Percentage Change Calculator
Work out the percent increase or decrease from an old value to a new one, compare two numbers with the percentage difference, or reverse a change to find the original value. Every answer comes with the working.
How to use the Percentage Change Calculator
- Choose a mode: Percent change, Percent difference, Find original or Apply % change.
- Enter your numbers. For a change, type the old (starting) value and the new value.
- Read the answer, for example “increase of 25%”, plus the difference and the multiplier.
- Check the working under the result to see exactly how it was calculated.
- Press Copy to paste the result into a report, spreadsheet or message.
Percentage change formula with examples
Percentage change = (new value − old value) ÷ old value × 100. A positive answer is an increase and a negative answer is a decrease.
| Old | New | Working | Result |
|---|---|---|---|
| 80 | 100 | (100 − 80) ÷ 80 × 100 | 25% increase |
| 100 | 80 | (80 − 100) ÷ 100 × 100 | 20% decrease |
| 50 | 150 | (150 − 50) ÷ 50 × 100 | 200% increase (tripled) |
| 1,200 | 1,020 | (1,020 − 1,200) ÷ 1,200 × 100 | 15% decrease |
| 4.5 | 4.95 | (4.95 − 4.5) ÷ 4.5 × 100 | 10% increase |
Notice that going from 80 to 100 is a 25% increase, but going back from 100 to 80 is only a 20% decrease. The base is always the starting value, which is why percentage changes are not symmetric.
Increase needed to recover from a loss
Because each change is measured from a different base, recovering from a fall always takes a larger percentage rise. This matters for investments, prices and sales figures:
| Decrease | Increase needed to get back |
|---|---|
| 10% | 11.11% |
| 20% | 25% |
| 25% | 33.33% |
| 33.33% | 50% |
| 50% | 100% |
| 75% | 300% |
The rule is: increase needed = d ÷ (1 − d), where d is the decrease as a decimal.
Which percentage should you use?
- Percent change – when one value came first: last year vs this year, price before vs after, starting weight vs current weight.
- Percent difference – when neither value is the reference: comparing two shops, two measurements or two products. It divides by the average, so the answer is the same in both directions.
- Find original – when you only know the final value and the percentage, such as a price after a 20% markup or a salary after a 5% raise.
- Apply % change – to add or take off a percentage, for example adding 8% sales tax or taking 15% off a price.
For changes over several years, an average yearly growth rate is more useful than the total change; the CAGR calculator works that out.
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 80 to 100 the change is (100 - 80) / 80 x 100 = 25%, an increase. A negative result is a decrease.
What is the difference between percentage change and percentage difference?
Percentage change has a direction: it measures how much a value moved from a starting point, so the old value is the base. Percentage difference compares two values on equal terms, dividing the gap by their average, so swapping the numbers gives the same answer. Use change for before-and-after data and difference for comparing two separate things.
If something rises 20% and then falls 20%, is it back where it started?
No. A 20% rise takes 100 to 120, and a 20% fall from 120 is 24, leaving 96. Each percentage is applied to a different base, so after a fall you need a bigger rise to recover: a 20% drop needs a 25% increase to get back.
How do I find the original number before a percentage increase?
Divide the new value by 1 plus the percentage as a decimal. If a price is 120 after a 20% increase, the original was 120 / 1.20 = 100. For a decrease, divide by 1 minus the percentage, so 75 after a 25% discount was 75 / 0.75 = 100.
Can you calculate a percentage change from zero?
Not in a meaningful way. Dividing by an old value of zero gives an infinite or undefined percentage, so any growth from zero is usually described with the absolute difference instead, for example "up from 0 to 50".
What is the difference between percent and percentage points?
Percentage points measure the simple gap between two percentages, while percent change measures the relative change. An interest rate moving from 4% to 5% has risen by 1 percentage point, which is a 25% increase.