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 do you 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.
What is the formula, and what does a worked example look like?
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.
Worked examples for the Percentage Change Calculator
Each figure below was produced by the same code as the calculator, so you can enter the inputs and get the same result. Rates and thresholds are the ones on the official pages linked under “How it is calculated”.
Rent rises from £950 to £1,045 a month
Old value is the starting point, new value the end point.
- Change: £1,045.00 − £950.00 = £95.00.
- Percentage change: £95.00 ÷ £950.00 × 100 = 10.0%.
Result: A 10.0% increase (a multiplier of 1.100).
Gas falls from $4.20 to $3.78 a gallon
A decrease gives a negative percentage change.
- Change: $3.78 − $4.20 = $-0.42.
- $-0.42 ÷ $4.20 × 100 = -10.0%.
Result: A 10.0% decrease.
Percentage change vs percentage points: a rate from 4.50% to 5.25%
The same pair of numbers gives two different, correct answers.
- Percentage points: 5.25 − 4.50 = 0.75 points.
- Percentage change: 0.75 ÷ 4.50 × 100 = 16.7%.
Result: A rise of 0.75 percentage points is a 16.7% increase in the rate itself.
How is the Percentage Change Calculator calculated, and where do the rates come from?
Percentage change = (new value − old value) ÷ |old value| × 100. A positive result is an increase, a negative one a decrease, and the multiplier (new ÷ old) turns the same idea into a factor you can apply to other numbers. The calculator also shows the absolute difference so you can see both the size and the rate of the change.
The old value is the base, which is why a change from 50 to 40 is −20% but a change from 40 to 50 is +25%: the same gap of 10 is measured against a different starting figure. A percentage change from zero is undefined, so the calculator asks for a non-zero starting value.
Official inflation figures are reported as percentage change over 12 months in the same way: the ONS publishes UK CPI that way, and the Bureau of Labor Statistics reports US CPI changes month to month and year on year. Use this calculator to reproduce a price change over any period you choose.
Read the sign before the size. A positive result means the new value is higher than the old, a negative result means it is lower, and zero means no change. When you describe a change in words, say what it is measured against: 'prices are 8% higher than a year ago' compares with the same month last year, not with last month, and the two can differ a lot when prices are seasonal.
- ONS – Inflation and price indices – How UK consumer price inflation (CPI, CPIH, RPI) is published as a percentage change over 12 months.
- US Bureau of Labor Statistics – Consumer Price Index – How US price changes are reported month to month and year on year.
What are the common mistakes and edge cases?
- Using the new value as the base. The base is always the old (starting) value.
- Mixing up percentage points and percent. Going from 4.5% to 5.25% is 0.75 percentage points, or 16.7% higher in relative terms.
- Expecting an increase and a decrease of the same percentage to cancel out. +20% then −20% leaves you 4% below where you started.
- Averaging yearly percentage changes to get a multi-year change. Percentages compound, so multiply the factors instead.
- Calculating change from zero. It cannot be expressed as a percentage; describe it as an absolute change.
More in this category: Percentages & Pricing calculators.
What is a percentage increase or decrease?
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 do you find 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 does percentage change matter?
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.
Worked problem: ticket prices and the number of customers
A question that people search word for word: a movie theatre charges $5 a ticket and averages 300 customers a night. If the price rises to $7, the theatre estimates that nightly ticket sales will be $1,750. What is the percentage change in the average number of customers?
Sales are the price times the number of customers, so after the rise there are $1,750 ÷ $7 = 250 customers. The percentage change is (250 − 300) ÷ 300 × 100 = **−16.67%**, which rounds to **−17%**. Before the rise, sales were $5 × 300 = $1,500, so revenue goes up 16.67% while customers go down. Enter 300 as the old value and 250 as the new value to check it.
Why +50% then −50% does not get you back
A percentage change is always measured against the starting value, so reversing it needs a different percentage. A price of 100 that rises 50% becomes 150. Cutting 50% from 150 gives 75, not 100. To get back, you need a fall of 50 ÷ 150 = 33.33%.
| Rise | 100 becomes | Fall needed to return to 100 |
|---|---|---|
| 10% | 110 | 9.09% |
| 25% | 125 | 20.00% |
| 50% | 150 | 33.33% |
| 100% | 200 | 50.00% |
The reverse is also true: a 20% fall needs a 25% rise to recover. This is why the percentage change calculator reports the direction and the base value, and why two opposite changes of the same size lose or gain value.
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.
Customers fall from 300 to 250 (1,750 ÷ 7), a change of −16.67%, or −17% to the nearest whole number.
Because each percentage applies to a different base. 100 up 50% is 150, and 150 down 50% is 75. You would need a 33.33% fall to return to 100.
Subtract the new value from the old, divide by the old value and multiply by 100. The calculator shows the result as a negative percentage change.
Add the percentage to 100 and divide by 100: +12% is ×1.12 and −12% is ×0.88. Multiply a value by the multiplier to apply the change.
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.