Percentage Change Calculator
Use this percentage increase decrease calculator to compare two numbers or apply a percentage to a value, with every step shown.
Quick answer: Percentage change is the difference between the new and old value divided by the old value, multiplied by 100. Going from 40 to 50 is a 25% increase, because (50 − 40) ÷ 40 × 100 = 25. A negative result is a percentage decrease. The calculator also adds or takes off a percentage from any number.
How to use the Percentage Change Calculator
- Choose the calculation. Pick percentage change between two numbers, or increase or decrease a number by a percentage.
- Enter the numbers. Type the old and new values, or the starting number and the percentage.
- Read the steps. See the result with the formula and every step shown so you can check it by hand.
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.
Percentage Increase and Decrease, Explained
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.
Finding the Percentage Change Between Two Numbers
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.
Mistakes people make with percentages
- 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.
The formula and why direction matters
Percentage change compares a new value with an old one and expresses the gap as a share of the old value: (new − old) ÷ old × 100. Going from 40 to 50 is a 25% increase because the 10 gained is a quarter of 40. Going back from 50 to 40 is a 20% decrease, because the same 10 is now measured against a larger starting point of 50.
That is why the calculator asks which number is the starting value. The base you divide by decides the answer, so the result changes if the two numbers swap places.
Percentage change examples: rises, falls and small starting values
The table applies the formula to four pairs of numbers, exactly as the calculator does. A small starting value produces large percentages, because the change is measured against a small base.
| Old value | New value | Change | Percentage change |
|---|---|---|---|
| 250 | 300 | +50 | +20% |
| 80 | 68 | −12 | −15% |
| 2 | 5 | +3 | +150% |
| 0 | 20 | +20 | Cannot be calculated |
The last row is not a gap in the table: a change from zero has no percentage, because dividing by zero is undefined, and the calculator asks for a non-zero starting value instead. When a starting value is tiny, give the absolute change alongside the percentage so the result is not misleading. For selling prices, the profit margin calculator measures profit against the price rather than against an old value.
Percent versus percentage points
A rate that moves from 4% to 5% has risen by one percentage point, but by 25% in relative terms. News about interest rates, inflation, polls and unemployment mixes the two constantly. Use the calculator on the two values themselves for the relative change, and simple subtraction for the change in points.
Why a rise and a matching fall do not cancel out
Successive percentages apply to different bases. A price of 100 that rises 50% becomes 150; a 50% fall then takes it to 75, not back to 100. The recovery needed after a fall is always larger than the fall itself.
| Fall | Rise needed to get back |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 25% | 33.3% |
| 50% | 100% |
Adding or taking off a percentage
To apply a percentage directly, multiply by a factor: 1.15 to add 15% and 0.80 to take off 20%. Adding 15% to 60 gives 69, and taking 20% off 60 gives 48. The increase and decrease modes do exactly this and show the working line by line.
Percentage change or percentage difference?
Percentage change assumes one value came first. When neither number is the original, for example comparing two products, some people use the symmetric percentage difference: the gap divided by the average of the two. For 40 and 50 that is 10 ÷ 45 ≈ 22.2%, against a 25% change from 40. This calculator reports change from the first value, so use the average method by hand when you need a neutral comparison.
For related jobs, the reverse percentage calculator works back to an original price and the discount calculator chains several percentage steps.
Frequently Asked Questions (FAQs)
Subtract the old value from the new value, divide by the old value and multiply by 100. A positive result is an increase and a negative one a decrease. For 40 rising to 50: (50 − 40) ÷ 40 × 100 = 25%. From 50 down to 40: (40 − 50) ÷ 50 × 100 = −20%. The calculator labels the result as an increase or a decrease for you.
Percentage points measure the simple gap between two percentages, while percentage change measures that gap relative to the starting figure. If a rate goes from 4% to 5%, it has risen by 1 percentage point but by 25% in relative terms. Enter 4 and 5 in the calculator for the relative change, and subtract them yourself for the change in points.
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.
Subtract the old value from the new value, divide by the old value and multiply by 100. The percentage increase from 50 to 75 is (75 − 50) ÷ 50 × 100 = 50%.
Percentage change = (new − old) ÷ old × 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%. A negative result means a percentage decrease instead.
Enter the old and new value. The calculator gives the percentage change relative to the old value. For a symmetric percentage difference, divide the gap by the average of the two numbers instead.
Choose Increase by %, enter the number and 15. The result is the number multiplied by 1.15, with the increase shown separately.
Choose Decrease by %, enter the number and 20. The result is the number multiplied by 0.8, and the amount taken off is shown.
The change is 20, which is 25% of the starting value of 80. So 80 to 100 is a 25% increase, and 100 back to 80 is a 20% decrease – the two directions are never the same percentage.
Estimates only – not financial advice. Results use only the numbers you enter and standard percentage maths. They do not account for taxes, fees or other charges that may apply to a real price or payment. Check important figures with the seller, your payslip or a qualified adviser. See our full disclaimer.
Guides that use this calculator
- How to Calculate Percentage Increase and Decrease: Formula and Examples – Percentage change = (new − old) ÷ old × 100. Going from 40 to 50 is +25%. Worked examples, a quick table and the mistakes that give wrong answers.
- Percentages Explained: Of, Increase, Decrease and Reverse – 15% of 80 is 12; 12 is 15% of 80; add 15% to 80 for 92; a 15% rise that ended at 92 started at 80. Four percentage questions, each with a worked example.