Percentage Change Formula & How to Calculate It

This calculator works out the percentage change between two numbers: you enter an original value and a new value, and it returns the percentage increase or decrease, plus the absolute difference. The formula is simple: subtract the original from the new, divide by the original, then multiply by 100.

Formula

Percentage change = ((New value − Original value) ÷ Original value) × 100

In symbols: %Δ = ((B − A) / A) × 100

• A = original (or old, or starting) value
• B = new (or final, or later) value
• %Δ = percentage change (can be positive or negative)

If the result is positive, it’s a percentage increase; if negative, it’s a percentage decrease. The absolute difference (B − A) is the raw change, not adjusted for the size of the original value.

Worked Example

Using the default values from the calculator: original value = 100, new value = 125.

1. Subtract the original from the new: 125 − 100 = 25
2. Divide by the original: 25 ÷ 100 = 0.25
3. Multiply by 100: 0.25 × 100 = 25%

The percentage change is 25% (an increase). The absolute difference is 25. That matches the calculator’s output.

When to Use Percentage Change

Percentage change is used whenever you want to compare a value before and after a change, especially when the size of the original value matters. Common uses include:

• Tracking price increases or decreases on products
• Measuring growth in sales, revenue, or population
• Comparing exam scores or grades over time
• Evaluating weight loss or gain (e.g., from 80 kg to 72 kg)
• Analyzing stock price movements

It’s different from percentage difference (which uses the average of the two values as the denominator) and from percentage points (which measure the arithmetic difference between two percentages, not the relative change). For example, if an interest rate rises from 4% to 5%, that’s a 1 percentage point increase, but a 25% increase in the rate itself.

How to Read the Result

A positive result means the new value is larger than the original. A negative result means it’s smaller. The magnitude tells you how large the change is relative to the starting point.

• +50% means the new value is 1.5 times the original.
• −50% means the new value is half the original.
• +100% means the new value is double the original.
• −100% means the new value is zero.

Be careful with very small original values: a change from 1 to 3 is a 200% increase, which sounds dramatic, but the absolute difference is only 2. Always consider the context and the absolute difference alongside the percentage.

Common Mistakes and Pitfalls

Several errors are easy to make when calculating percentage change:

• Dividing by the new value instead of the original. The denominator must always be the original value, not the new one. For example, a change from 100 to 150 is 50%, not 33.3% (which would be 50 ÷ 150).
• Confusing percentage change with percentage points. A move from 10% to 15% is a 5 percentage point change, but a 50% relative increase.
• Sign errors. When the new value is smaller, the numerator is negative, giving a negative percentage. Don’t drop the minus sign.
• Rounding too early. Round only the final result, not intermediate steps, to avoid small inaccuracies.

Another common trap: reversing the order. If you want the change from A to B, use (B − A)/A. If you accidentally use (A − B)/B, you get a different number. For example, from 100 to 150: (150−100)/100 = 50%, but (100−150)/150 = −33.3%. The direction matters.

Limitations and When Not to Use It

Percentage change is not always the best tool:

• When the original value is zero or negative. If A = 0, the formula divides by zero and is undefined. If A is negative, the result can be misleading (e.g., a change from −10 to −5 gives +50%, which may not mean what you expect).
• When comparing across different scales. A 10% increase on a $1 item is $0.10, while on a $100 item it’s $10. The percentage is the same, but the absolute impact differs.
• When values are already percentages. If you have two percentages (e.g., 20% and 30%), the percentage change formula still works, but many people confuse it with percentage points. Always specify which one you mean.

For such cases, consider using absolute difference, percentage points, or a different ratio.

Frequently Asked Questions

How do I calculate percentage change in Excel?

In Excel, if the original value is in cell A1 and the new value is in B1, enter =(B1-A1)/A1 in a cell and format it as a percentage. Excel will multiply by 100 automatically when you apply the percent format. If the result shows a decimal like 0.25, just change the cell format to Percentage.

What is the difference between percentage change and percentage difference?

Percentage change uses the original value as the denominator and is directional (positive for increase, negative for decrease). Percentage difference uses the average of the two values as the denominator and is always positive (or absolute). For example, from 100 to 150: percentage change is 50%, percentage difference is (50/125)×100 = 40%.

Can percentage change be more than 100%?

Yes. If the new value is more than double the original, the percentage change exceeds 100%. For example, from 50 to 150 is a 200% increase. There is no upper limit; the only limit is that the original value cannot be zero.

How do I calculate the original value if I know the percentage change?

Rearrange the formula: Original = New / (1 + (percentage change / 100)). For example, if a price increased by 20% and the new price is $120, the original price is 120 / 1.20 = $100. If it decreased by 20%, use 120 / 0.80 = $150.

What does a negative percentage change mean?

A negative percentage change means the new value is smaller than the original. For example, a change from 80 to 60 is (60−80)/80 × 100 = −25%, indicating a 25% decrease. The minus sign is essential; without it, the direction is lost.

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in a | Original value | - | 100 | 0
in b | New value | - | 125 | 0
out pct | Percentage change | % | (b - a) / a * 100 | 2
out diff | Absolute difference | - | b - a | 2