Percentage Change Calculator
Enter an old and a new value to see the percentage change, the reverse change and the percentage difference between them.
🔒 Runs entirely in your browser. Nothing you enter is sent to a server.
Prices go up, traffic goes down, salaries grow. Percentage change puts all of these on the same scale, so you can say “sales rose 30%” instead of “sales went from 50 to 65”. This calculator gives the percentage change in either direction, plus related figures that are easy to confuse.
How to use the percentage change calculator
- Enter the original value, the starting or “before” number.
- Enter the new value, the “after” number.
You get:
- Percentage change: how much the value grew or shrank, relative to the original.
- Absolute change: the plain difference.
- Change needed to go back: the percentage that would return the new value to the original.
- Percentage difference: the gap relative to the average of the two, with no direction.
- Multiplier: how many times larger the new value is.
The formulas
Percentage change = (New − Old) ÷ |Old| × 100
Percentage difference = |New − Old| ÷ ((|New| + |Old|) ÷ 2) × 100
Multiplier = New ÷ OldA positive change is an increase and a negative one is a decrease. Dividing by the absolute value of the old number keeps the sign meaningful even when the starting value is negative.
Worked example
A product’s price rises from $50 to $65.
- Absolute change = 65 − 50 = +15
- Percentage change = 15 ÷ 50 × 100 = +30%
- Multiplier = 65 ÷ 50 = 1.3×
- To go back from 65 to 50: (50 − 65) ÷ 65 × 100 ≈ −23.08%
- Percentage difference = 15 ÷ 57.5 × 100 ≈ 26.09%
So a 30% price rise is undone by a 23.08% cut, not a 30% one.
The asymmetry of gains and losses
Percentage gains and losses are not symmetrical. Each needs a bigger recovery than the original move:
| Fall | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 25% | 33.3% |
| 50% | 100% |
| 75% | 300% |
This is why large losses in investments are so damaging: a portfolio that halves needs to double just to break even.
Percent versus percentage points
When the values are themselves percentages, be precise about which you mean. If unemployment goes from 4% to 5%:
- It rose by 1 percentage point.
- It rose by 25 percent, because (5 − 4) ÷ 4 = 0.25.
News reports mix these up often. Both are correct, but they describe different things.
Tips and pitfalls
- Choose the right base. “Before” goes in the original field. Swapping them gives the reverse change, not the same number with the sign flipped.
- Do not average percentage changes. A +50% year followed by a −50% year leaves you at 75% of where you started, not even.
- Chain changes by multiplying. A 10% rise then a 20% rise is 1.1 × 1.2 = 1.32, a total of 32%, not 30%.
- Small bases exaggerate. Growing from 2 to 6 users is a 200% increase, but it is still only four users. Report the absolute change too.
Frequently asked questions
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 50 to 65 is (65 − 50) ÷ 50 × 100 = 30%, an increase.
Why is a 50% drop not undone by a 50% rise?
Because each percentage is taken from a different starting point. 100 falling 50% gives 50, and 50 rising 50% gives only 75. To get back to 100 you need a 100% rise.
What is the difference between percentage change and percentage difference?
Percentage change has a direction, from an old value to a new one. Percentage difference compares two values with no order, dividing the gap by their average. Use change for before-and-after figures, and difference when comparing two things side by side.
What is the difference between percent and percentage points?
If an interest rate rises from 4% to 5%, it went up 1 percentage point, but by 25% in relative terms. Percentage points measure the gap between two percentages, while percent change measures relative growth.
Why can't the original value be zero?
Dividing by zero is undefined. Going from 0 to any other number is an infinitely large percentage change, so the result can't be expressed as a percentage.