Change in Percent Formula: How to Calculate It

This calculator works out the percentage change between an original value and a new value, showing the result as a percentage increase or decrease. You enter the starting number and the final number, and you get the percent change, along with the absolute difference. The formula is simple: divide the difference by the original value and multiply by 100.

Formula

The percent change formula is written as:

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

Where:

• Original Value – the starting amount (no unit, or any unit as long as both values share it)
• New Value – the amount after the change (same unit as original)
• Percent Change – the result, expressed as a percentage. A positive result means an increase; a negative result means a decrease.

The absolute difference is simply New Value − Original Value. It tells you the raw amount of change, without normalizing by the starting point.

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 by the original: 25 ÷ 50 = 0.5
3. Multiply by 100: 0.5 × 100 = 50%

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

When to Use Percent Change

Percent change is used whenever you want to express a change relative to the starting point, not just as a raw difference. Common situations include:

• Tracking price increases or discounts on products
• Measuring growth in revenue, population, or sales
• Comparing test scores before and after a course
• Calculating weight loss or gain as a percentage of starting weight
• Evaluating changes in temperature, speed, or other measurements

It is especially useful when comparing changes of different magnitudes. A $10 increase on a $20 item is a 50% change, while a $10 increase on a $200 item is only 5% – the percent change makes that distinction clear.

How to Read the Result

A positive percent change means the new value is higher than the original; a negative percent change means it is lower. A result of 0% means no change. The magnitude tells you the size of the change relative to the starting point.

For example, if a stock price goes from $100 to $120, the percent change is +20%. If it then drops from $120 back to $100, the percent change is −16.67% (not −20%), because the original value for the second calculation is 120. This asymmetry is important – a 50% increase requires a 33.33% decrease to return to the original value.

Common Mistakes and Pitfalls

One frequent error is using the new value as the denominator instead of the original. The formula always divides by the original value, not the new one. For the example above, dividing by 75 gives 33.33% instead of the correct 50%.

Another mistake is mixing up units. Both values must be in the same unit – you cannot divide a difference in dollars by a value in euros. Always convert to a common unit first.

Rounding too early can also distort the result. If you round the difference or the ratio before multiplying by 100, the final percentage may be off. Keep full precision until the final step, then round to the desired number of decimal places.

Finally, percent change is not symmetric. A change from A to B is not the negative of the change from B to A, as shown above. Always identify which value is the original.

Limitations of the Formula

The percent change formula assumes the original value is not zero. If the original is zero, division by zero is undefined, and the formula cannot produce a meaningful result. In that case, you should report the absolute difference instead.

The formula also does not account for the sign of the values. If you are calculating percent change with negative numbers (e.g., temperature from −5°C to 5°C), the result can be misleading. For instance, going from −5 to 5 gives a percent change of 200%, but that does not mean the temperature doubled in a physical sense. Use percent change with caution when negative values are involved.

Additionally, percent change is a relative measure – it does not tell you the absolute magnitude of the change. A 50% increase from 2 to 3 is much smaller in absolute terms than a 50% increase from 200 to 300. Always consider the context.

Alternatives to Percent Change

Depending on what you need, other measures may be more appropriate:

• Absolute difference – simply new minus original. Useful when the starting point is small or zero.
• Percentage points – used when comparing two percentages themselves. For example, if the interest rate rises from 2% to 3%, that is a 1 percentage point increase, but a 50% increase in the rate.
• Ratio – new divided by original. A ratio of 1.5 means the new value is 1.5 times the original, which is the same as a 50% increase.
• Logarithmic change – sometimes used in finance and economics to make changes symmetric and additive over time.

Choose the measure that best answers your specific question. Percent change is most useful when you want a normalized, easy-to-understand comparison relative to a starting point.

Frequently Asked Questions

What is the percent change from 50 to 75?
Using the formula: ((75 − 50) / 50) × 100 = 50%. So it is a 50% increase.

How do I calculate percent decrease?
Percent decrease is just a negative percent change. If the new value is smaller than the original, the formula yields a negative number. For example, from 80 to 60: ((60 − 80) / 80) × 100 = −25%, meaning a 25% decrease.

Can percent change be more than 100%?
Yes, if the new value is more than double the original. For instance, from 10 to 30 gives a 200% increase. There is no upper limit.

What if the original value is zero?
The formula is undefined because you cannot divide by zero. In that case, you cannot calculate percent change; report the absolute difference instead.

Is percent change the same as percentage difference?
Not exactly. Percentage difference typically uses the average of the two values as the denominator, while percent change uses the original value. For example, from 50 to 75, percent change is 50%, but percentage difference is (25 / 62.5) × 100 = 40%.

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