Percentage Change Calculator
Use this percentage increase decrease calculator to compare two numbers or apply a percentage to a value, with every step shown.
Formula & worked example
Formula: Percentage change = (new − old) ÷ |old| × 100.
Example: From 40 to 50: (50 − 40) ÷ 40 × 100 = 25% increase. From 50 to 40: −20%.
Method & source: Standard percentage-change formula (new − old) ÷ |old| × 100. See how we test our calculators.
Next step: try stacked discounts or reverse percentages or profit margin.
What Is a Percentage Change Calculator?
A percentage change calculator shows how much a number has grown or shrunk relative to where it started. It is the fastest way to answer questions like “what is the percentage increase from 40 to 50?” or “how big was that price drop?”.
This percentage increase decrease calculator also works the other way round: give it a value and a percentage and it returns the increased or decreased figure, with the formula and every step written out.
How Our Percentage Change Calculator Works
Pick one of three modes and enter your numbers.
- Change between two values: Percentage change = (new − old) ÷ |old| × 100.
- Increase by a percentage: New value = value × (1 + percent ÷ 100).
- Decrease by a percentage: New value = value × (1 − percent ÷ 100).
- Step-by-step working: Each calculation is shown with your own numbers substituted in.
- Clear direction: Results are labelled as an increase, a decrease or no change.
Seeing the working means you can check the answer, learn the method and reuse it in a spreadsheet.
Why Percentage Change Matters
Percentages put changes into context. A £5 rise means something very different on a £10 item than on a £500 one.
- Compare prices before and after a sale or rise.
- Track growth in sales, followers, savings or salary.
- Measure weight, grades or performance changes over time.
- Understand inflation, interest and exchange-rate moves.
- Explain results clearly in reports and presentations.
Once you can calculate percentage increase and decrease quickly, headlines and price tags become much easier to judge.
Worked walkthrough: a rent increase
Monthly rent rose from 850 to 935. The difference is 85, and 85 divided by the old value of 850 is 0.10, so the rent increased by 10%. If the landlord had instead asked for a further 8% on 935, the “increase by percentage” mode gives 935 × 1.08 = 1,009.80. Reversing a rise is not symmetrical: to get back from 935 to 850 you would need a decrease of about 9.09%, not 10%, because the percentage is now taken from a larger number.
Practical tips for percentage change calculations
- Always divide by the old (starting) value, not the new one. Dividing by the wrong number is the most common percentage mistake.
- Do not confuse percent with percentage points. A rate rising from 4% to 5% is a 1 percentage point rise but a 25% increase.
- Successive percentages do not add up. A 10% rise followed by a 10% fall leaves you 1% below where you started.
- For a negative starting value the result is not really meaningful; the tool shows a note and measures against the size of the old value.
- Use the “decrease by %” mode to check a discount quickly, then use the Reverse Percentage Calculator if you only know the sale price.
Frequently Asked Questions (FAQs)
Subtract the old value from the new value, divide by the old value and multiply by 100. For 40 rising to 50: (50 − 40) ÷ 40 × 100 = 25% increase.
Use the same formula. If the new value is lower the result is negative, which means a decrease. From 50 to 40: (40 − 50) ÷ 50 × 100 = −20%.
Because the second percentage applies to a larger number. 100 up 50% is 150, and 150 down 50% is 75, not 100.
No. A percentage change from zero is undefined because you cannot divide by zero, so the calculator asks for a non-zero starting value.
The calculator divides by the absolute value of the starting number, so an increase always produces a positive percentage and a decrease a negative one.