How to use the percentage calculator
Pick what you want to work out at the top of the calculator:
- Change from A to B gives the percentage increase or decrease from a starting value to a new one, such as an old and a new price, or your pay before and after a raise. Increases show a plus sign and decreases a minus sign.
- Add or take off % increases or decreases a number by a percentage, such as 25% off a price or a 5% pay rise.
- Difference compares two values when neither one is the starting point, such as the same item in two shops.
The answer updates as you type, with the working underneath so you can check it. Copy result copies a one-line summary.
The percentage change formula
Percentage change = (new value − starting value) ÷ starting value × 100
This is the same method the US Bureau of Labor Statistics sets out for price changes: subtract the earlier value from the later one, then "divide that difference by the earlier index value", and multiply by 100. A positive answer is an increase and a negative one is a decrease.
| Example | From | To | Working | Change |
|---|---|---|---|---|
| Test score | 64 | 80 | 16 ÷ 64 | +25% |
| Price of a jacket | $80 | $60 | −20 ÷ 80 | −25% |
| Hourly pay | $18.00 | $18.90 | 0.90 ÷ 18 | +5% |
| Town population | 12,500 | 13,100 | 600 ÷ 12,500 | +4.8% |
The result also shows the new value as a percentage of the old one. A score of 80 is 125% of 64, which is the same as saying it went up by 25%.
Working out a pay rise percentage
Choose Change from A to B, put your old pay in A and your new pay in B. A salary going from $42,000 to $44,100 is a rise of $2,100, and 2,100 ÷ 42,000 × 100 = 5%. In the UK, £28,000 to £29,400 is also a 5% pay rise. Use the same kind of figure for both: annual to annual, or hourly to hourly, and both before tax or both after.
To go the other way and see what a rise is worth, choose Add or take off %: $18 an hour plus 5% is 18 × 1.05 = $18.90.
Adding or taking off a percentage
To increase a number by a percentage, multiply it by 1 plus the percentage as a decimal. To decrease it, multiply by 1 minus the percentage. A $40 jacket with 25% off costs 40 × 0.75 = $30.
A rise and a fall of the same percentage do not cancel out, because the second one starts from a different number. A price of $80 that goes up 25% becomes $100. Take 25% off $100 and you get $75, not $80. To undo a 25% increase you need a 20% decrease, since 20 is 20% of 100.
Percentage difference is not percentage change
Percentage change has a direction: it starts from one value and measures the move to the other. Percentage difference compares two values on an equal footing, by dividing the gap by their average:
Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
The bars around A − B mean the size of the gap, ignoring any minus sign. If one shop sells an item for $45 and another for $55, the gap is 10 and the average is 50, so the percentage difference is 20%, whichever shop you name first. Compare that with percentage change: from $45 up to $55 is +22.22%, but from $55 down to $45 is −18.18%. Use change when there is a before and an after, and difference when there is not.
Percent or percentage points?
When the values are already percentages, a change can be described two ways. The UK Office for National Statistics puts it simply: "A percentage point is the difference between percentages. A value of 10% falling by 1 percentage point becomes 9%", whereas "A fall of 1% would result in a value of 9.9%."
So if a class's pass rate goes from 60% to 66%, it rose by 6 percentage points, which is a 10% increase (6 ÷ 60). Both are correct; say which one you mean.
Zero and negative numbers
- Starting from 0. Percentage change divides by the starting value, and nothing can be divided by 0. Going from 0 to 30 is an increase of 30, but not any percentage, so the calculator says the result is undefined and shows the plain difference.
- Negative starting values. If A is below zero, the calculator divides by its size without the minus sign, so a rise always shows as an increase: from −10 to −5 is +50%. Percentages of values that are below zero, or that cross zero, are often not meaningful, so treat them with care.
- Taking off more than 100% gives a negative result, which is rarely what you want for a price.
Questions and answers
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 64 to 80: 80 minus 64 is 16, 16 divided by 64 is 0.25, and 0.25 times 100 is a 25% increase.
How do I calculate a percentage decrease?
The same way. The new value is smaller, so the answer is negative. From $80 to $60: 60 minus 80 is minus 20, divided by 80 is minus 0.25, so the price fell by 25%.
What percentage pay rise have I had?
Choose Change from A to B, enter your old pay as A and your new pay as B. From 42,000 to 44,100 is a 5% rise. Compare like with like: both annual or both hourly, both before tax or both after.
Why does a 25% rise followed by a 25% cut not get me back to where I started?
Because the cut is 25% of the bigger number. 80 plus 25% is 100, and 100 minus 25% is 75. To undo a 25% rise you need a 20% cut.
What is the difference between percentage change and percentage difference?
Percentage change measures a move from a starting value, so its size depends on which value comes first. Percentage difference divides the gap by the average of the two values, so it is the same either way round.
Why can I not work out a percentage change from zero?
The formula divides by the starting value, and dividing by zero has no answer. Describe the change as a plain number instead, such as "up by 30 from zero".
Sources
Checked on 7 October 2026. If a rule has changed, please tell us.