Percentage Change Calculator — Step-by-Step Solutions

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New Value

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The Percentage Change Calculator determines the percentage increase or decrease between two values. It handles percentage change, percentage difference, percentage error, and reverse percentage calculations.

Enter your original and new values to see the percentage change instantly with step-by-step working. Useful for financial analysis, scientific measurements, and everyday calculations.

How to Use the Percentage Change Calculator

Select the calculation mode: Percentage Change, Percentage Difference, Percentage Error, or Reverse Percentage.
Enter the original (old) value and the new value in the corresponding fields.
The result appears instantly, showing whether the change is an increase or a decrease.
Review the step-by-step working and use the share button to save your calculation.

Formula and Theory

Percentage change measures how much a value has increased or decreased relative to its original value. The formula is: Percentage Change = ((New Value - Old Value) / |Old Value|) * 100. A positive result indicates an increase, and a negative result indicates a decrease.

Percentage difference compares two values symmetrically, using their average as the denominator: Percentage Difference = (|A - B| / ((A + B) / 2)) * 100. It is always non-negative and does not require designating one value as the "original".

Successive percentage changes are not additive. An increase of 20% followed by a decrease of 20% does not return to the original value. Starting from 100: 100 * 1.20 = 120, then 120 * 0.80 = 96. The net result is a 4% loss, not zero.

Worked Examples

Example 1: Percentage increase

Problem: A product price rises from 80 to 100. What is the percentage change?

Solution: Change = ((100 - 80) / 80) * 100 = (20 / 80) * 100 = 25%.

Answer: 25% increase

Example 2: Percentage decrease

Problem: The temperature drops from 40 to 32 degrees. What is the percentage change?

Solution: Change = ((32 - 40) / 40) * 100 = (-8 / 40) * 100 = -20%.

Answer: 20% decrease

Example 3: Successive changes

Problem: A share price starts at 200, increases by 50%, then decreases by 30%. What is the net change?

Solution: After increase: 200 * 1.50 = 300. After decrease: 300 * 0.70 = 210. Net change: ((210 - 200) / 200) * 100 = 5%.

Answer: 5% net increase

Example 4: Real-world: cost of living adjustment

Problem: Rent rises from 1,200 to 1,350 per month. What is the percentage increase?

Solution: Change = ((1350 - 1200) / 1200) * 100 = (150 / 1200) * 100 = 12.5%.

Answer: 12.5% increase

Frequently Asked Questions

What is the difference between percentage change and percentage difference?

Percentage change has a clear "before" and "after" value and uses the original as the denominator. Percentage difference treats both values equally and uses their average as the denominator. Use percentage change when you have a baseline, and percentage difference when comparing two independent measurements.

Why does a 50% increase followed by a 50% decrease not cancel out?

Because the base changes. A 50% increase on 100 gives 150. Then 50% of 150 is 75, not 50. So a 50% decrease from 150 gives 75, which is 25% less than the original 100.

How do I find the original value from a percentage change?

Use the formula: Original Value = New Value / (1 + Change% / 100). For example, if the new price is 120 after a 20% increase, the original was 120 / 1.20 = 100.

Can percentage change exceed 100%?

Yes. If a value more than doubles, the percentage increase exceeds 100%. For instance, going from 50 to 150 is a 200% increase.

What is percentage error?

Percentage error measures how far an experimental or estimated value is from the true (accepted) value: Percentage Error = (|Measured - True| / |True|) * 100. It is commonly used in science to assess measurement accuracy.