Percentage Change Calculator
Percentage increase, decrease and difference between two numbers.
Percentage change between two numbers
Enter the starting (old) value and the finishing (new) value. The result is positive for an increase and negative for a decrease.
Percentage change
+15%
A increase of 15%: 80 became 92.
Before and after
Why +10% then −10% doesn't get you back
Each percentage is taken from a different base. Starting at 100, a 10% rise gives 110; a 10% fall from there takes off 11 and leaves 99, a net change of -1%. Going down first and then up lands in the same place (99).
| If it falls by | 100 becomes | Rise needed to recover |
|---|---|---|
| 10% | 90 | 11.11111111% |
| 20% | 80 | 25% |
| 25% | 75 | 33.33333333% |
| 50% | 50 | 100% |
| 75% | 25 | 300% |
How to Use the Percentage Change Calculator
Enter an old value and a new value and the percentage change calculator shows the increase or decrease as a percentage, the absolute change and the multiplier, with every step of the working. The other tabs cover the questions that usually sit next to it: percentage difference between two numbers, the change between two rates in percentage points, the average percentage change per year over several years, increasing or decreasing a number by a percentage, a reverse percentage calculator for finding the original, and X% of Y.
Percentage Formulas
Average change per year = ((end ÷ start)1 ÷ years − 1) × 100
Example: a rate falling from 4.35% to 3.6% is −0.75 percentage points (−75 basis points), but a 17.24% fall in the rate itself. A population growing from 25,000,000 to 27,500,000 over 5 years has risen 10% in total, which is an average of about 1.92% a year compounded, not 2%.
Multiplier = new ÷ old
Positive means an increase, negative means a decrease. The old value cannot be zero.
Symmetric: it uses the average of the two numbers as the base, so a and b can be swapped.
Decrease by X% = number × (1 − X ÷ 100)
Reverse = final value ÷ (1 ± X ÷ 100)
X% of Y = X ÷ 100 × Y and X is what % of Y = X ÷ Y × 100
Worked Examples
Percentage increase, 80 to 92. The change is 92 − 80 = 12. Divide by the old value: 12 ÷ 80 = 0.15, and multiply by 100 for an increase of 15%. The multiplier is 92 ÷ 80 = 1.15. Applying the other way round, 80 increased by 15% is 80 + 12 = 92.
Percentage decrease, 250 to 200. The change is 200 − 250 = −50, and −50 ÷ 250 = −0.2, so the result is −20%, a decrease of 20%. The multiplier is 0.8.
Percentage difference, 40 and 60. The gap is |40 − 60| = 20 and the average is (40 + 60) ÷ 2 = 50, so the difference is 20 ÷ 50 × 100 = 40%. Measured as a change from 40 to 60 it would be 50%, which is why the two ideas should not be mixed up.
Reverse percentage, 115 after a 15% increase. The multiplier is 1.15, so the original is 115 ÷ 1.15 = 100. For a value of 80 after a 20% decrease the multiplier is 0.8 and the original is 80 ÷ 0.8 = 100.
Percentage Change vs Percentage Difference vs Percentage Points
These three get mixed up all the time. Percentage change has a direction and a starting point: use it for prices, populations, results or anything that moves from an earlier value to a later one. Percentage difference has no direction: use it to compare two measurements, such as two quotes or two test results, when neither is the baseline. Percentage points are used only when both numbers are already percentages. A rate that moves from 4% to 5% has risen by 1 percentage point, but by 25% in relative terms. News stories use these interchangeably when they should not, so check which one is meant.
Why Percentages Don't Simply Cancel
A 10% rise followed by a 10% fall leaves you at 99 if you started at 100, not back at 100, because the fall is worked out on the higher number. The card under the calculator shows how large a rise is needed to recover from different falls. A 50% fall needs a 100% rise, and the bigger the fall, the more disproportionate the climb back up.
Frequently Asked Questions
- What is the percent change formula?
- Percentage change = (new value − old value) ÷ |old value| × 100. A positive answer is an increase and a negative answer is a decrease. For example, going from 80 to 92 is (92 − 80) ÷ 80 × 100 = 15%, an increase of 15%.
- How do I calculate percentage change between two numbers?
- Subtract the old number from the new one, divide by the old number, then multiply by 100. The old number is the one you are measuring from, so the order matters: 250 down to 200 is −20%, but 200 up to 250 is +25%. If neither number is really the starting point, you want percentage difference instead.
- How do I calculate a percentage increase between two numbers?
- Use the same formula: (new − old) ÷ old × 100, where the new number is larger. A rise from 40 to 60 is (60 − 40) ÷ 40 × 100 = 50%. To go the other way and apply a known increase, multiply by 1 plus the percentage as a decimal, so 80 increased by 15% is 80 × 1.15 = 92.
- How do I use a percentage decrease calculator?
- Enter the original value and the lower new value on the Percentage change tab, or enter a starting number and a percentage on the Increase / decrease tab and choose Decrease. A fall from 250 to 200 is a 20% decrease, and 80 reduced by 20% is 80 × 0.8 = 64. A decrease is shown as a negative percentage change.
- What does a negative percentage change mean?
- A negative percentage change means the value went down. −20% means the new value is 20% lower than the old one, which is a multiplier of 0.8. If the starting value itself is negative, the formula uses its absolute value so that moving to a larger number still counts as an increase, but take care reading results in that case because the multiplier can look the wrong way round.
- What is the difference between percentage change, percentage difference and percentage points?
- Percentage change measures from a starting value to a finishing value. Percentage difference compares two numbers symmetrically, dividing their gap by their average, so the order does not matter: 40 and 60 differ by 40%, while 40 to 60 is a 50% change. Percentage points are the plain subtraction of two percentages: moving from 4% to 5% is 1 percentage point, which is a 25% increase in the rate.
- Why does a 50% fall need a 100% rise to recover?
- Because the rise is applied to a smaller number. After a 50% fall, 100 becomes 50, and getting back to 100 means doubling 50, which is a 100% rise. In general, recovering from a fall of d% needs a rise of d ÷ (100 − d) × 100%, which is why a 10% fall needs about an 11.1% rise and a 75% fall needs 300%.
- How does a reverse percentage calculator work?
- If a value is the result of a percentage change, divide it by the multiplier to find the original. After a 15% increase the multiplier is 1.15, so a final value of 115 came from 115 ÷ 1.15 = 100. After a 20% decrease the multiplier is 0.8, so 80 came from 80 ÷ 0.8 = 100. Taking 15% off 115 gives 97.75, not 100, because the 15% was worked out on the original.
- How do I calculate the average percentage change per year?
- Divide the ending value by the starting value, raise the result to the power of 1 ÷ the number of years, subtract 1 and multiply by 100. For 25,000,000 growing to 27,500,000 over 5 years: 1.1 to the power of 0.2 is about 1.0192, so the average growth is about 1.92% a year. Simply dividing the 10% total by 5 gives 2%, which slightly overstates it because it ignores compounding.
- Why can't I work out percentage change from zero?
- The formula divides by the old value, and dividing by zero is undefined: any change from 0 is an unbounded percentage of 0. Report the absolute change instead, or describe the result in words such as from nothing to 25 units. A similar problem arises for percentage difference when both numbers are zero, or when they are exact opposites such as 5 and −5, because their average is zero.