The order decides whether the answer is an increase or a decrease.
- To apply a percent, enter the starting number, choose Increase or Decrease, and type the percent.
- The answer shows the percent, the difference in plain numbers and the multiplier. Below that, each step is written out.
The percent change formula
percent change = (new − old) ÷ |old| × 100
new value = old value × (1 + percent ÷ 100) for a rise
new value = old value × (1 − percent ÷ 100) for a fallThe bars around old mean "ignore the minus sign". That only matters when the starting value is negative, like a temperature or a balance below zero. A positive answer is an increase and a negative one is a decrease.
Dividing by the old value is the whole point. Percent change always asks "how big was the move compared with where we started?" That is also why a change from 0 has no percent: there is nothing to compare it with.
Worked example: a price rise from 1,250 to 1,400
A supplier raises a monthly fee from 1,250 to 1,400. How big is the rise?
- Difference: 1,400 − 1,250 = 150
- Compared with the old fee: 150 ÷ 1,250 = 0.12
- As a percent: 0.12 × 100 = 12%
That is a 12% increase. The multiplier is 1.12, which is handy in a spreadsheet: multiply any old figure by 1.12 to get the new one. Switch to Increase or decrease by a percent, enter 1,250 and 12%, and you land back on 1,400.
Increases and decreases are not mirror images
A 50% fall followed by a 50% rise does not get you back to where you began. Start at 200, drop 50% to 100, then rise 50% to 150. The rise is worked out on the smaller number, so it adds back less than the fall took away.
| Fall | Rise needed to get back |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 25% | 33.3% |
| 50% | 100% |
| 75% | 300% |
This matters for prices, traffic and sales figures alike. If a busy month was 25% down on the one before, you need a 33.3% rise just to be level again.
Mistakes to watch for
- Dividing by the new value instead of the old one. From 80 to 100 is a 25% increase; from 100 to 80 is a 20% decrease. Same gap, different starting point.
- Calling a change in a rate a percent change. Moving from 3% to 4% is 1 percentage point, but a 33% increase in the rate itself.
- Adding percent changes over several years. Three years of 10% growth is 33.1% in total, not 30%, because each year builds on the one before. For yearly averages, the CAGR calculator is the right tool.
Frequently asked questions
How do I calculate a percentage increase?
Take the old value from the new one, divide by the old value, and multiply by 100. From 80 to 92 is 12 ÷ 80 × 100 = 15%. If the answer comes out negative, it is a decrease rather than an increase. The calculator does the sum as you type and says which way the change went.
How do I add a percentage to a price?
Multiply the price by 1 plus the percent as a decimal. To add 8% to 450, multiply by 1.08 and you get 486. Choose Increase or decrease by a percent, pick Increase and enter 8. To take a percent off instead, multiply by 1 minus the decimal, so 0.92 for 8% off.
What is the average rate of change formula?
The average rate of change is the change in a value divided by the change in time, or any other input. If sales went from 1,000 to 1,600 over 3 months, the average rate is 600 ÷ 3 = 200 a month. That is a straight-line average. For an average percent per period that builds on itself, use the growth rate calculator.
Why is a 50% drop not undone by a 50% rise?
Because each percent is worked out on a different starting number. After a 50% drop from 200 you are at 100, and 50% of 100 is only 50, so you climb back to 150. To get back to 200 you need a 100% rise. The table on this page shows the rise needed for other falls.
What is the difference between percent change and percent difference?
Percent change has a direction: it compares a new value with an old one, so the order matters. Percent difference compares two values that have no before and after, like two quotes, and uses their average as the base. For that, use the percentage difference calculator.
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