Percentage Rate Change Calculator: Formula & Examples

This calculator works out the percentage change between an old (original) value and a new value, telling you how much something increased or decreased as a percentage of the original. You enter the original number and the new number, and you get back the percentage rate of change, plus the absolute difference between the two values. The result is positive for an increase and negative for a decrease.

Formula

The percentage rate of change is calculated with this standard formula:

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

• Original value (a) – the starting amount, before the change. It is the baseline you compare against.
• New value (b) – the amount after the change.
• Percentage change – the relative change, expressed as a percentage. A positive result means an increase; a negative result means a decrease.

The absolute difference (b − a) tells you the raw size of the change, but the percentage puts that change into context relative to the original value.

Worked Example

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

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

The percentage change is 25%, meaning the new value is 25% larger than the original. The absolute difference is 25.

When to Use This Calculator

Percentage rate change is used in dozens of everyday situations where you want to compare a before-and-after number:

• Price changes – a product goes from $50 to $60; that is a 20% increase.
• Salary or rent adjustments – a raise from $40,000 to $42,000 is a 5% increase.
• Population growth – a town grows from 10,000 to 10,800 residents, a rise of 8%.
• Test scores or grades – a score improving from 70 to 85 is a 21.43% improvement.
• Business metrics – sales, traffic, or production output changes between two periods.
• Scientific measurements – comparing experimental results to a control or baseline.

In all these cases, the percentage change tells you the relative size of the shift, which is often more meaningful than the raw difference. A $5 increase on a $10 item is huge (50%), but the same $5 on a $500 item is trivial (1%).

How to Read the Result

The output is a percentage that represents the relative change from the original value. Here is how to interpret it:

• Positive percentage – the new value is higher than the original. For example, +15% means the new value is 15% more than the original.
• Negative percentage – the new value is lower than the original. A result of −10% means the new value is 10% less than the original.
• Zero – the two values are identical.

You can also reverse the calculation. If you know the original value and the percentage change, the new value is: original × (1 + percentage/100). For a 20% increase on 100, that gives 100 × 1.20 = 120.

Common Mistakes and Pitfalls

Even with a simple formula, people often trip up on these points:

• Dividing by the wrong value. Percentage change always divides by the original value, not the new one. If a price drops from $80 to $60, the change is −25% (20 ÷ 80), not −33.3% (20 ÷ 60).
• Confusing percentage change with percentage points. If an interest rate goes from 4% to 5%, that is a 1 percentage point increase, but a 25% increase relative to the original rate. Both are correct, but they answer different questions.
• Ignoring the sign. A decrease shows as a negative number. If you only care about the size of the change, use the absolute value, but keep the sign to know the direction.
• Rounding too early. Round only the final result. If you round intermediate steps, you can introduce noticeable errors, especially with small percentages.
• Zero original value. The formula is undefined when the original value is zero. You cannot divide by zero, so this calculator requires a non-zero original value.

Limitations of the Formula

The percentage change formula is simple and widely used, but it has a few limits worth knowing:

• It does not tell you the direction of causality. A 20% increase in sales could be due to many factors; the formula only measures the change, not why it happened.
• It is sensitive to small baselines. A change from 1 to 2 is a 100% increase, which sounds dramatic, but the absolute change is only 1 unit. Always consider the absolute difference alongside the percentage.
• It is not symmetric for increases vs. decreases. A 50% increase (from 100 to 150) requires a 33.3% decrease to get back to 100. The percentage change depends on which value you call “original.�
• It assumes a linear relationship. For compound growth (e.g., interest over multiple periods), you need a different formula that accounts for compounding.

For most single-step comparisons, however, this formula is exactly what you need.

Alternatives and Related Calculations

Depending on your situation, you might need a different type of calculation:

• Percentage difference – used when comparing two values without a clear “original.� The formula divides by the average of the two values, giving a symmetric result. For example, comparing 100 and 120 gives a percentage difference of about 18.2%.
• Percentage of a number – to find what percentage one number is of another (e.g., 30 is what percent of 150? Answer: 20%).
• Percentage increase/decrease from a known original – this is exactly what this calculator does.
• Compound annual growth rate (CAGR) – for multi-year growth, use CAGR = ((Ending/Beginning)^(1/n)) − 1, where n is the number of periods.
• Percent error – used in science to compare a measured value to an accepted value, with the formula |(measured − accepted) / accepted| × 100.

Each of these serves a different purpose, so choose the one that matches your question.

Frequently Asked Questions

What is the difference between percentage change and percentage difference?

Percentage change divides by the original value, while percentage difference divides by the average of the two values. For example, going from 100 to 120: percentage change is +20%, but percentage difference is (20 / ((100+120)/2)) × 100 = 18.18%. Percentage change is used when you have a clear baseline; percentage difference is used when comparing two values without a baseline.

Can the original value be zero?

No. The formula divides by the original value, and division by zero is undefined. If your original value is zero, you cannot calculate a percentage change. In that case, you might describe the change in absolute terms or use a different measure.

How do I calculate the percentage change if the new value is smaller?

The formula still works the same way. For example, original = 200, new = 150: ((150 − 200) / 200) × 100 = −25%. The negative sign indicates a decrease of 25%.

What does a 100% increase mean?

A 100% increase means the new value is double the original. For example, from 50 to 100 is a 100% increase. Similarly, a 200% increase means the new value is three times the original (from 50 to 150).

How is percentage change used in finance?

In finance, percentage change is used to measure returns on investments, price changes in stocks, inflation rates, and growth in revenue or earnings. For example, if a stock price goes from $100 to $110, the percentage change is +10%, which is the simple return over that period.

Is percentage change the same as percent error?

No. Percent error is used when comparing a measured value to an accepted or theoretical value, and it uses the absolute value of the difference in the numerator. Percentage change is used for any before-and-after comparison and keeps the sign to show direction.

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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