Percentage Change Calculator

1. Enter the original (old) value and new value.
2. Read the highlighted result first, then the breakdown below it. Load the worked example to check the math by hand.

Percentage change divides the change by the starting value. Because the starting value is the base, the same pair of numbers gives different answers depending on direction: 80 → 100 is a 25% increase, but 100 → 80 is a 20% decrease.

• Change = new value − old value
• Percent change = change ÷ |old value| × 100
• Positive = increase, negative = decrease
• If the old value is 0, percent change is undefined (unless the new value is also 0)

The percent change tells you how big the move was relative to where it started. Positive means the value grew; negative means it shrank. The multiple shows the same thing as a factor — 1.25× is a 25% increase.

Common mistakes and assumptions

• Dividing by the new value instead of the old one.
• Assuming equal percentage rises and falls cancel out — they don't.
• Reporting a percent change from zero. It is undefined; use the raw change.
• Mixing up percent change with percentage points when comparing rates.

A product's price rises from $80 to $100.

1. 1Change = 100 − 80 = 20.
2. 2Percent change = 20 ÷ 80 × 100 = 25%.
3. 3The new price is 1.25 × the old price — a 25% increase.
4. 4Reversing it, 100 → 80 is a 20 ÷ 100 = 20% decrease, not 25%.

What is the formula for percentage change?

Subtract the old value from the new value, divide by the old value, and multiply by 100. A positive result is an increase and a negative result is a decrease.

Why isn't a 25% increase undone by a 25% decrease?

Each change uses a different base. 80 up 25% is 100, but 100 down 25% is 75. To return from 100 to 80 you need a 20% decrease.

What is percent change when the starting value is zero?

It is undefined, because you cannot divide by zero. Report the raw change (for example, 'up 40 units from zero') or use percentage difference, which uses the average of both values as its base.

Is percentage change the same as percentage difference?

No. Percentage change has a direction and uses the old value as its base. Percentage difference compares two values symmetrically against their average, so swapping them gives the same answer.

How is this different from percentage points?

If a rate goes from 4% to 5%, it rose 1 percentage point but changed 25% in relative terms. Use this calculator for the relative change and subtract directly for percentage points.