Percentage Change Calculator: Formula & Examples

This calculator works out the percentage change between two numbers: enter the original (or old) value and the new value, and it returns the percentage increase or decrease, plus the absolute difference. The result tells you how much the new value has moved relative to the original, expressed as a percentage. It is the same formula used in finance, retail, science, and everyday comparisons.

Formula

The percentage change formula is:

Percentage change = ((New value – Original value) / Original value) × 100%

Where:

• Original value – the starting (old) number, the base of comparison.
• New value – the number after the change.
• Percentage change – the result, in percent. A positive result means an increase; a negative result means a decrease.

The formula works for any real numbers, but the original value must not be zero (division by zero is undefined).

Worked Example

Using the default values from the calculator: original value = 100, new value = 150.

1. Subtract the original from the new: 150 – 100 = 50
2. Divide by the original: 50 ÷ 100 = 0.5
3. Multiply by 100 to get a percentage: 0.5 × 100 = 50%

The percentage change is 50% (an increase). The absolute difference is 50. This matches the calculator’s output.

How to Read the Result

A positive percentage change means the new value is larger than the original; a negative percentage change means it is smaller. For example, a result of -20% means the new value is 20% less than the original. The size of the percentage depends on the original value: a change of 10 on a base of 100 is 10%, but the same absolute change on a base of 1000 is only 1%. Always keep the original value in mind when interpreting the percentage.

Common Mistakes and Pitfalls

• Dividing by the new value instead of the original – the formula always uses the original (old) value as the denominator. Using the new value gives a different, incorrect result.
• Confusing percentage change with percentage points – if a rate goes from 10% to 15%, the percentage change is 50% (because 5/10 = 0.5), but the increase in percentage points is only 5. Both are valid but mean different things.
• Reversing the subtraction – subtracting the new from the original flips the sign, turning an increase into a decrease.
• Ignoring the sign – a negative result is a decrease, not a smaller increase. Write the sign explicitly.
• Rounding too early – round only the final result to avoid accumulating errors, especially when doing multiple steps.

When to Use Percentage Change

Percentage change is used whenever you need to compare a change relative to a starting point. Common applications include:

• Finance: stock price movements, portfolio returns, inflation rates.
• Retail: price increases or discounts (a 20% discount is a percentage change of -20%).
• Business: sales growth, profit margin changes, cost reductions.
• Science: experimental measurements, population growth, reaction yields.
• Everyday life: comparing salaries, test scores, or any quantity that changes over time.

It is most useful when the original value is meaningful and non-zero. If the original value is zero, the percentage change is undefined – no percentage can express a change from zero.

Limitations and Alternatives

The percentage change formula assumes the original value is a valid baseline. It does not work well when the original value is very small (a tiny change can produce a huge percentage) or when the original value is zero. In those cases, consider using the absolute difference or a different metric like percentage points. Also, percentage change is not symmetric: a 50% increase followed by a 50% decrease does not return to the original value (e.g., 100 → 150 → 75). This is a common trap in financial and statistical reasoning.

Frequently Asked Questions

How do I calculate percentage change between two numbers?

Subtract the original value from the new value, divide that difference by the original value, then multiply by 100. For example, from 50 to 60: (60-50)/50 × 100 = 20% increase.

What if the new value is lower than the original?

You get a negative percentage change, which indicates a decrease. For instance, from 80 to 60: (60-80)/80 × 100 = -25%.

Can the percentage change be more than 100%?

Yes, if the new value is more than double the original. For example, from 10 to 30 is a 200% increase, because the difference (20) is twice the original (10).

What is the difference between percentage change and percentage difference?

Percentage change uses the original value as the denominator and is directional (positive or negative). Percentage difference, often used for comparing two values without a clear baseline, divides the absolute difference by the average of the two values and is always positive.

Why do I get a different answer when I reverse the order?

Because the denominator changes. Going from 100 to 150 is a 50% increase, but going from 150 to 100 is a -33.33% change. The percentage change is not reversible.

What if the original value is zero?

The formula is undefined because you cannot divide by zero. In such cases, percentage change is not a valid measure; use the absolute change instead.

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in old | Original value | - | 100 | 0
in new | New value | - | 150 | 0
out pct | Percentage change | % | ((new - old) / old) * 100 | 2
out diff | Absolute difference | - | new - old | 2