Percentage Change Calculator
Percent change tells you how big a change is compared with where you started. Enter the old value and the new value; the calculator works out whether it went up or down and by what percentage.
Answer
40 → 50 is a change of +10 (+25%).
Step by step
- Find the change: new − old = 50 − 40 = 10.
- Divide by the original value: 10 ÷ 40 = 0.25.
- Multiply by 100 to get a percentage: 0.25 × 100 = 25%.
Answer: 25% increase
Still stuck? Ask the tutor about these steps
How it works
(new − old) ÷ |old| × 100Subtract the old value from the new one. A positive result is an increase, a negative one is a decrease.
Divide that difference by the old value — always the starting point, never the new value. This is the step most people get wrong.
Multiply by 100 to turn the decimal into a percentage.
Percent changes are not symmetric: going from 40 to 50 is a 25% increase, but going back from 50 to 40 is a 20% decrease, because the starting value is different each time.
Worked example
A game’s price went from $40 to $50. What is the percent change?
- 50 − 40 = 10
- 10 ÷ 40 = 0.25
- 0.25 × 100 = 25% increase
Frequently asked questions
What is the formula for percentage change?
Percent change = (new value − old value) ÷ old value × 100. A positive answer is an increase and a negative answer is a decrease.
Why do I divide by the old value?
Because the change is measured relative to where you started. Dividing by the new value answers a different question and gives the wrong percentage.
What if the old value is negative?
The calculator divides by the absolute value of the old number, so a rise from −20 to −10 shows as a 50% increase, which matches the direction of the change.
Is percent change the same as percentage difference?
No. Percent change has a clear “before” and “after”. Percentage difference compares two values with no order and divides by their average. Use the percentage difference calculator for that.