What is the percent change?
Enter an old and a new value to get the percentage change, or enter the change to find either value.
- Percentage change
- 25%
From 100 to 125 is a change of 25%.
- Difference
- 25
- Increase or decrease
- Increase
Percentage change: 25%. From 100 to 125 is a change of 25%.
How to calculate
Finds the percentage change from an old value to a new one, or either value from the other and the change.
Example with the default inputs (From (old value) 100, To (new value) 125): From 100 to 125 is a change of 25%.
Formula: p = (B − A) ÷ |A| × 100, where A is the old value, B the new value, and p the percentage change.
- The change is measured against the size of the old value, |A|, so a rise from −50 to 25 is +150%.
- There is no percentage change from 0: the old value must not be 0.
- Finding the old value from the new value and the change can give two answers, one positive and one negative: both are shown.
Worked examples
Each example is checked against the calculator on every build.
- From (old value) 100, To (new value) 125 gives Percentage change 25%, Difference 25, Increase or decrease Increase.Source: hand calculation in content.mdx: (125 − 100) ÷ 100 × 100 = 25%
- From (old value) 80, To (new value) 60 gives Percentage change -25%, Difference -20, Increase or decrease Decrease.Source: hand calculation in content.mdx: (60 − 80) ÷ 80 × 100 = −25%
- From (old value) 50, Percentage change 50% gives To (new value) 75.Source: hand calculation in content.mdx: 50 + 50% of 50 = 75
- To (new value) 75, Percentage change 50% gives From (old value) 50.Source: hand calculation in content.mdx: 75 ÷ 1.5 = 50
- From (old value) -50, To (new value) 25 gives Percentage change 150%, Difference 75, Increase or decrease Increase.Source: hand calculation in content.mdx: (25 − (−50)) ÷ |−50| × 100 = 75 ÷ 50 × 100 = 150%
- To (new value) 10, Percentage change 200% gives From (old value) 3.333333.Source: hand calculation in content.mdx: 10 ÷ 3 = 3.333…, or 10 ÷ (1 − 2) = −10; Python 3: 10 / 3 = 3.3333333333333335
How it works
For an old value A and a new value B, the percentage change p is:
p = (B − A) ÷ |A| × 100
|A| is the size of A without its sign, so for a positive A this is the familiar (B − A) ÷ A × 100. A positive p is an increase and a negative p is a decrease.
Fill in any two of the three and the calculator finds the third:
- Percentage change: p = (B − A) ÷ |A| × 100.
- New value: B = A + |A| × p ÷ 100. For a positive A this is A × (1 + p ÷ 100).
- Old value: if A is positive, A = B ÷ (1 + p ÷ 100); if A is negative, A = B ÷ (1 − p ÷ 100). Each answer counts only if it has the sign it assumed, so there can be no answer, one, or two (one positive and one negative). The calculator shows every one.
It also shows the difference, B − A, and whether it is an increase, a decrease, or no change.
Assumptions
- The old value must not be 0: there is no percentage change from 0.
- The change is measured against |A|, the size of the old value, so a rise is always a positive percentage, even from a negative start.
- Percentages are in percent points: type 25 for 25%.
- An old value of 0 gives no answer, and the page says: "The old value cannot be 0: a percentage change is measured against it."
Worked examples by hand
From 100 to 125. (125 − 100) ÷ 100 × 100 = 25%, an increase of 25.
From 80 to 60. (60 − 80) ÷ 80 × 100 = −20 ÷ 80 × 100 = −25%, a decrease of 20 (difference −20).
50 increased by 50%. 50 + 50 × 50 ÷ 100 = 50 + 25 = 75.
What rose 50% to reach 75? A = 75 ÷ (1 + 0.5) = 50. The negative case, 75 ÷ (1 − 0.5) = 150, is not negative, so it does not count.
From −50 to 25. The difference is 25 − (−50) = 75, and 75 ÷ |−50| × 100 = 150%, an increase.
What changed by +200% to reach 10? Positive case: A = 10 ÷ (1 + 2) = 3.333333, and 3.333333 + 200% of 3.333333 = 10. Negative case: A = 10 ÷ (1 − 2) = −10, and from −10 to 10 is a rise of 20, which is 200% of |−10|. Both fit.
Other questions people ask
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value, and multiply by 100: (new − old) ÷ old × 100. From 100 to 125 the change is (125 − 100) ÷ 100 × 100 = 25%. A positive answer is an increase and a negative answer is a decrease.
Is a percentage change the same as a percentage difference?
No. A percentage change has a direction: it measures the new value against the old one, so 100 to 125 is +25% but 125 to 100 is −20%. A percentage difference compares two values with no before and after, against their average, so both orders give 22.22%.
Why does a 50% rise and a 50% fall not get me back where I started?
Because each change is measured against a different starting value. 100 up 50% is 150, and 150 down 50% is 75. To get from 150 back to 100 you need a fall of 33.33%.
How do I find the original value before a percentage change?
Divide the new value by 1 plus the change as a decimal. If a price is 75 after a 50% rise, the original was 75 ÷ 1.5 = 50. After a 20% fall to 80, it was 80 ÷ 0.8 = 100.
How is the percentage change worked out when the old value is negative?
The change is divided by the size of the old value, |old|, so that a rise always shows as a positive percentage. From −50 to 25 is a rise of 75, and 75 ÷ 50 × 100 = +150%. Dividing by −50 instead would give −150%, which would call a rise a decrease.
What is the percentage change from 0?
There is none. Any change from 0 is infinitely many times 0, so the formula divides by zero. Report the change as an amount (for example, from 0 to 25 is a rise of 25) instead.
What is the difference between percent change and percentage points?
Percentage points are the plain difference between two percentages. A rate that goes from 4% to 5% rises by 1 percentage point, which is a percentage change of (5 − 4) ÷ 4 × 100 = 25%.