Percentage Change Calculator: Formula & Examples

This calculator works out the percentage change between two numbers: you enter an original (old) value and a new value, and it returns the percentage increase or decrease, plus the absolute difference. The formula is (new − old) ÷ old × 100, expressed as a percentage.

Formula

The percentage change formula is:

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

Where:

• Original value — the starting number, before the change (no unit, or any consistent unit).
• New value — the number after the change (same unit as the original).
• Percentage change — the result, in percent (%). A positive result means an increase; a negative result means a decrease.

The same formula works for any quantity that can be measured on a ratio scale: prices, populations, weights, speeds, scores, temperatures in kelvin, and so on. The only requirement is that both values use the same unit and that the original value is not zero.

Worked Example

Using the default values from the calculator above — original value 50, new value 75:

1. Subtract the original from the new: 75 − 50 = 25.
2. Divide by the original: 25 ÷ 50 = 0.5.
3. Multiply by 100: 0.5 × 100 = 50%.

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

When to Use Percentage Change

Percentage change is the standard way to compare a value before and after a single event or period. Common uses include:

• Tracking price increases or discounts on a product.
• Measuring population growth or decline between census years.
• Comparing sales, revenue, or profits from one quarter to the next.
• Assessing weight loss or gain over a diet or training program.
• Evaluating changes in test scores, speeds, or temperatures.

The key advantage of percentage change over the absolute difference is that it normalises the change relative to the starting point. A change from 10 to 11 and a change from 100 to 110 both have an absolute difference of 1 and 10, respectively, but both are a 10% increase. This lets you compare changes of very different scales fairly.

How to Read the Result

If the result is positive, the new value is larger than the original — that is a percentage increase. If the result is negative, the new value is smaller — a percentage decrease. For example:

• Original 200, new 150: ((150 − 200) ÷ 200) × 100 = −25%, a 25% decrease.
• Original 80, new 100: ((100 − 80) ÷ 80) × 100 = 25%, a 25% increase.

Notice that a 25% increase followed by a 25% decrease does not return you to the original value. Starting at 80, a 25% increase gives 100; a 25% decrease of 100 gives 75, not 80. This asymmetry is a common source of confusion and is worth remembering when interpreting successive changes.

Common Mistakes and Misconceptions

Several errors appear frequently when people compute percentage change by hand:

• Dividing by the new value instead of the original. The formula always divides by the original (the starting point), not the new value. Dividing by the new value gives a different, incorrect number.
• Confusing percentage change with percentage points. If a rate goes from 10% to 15%, that is a 5 percentage point increase, but a 50% increase relative to the original rate. Both statements are true but mean different things.
• Using the formula when the original value is zero. Division by zero is undefined. If the original value is zero, percentage change cannot be computed; you can only report the absolute difference.
• Mixing units. Both values must be in the same unit. Comparing 5 kg to 500 g without converting first gives a meaningless result.
• Rounding too early. Round intermediate steps only at the end, or the final percentage may be off by more than expected.

Limits of the Formula

The percentage change formula is simple and robust, but it has boundaries. It assumes both values are on a ratio scale, meaning zero means “none of this quantity.� This works for prices, lengths, masses, counts, and most physical measurements. It does not work for interval scales like Celsius or Fahrenheit temperatures, where zero is arbitrary; a change from 10°C to 20°C is not a 100% increase in heat in any physically meaningful sense. For temperatures, use kelvin if you want a percentage.

The formula also treats increases and decreases symmetrically in magnitude but not in effect. A 100% increase doubles the value; a 100% decrease reduces it to zero. You cannot have a decrease greater than 100%, because that would imply the new value is negative, which may or may not be meaningful depending on the quantity.

Finally, percentage change is a single summary number. It does not tell you anything about the distribution of the change, whether it was steady or sudden, or whether the two values are outliers. For a full picture, always look at the actual numbers alongside the percentage.

Alternatives to Percentage Change

Depending on the question you are asking, another measure may be more appropriate:

• Absolute difference — simple subtraction (new − old). Useful when the scale is fixed and meaningful (e.g., a 5-point score change).
• Relative difference — the absolute difference divided by the average of the two values, often used in scientific comparisons where neither value is clearly the “original.â€�
• Percentage of — new ÷ old × 100, giving the new value as a proportion of the old. A result of 150 means the new value is 150% of the old, i.e., 50% more.
• Log change — ln(new ÷ old), used in finance and economics for continuous growth rates that are additive over time.
• Index numbers — setting the original to 100 and expressing the new value relative to it, common in price indices.

Choose the measure that matches the question. If you want “how much bigger or smaller,� use percentage change. If you want “what fraction of the old is the new,� use percentage of. If you are comparing two values without a clear baseline, consider relative difference.

Frequently Asked Questions

How do I calculate percentage change without a calculator?

Subtract the original value from the new value, divide that result by the original value, then multiply by 100. For example, from 40 to 50: (50 − 40) ÷ 40 = 0.25, then 0.25 × 100 = 25%. A positive answer is an increase; a negative answer is a decrease.

What is the difference between percentage change and percentage difference?

Percentage change divides by the original value, so it depends on which number you call the original. Percentage difference divides by the average of the two values and is symmetric — it gives the same result regardless of order. Use percentage change when there is a clear before-and-after relationship; use percentage difference when comparing two values with no baseline.

Can percentage change be more than 100%?

Yes. If the new value is more than double the original, the increase is greater than 100%. For example, from 10 to 30 is a 200% increase. There is no upper limit for increases. Decreases, however, cannot exceed 100%, because that would mean the new value is negative.

What if the original value is zero?

You cannot compute a percentage change when the original value is zero, because the formula requires division by zero. In that case, report the absolute difference instead, or describe the change in words (e.g., “went from zero to 50�).

Is a 50% increase followed by a 50% decrease back to the original?

No. Starting at 100, a 50% increase gives 150. A 50% decrease of 150 gives 75, not 100. To return to the original after a 50% increase, you need a 33.33% decrease. This asymmetry is inherent to percentage changes and is a common trap in financial and statistical reasoning.

How do I reverse a percentage change to find the original value?

If you know the new value and the percentage change, divide the new value by (1 + percentage/100) for an increase, or by (1 − percentage/100) for a decrease. For example, if a price increased by 20% to 120, the original was 120 ÷ 1.20 = 100.

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in a | Original value | - | 50 | 0
in b | New value | - | 75 | 0
out pct | Percentage change | % | ((b - a) / a) * 100 | 2
out diff | Absolute difference | - | b - a | 2