Percent Change Calculator: Formula & Examples

This percent change calculator works out the percentage increase or decrease between two numbers. You enter the original (old) value and the new value, and it returns the percent change, telling you whether it went up or down and by how much. The result is given as a signed percentage, so a positive number means an increase and a negative number means a decrease.

Formula

The percent change formula is:

Percent Change = ((New Value − Original Value) ÷ Original Value) × 100

Where:

• Original Value – the starting amount (the “oldâ€� number), unitless in the formula but you can think of it as dollars, kilograms, people, etc.
• New Value – the amount after the change (the “newâ€� number), in the same unit as the original.
• Percent Change – the result, expressed as a percentage. A positive value indicates an increase; a negative value indicates a decrease.

The absolute difference (New − Original) is also shown, but the key output is the percent change.

Worked Example

Using the default values from the calculator above: Original = 50, New = 75.

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

So the percent change is 50%, meaning the new value is 50% larger than the original. The calculator shows the same result: 50.00%.

When to Use Percent Change

Percent change is used whenever you want to express a change relative to the starting point. Common situations include:

• Price increases or discounts (e.g., a shirt went from $20 to $25 – that’s a 25% increase).
• Population growth or decline over a period.
• Test score improvements (e.g., from 80 to 90 – that’s a 12.5% increase).
• Comparing sales figures month to month.
• Tracking weight loss or gain in percentage terms.

The key is that you always compare the change to the original value, not the new value. That’s why the same absolute change can produce different percentages depending on the starting point. For example, going from 100 to 110 is a 10% increase, but going from 200 to 210 is only a 5% increase, even though both added 10.

How to Read the Result

The result is a signed percentage. A positive number (e.g., +25%) means the new value is higher than the original. A negative number (e.g., −25%) means the new value is lower. Zero means no change.

Be careful with the word “percent� – it literally means “per hundred.� So a 100% increase means the value doubled (new = 2 × original). A 100% decrease would mean the new value is zero (which is only possible if the original is zero, but that’s a special case – see below).

Also note that percent change is not symmetric. A 50% increase followed by a 50% decrease does not bring you back to the original. For example, 100 increased by 50% gives 150, then decreased by 50% gives 75 – not 100. That’s because the second percentage is applied to a different base.

Common Mistakes and Pitfalls

• Dividing by the new value instead of the original. This is the most frequent error. Always divide by the original (the starting point).
• Forgetting the sign. If the new value is smaller, the result is negative. Some people report only the magnitude, but the sign conveys direction.
• Mixing up units. The formula works with any unit as long as both values use the same unit. Don’t compare apples to oranges – if one is in dollars and the other in cents, convert first.
• Original value of zero. If the original value is 0, the formula divides by zero, which is undefined. In that case, percent change is not meaningful – you might say the change is “infiniteâ€� or just report the absolute difference.
• Rounding too early. If you round intermediate steps, you can get a slightly different final answer. Keep full precision until the end, then round to the desired number of decimals.

Percent Change vs. Percentage Point Change

A common confusion is between percent change and percentage point change. They are not the same.

Percent change is a relative measure: it compares the size of the change to the original value. Percentage point change is an absolute measure: it simply subtracts one percentage from another.

For example, if an interest rate goes from 4% to 5%, that’s a 1 percentage point increase. But the percent change is (5−4)/4 × 100 = 25%. Both are correct, but they answer different questions. The calculator above gives you the percent change; if you need the percentage point difference, just subtract the two percentages directly.

Limitations of the Formula

The percent change formula is simple and widely applicable, but it has limits:

• It assumes the change is a single step. For multi-step changes, you’d need to chain the formula or use a compound growth calculation.
• It doesn’t tell you anything about the absolute size. A 50% change from 2 to 3 is tiny in absolute terms, while a 50% change from 1,000 to 1,500 is large. Always consider the context.
• It’s not suitable when the original value is zero or negative. If you’re dealing with negative numbers (e.g., temperatures), the percent change can be misleading. For example, going from −10°C to −5°C is a 50% increase in the mathematical sense, but in everyday terms, it’s a 5-degree warming – the percentage is not intuitive.
• For financial or statistical use, be aware that percent change is not the same as logarithmic return. For small changes they are close, but for large changes they diverge.

Frequently Asked Questions

What is the formula for percent change?

The formula is: ((New Value − Original Value) ÷ Original Value) × 100. Multiply the result by 100 to get a percentage. The sign tells you whether it’s an increase (positive) or decrease (negative).

How do I calculate a 20% increase?

To increase a number by 20%, multiply it by 1.20. For example, 50 increased by 20% is 50 × 1.20 = 60. To decrease by 20%, multiply by 0.80. This is the reverse of finding percent change: if you know the original and the percent change, you can find the new value.

What is the difference between percent change and percentage difference?

Percent change uses the original value as the base. Percentage difference (also called relative difference) uses the average of the two values as the base. For example, going from 10 to 20: percent change = (20−10)/10 × 100 = 100%. Percentage difference = (20−10)/((10+20)/2) × 100 = 66.67%. They answer different questions – change over time vs. difference between two points.

Can percent change be more than 100%?

Yes. A percent change greater than 100% simply means the new value is more than double the original. For instance, going from 50 to 150 is a 200% increase. There is no upper limit; the new value can be many times the original.

What if the original value is zero?

If the original value is zero, the formula divides by zero, which is undefined. In practice, you cannot calculate a meaningful percent change from zero. Instead, you might report the absolute change or use a different measure, such as “increased by 5 units.�

How do I reverse a percent change?

To reverse a percent change, divide by (1 + percent/100). For example, if a value increased by 25% to 125, the original was 125 ÷ 1.25 = 100. This works for decreases too: if a value decreased by 20% to 80, the original was 80 ÷ 0.80 = 100.

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in old | Original value | - | 50 | 0
in new | New value | - | 75 | 0
out pct | Percent change | % | ((new - old) / old) * 100 | 2
out diff | Absolute difference | - | new - old | 2