Percent Change Calculator: Formula & Examples

This calculator works out the percentage change between two numbers: you enter an old (starting) value and a new (final) value, and it returns the percent increase or decrease, along with the absolute difference. The result tells you how much the new value has grown or shrunk relative to the old one, expressed as a percentage.

Formula

Percent change is calculated with this standard formula:

Percent Change = ((New Value − Old Value) / Old Value) × 100

• Old Value (a) – the starting amount, in any unit (dollars, items, people, etc.).
• New Value (b) – the amount after the change, in the same unit.
• Percent Change – the result, in percent (%).

If the result is positive, it’s a percentage increase. If negative, it’s a percentage decrease. The absolute difference (b − a) is also shown, so you can see the raw change independent of the percentage.

Worked Example

Using the default values from the calculator above:

1. Old value = 50, new value = 75.
2. Difference = 75 − 50 = 25.
3. Divide by old value: 25 ÷ 50 = 0.5.
4. Multiply by 100: 0.5 × 100 = 50%.

The percent change is 50%, meaning the new value is 50% larger than the old value. The absolute difference is 25.

When to Use Percent Change

Percent change is used whenever you want to compare a value over time or against a baseline. Common situations include:

• Tracking price increases or discounts (e.g., a product went from $50 to $75).
• Measuring population growth or decline.
• Comparing sales figures from one year to the next.
• Calculating grade improvements or test score changes.
• Observing weight loss or gain as a percentage.

It’s most meaningful when the old value is positive and not zero, because dividing by zero is undefined. Percent change is also sensitive to the direction of comparison: going from 50 to 75 is a 50% increase, but going from 75 back to 50 is a 33.33% decrease. Always keep the old value as the denominator.

How to Read the Result

A positive result means the new value is larger than the old value. For example, a 50% increase means the new value is 1.5 times the old value. A negative result means the new value is smaller; a −25% change means the new value is 75% of the old value.

The absolute difference is a separate number that does not depend on the old value. It’s useful when you need the raw change (e.g., “sales increased by 25 units�) rather than the relative change.

Be careful with the word “percentage points.� If a rate goes from 10% to 15%, the percent change is 50% (because (15−10)/10 × 100 = 50%), but the rate increased by 5 percentage points. These are different concepts; percent change compares the two rates, while percentage points describe the arithmetic difference.

Common Mistakes and Pitfalls

• Using the wrong denominator – always divide by the old value, not the new one. Dividing by the new value gives a different (and usually incorrect) result.
• Mixing up increase and decrease – a change from 100 to 80 is a −20% change, not +20%. The sign matters.
• Dividing by zero – if the old value is zero, percent change is undefined. In that case, report the absolute difference instead.
• Ignoring units – both values must be in the same unit. You can’t compare 50 meters to 75 yards without converting first.
• Rounding too early – round only the final result, not intermediate steps, to avoid rounding errors.

Limits of the Formula

The percent change formula assumes a linear relationship and works best when the old value is a meaningful baseline. It does not account for compounding or time. For example, a 50% increase followed by a 50% decrease does not return to the original value (100 → 150 → 75, a net −25%). If you need to measure growth over multiple periods, use compound annual growth rate (CAGR) instead.

Also, percent change can be misleading when the old value is very small. A change from 1 to 2 is a 100% increase, but the absolute difference is only 1. Always consider the absolute difference alongside the percentage.

Alternatives to Percent Change

Depending on what you want to express, you might use:

• Absolute difference – simple subtraction (b − a), useful when the baseline is small or zero.
• Percentage points – the arithmetic difference between two percentages, used for rates and probabilities.
• Ratio or multiplier – b / a, which tells you how many times larger the new value is (e.g., 1.5× means 50% increase).
• Compound annual growth rate (CAGR) – for multi-period growth, it gives the average yearly rate.
• Log change – sometimes used in finance and economics for symmetric comparisons.

Frequently Asked Questions

What is the difference between percent change and percent difference?

Percent change compares a new value to an old value using the old value as the denominator. Percent difference (also called relative difference) compares two values symmetrically by dividing the absolute difference by the average of the two values. For example, going from 50 to 75 is a 50% change, but the percent difference between 50 and 75 is (25 / 62.5) × 100 = 40%.

Can percent change be negative?

Yes. A negative percent change indicates a decrease. For instance, if a value drops from 80 to 60, the percent change is (60−80)/80 × 100 = −25%. The negative sign is essential; without it, you would incorrectly report an increase.

What does a 100% increase mean?

A 100% increase means the new value is double the old value. For example, from 10 to 20 is a 100% increase because (20−10)/10 × 100 = 100%. Similarly, a 200% increase means the new value is three times the old value.

How do I calculate percent change when the old value is zero?

You cannot calculate percent change when the old value is zero, because division by zero is undefined. In that case, report the absolute difference (the new value) and note that percentage change is not applicable. Some fields use a convention like “increase from 0 to 5 is a 500% increase� but that is mathematically incorrect and misleading.

What is the percent change from 25 to 20?

Using the formula: (20 − 25) / 25 × 100 = −20%. So it’s a 20% decrease. The absolute difference is −5.

Does percent change depend on the order of the values?

Yes. Percent change is not symmetric. Going from 50 to 75 is a 50% increase, but going from 75 to 50 is a 33.33% decrease. The denominator (old value) changes, so the result differs. If you need a symmetric measure, use percent difference instead.

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in a | Starting value | - | 50 | 0
in b | Final value | - | 75 | 0
out pct | Percent change | % | (b - a) / a * 100 | 2
out diff | Absolute difference | - | b - a | 2