Calculators
Percentage Change Formula: How to Calculate Increase or Decrease
The percentage change formula tells you how much a value has moved relative to where it started. It's used for prices, data metrics, financial figures, and scientific measurements. Here's the formula, how to interpret the result, and where it breaks down.
The formula
% Change = ((New − Old) ÷ |Old|) × 100
How to apply it — step by step
Example: a product price changes from £64 to £80
- Subtract: 80 − 64 = 16
- Divide by old: 16 ÷ 64 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
Result: +25% (price increased by 25%)
Example: monthly active users drop from 12,000 to 9,600
- Subtract: 9,600 − 12,000 = −2,400
- Divide by old: −2,400 ÷ 12,000 = −0.20
- Multiply by 100: −0.20 × 100 = −20%
Result: −20% (users decreased by 20%)
Percentage change vs percentage difference
Percentage change
Before → After. Has direction. Old value is the base.
Price went from £50 to £65 → +30%
Percentage difference
Comparing two things without a time direction. Average of both is the base.
Comparing £50 and £65 → 26.2% different
Use percentage change for before-and-after comparisons. Use percentage difference when comparing two values that don't have a natural "old" and "new" — for example, comparing two different products or two groups in a study.
Where the formula breaks down
If the starting (old) value is zero, the formula is undefined — you can't divide by zero. Report this as "new entry" or "from zero baseline" rather than as a percentage.
If the old value is negative (for example, a negative profit or a negative temperature), use its absolute value in the denominator. The formula gives a meaningful result as long as the denominator is not zero.
Percentage changes are not reversible. A 50% drop followed by a 50% gain does not return to the original — you end up at 75% of the start. To reverse a change, you need the reciprocal multiplier: to reverse a −50% change, apply a +100% change.
Calculate percentage change in seconds
Enter the old and new values. Get the change, the direction, and the formula.
Use the calculator →Frequently asked questions
What is the percentage change formula?
Percentage change = ((New Value − Old Value) ÷ |Old Value|) × 100. The vertical bars indicate absolute value — if the old value is negative, you use its positive equivalent in the denominator. A positive result means the value increased. A negative result means it decreased.
What is the difference between percentage change and percentage difference?
Percentage change measures how a single value has moved from a specific starting point to an ending point — it has direction (increase or decrease). Percentage difference compares two values without implying one came before the other: |A − B| ÷ ((A + B) / 2) × 100. Use percentage change for before-and-after comparisons; use percentage difference when comparing two things that are not related by time.
Can percentage change exceed 100%?
Yes — a percentage change greater than 100% just means the value more than doubled. If something goes from £5 to £15, the change is ((15 − 5) ÷ 5) × 100 = 200%. A 200% increase means the value grew by twice the original amount, reaching three times the original. There is no upper or lower mathematical limit to percentage change.
What happens when the starting value is zero?
The formula breaks down — you cannot divide by zero. If a metric goes from 0 to any positive value, the percentage change is mathematically undefined. In practice, this is usually reported as 'new' or 'from baseline' rather than as a percentage change. If your starting value is 0, the percentage change formula does not apply.
How do you calculate percentage change in Excel?
Use the formula: =(B1-A1)/ABS(A1)*100 where A1 is the old value and B1 is the new value. ABS() handles negative starting values correctly. Alternatively, =(B1-A1)/A1 gives you the decimal form — format the cell as a percentage to display it as a percentage. If A1 could be zero, wrap with an IF statement: =IF(A1=0,"N/A",(B1-A1)/ABS(A1)*100).
Is a 50% decrease the same as a 50% increase in reverse?
No — and this is a common misconception. If a value drops by 50% (from 100 to 50), it needs a 100% increase to get back to 100. A 50% increase on 50 gives 75, not 100. Percentage changes are not symmetric because the base changes. A −50% and +100% applied in sequence returns to the start; a −50% and +50% ends up at 75% of the original.