Percentage Change Calculator

Percentage change puts raw numbers into context.

A stock price moving from $50 to $55 is a 10% increase. Revenue dropping from $200,000 to $180,000 is a 10% decrease. Without the percentage, you are left comparing absolute numbers that may not be directly comparable across different scales. This percentage change calculator computes the percentage increase or decrease between any two values, showing the formula and calculation steps so you can verify and understand the result.

Enter the original value and the new value, and the calculator returns the percentage change along with the absolute difference. It handles positive changes (increases), negative changes (decreases), and edge cases like changes from or to zero. The step-by-step breakdown shows how the formula is applied, making this tool equally useful for quick calculations and for learning.

Whether you are tracking investment returns, comparing sales figures, analyzing test score improvements, or calculating price changes, percentage change is the standard way to express how much something has grown or shrunk relative to its starting point.

The Percentage Change Formula

Percentage change measures how much a value has changed relative to its original amount:

Percentage Change = ((New Value – Old Value) / Old Value) x 100

A positive result indicates an increase. A negative result indicates a decrease.

Example 1: Price increase. A product was $80 and is now $92. Percentage change = ((92 – 80) / 80) x 100 = (12 / 80) x 100 = 15% The price increased by 15%.

Example 2: Sales decrease. Monthly sales were 500 units and dropped to 425 units. Percentage change = ((425 – 500) / 500) x 100 = (-75 / 500) x 100 = -15% Sales decreased by 15%.

The key point is that percentage change is always measured relative to the original (starting) value. This is important because the same absolute change represents different percentages depending on the starting point. A $10 increase on a $50 item is 20%, but a $10 increase on a $500 item is only 2%.

Percentage Change vs Percentage Difference

These two concepts are frequently confused but serve different purposes.

Percentage change compares a new value to an original value. It has a direction (increase or decrease) and a clear reference point (the original value). Use percentage change when one value is "before" and one is "after."

Percentage difference compares two values without designating one as original. It uses the average of the two values as the reference point:

Percentage Difference = (|Value 1 – Value 2| / ((Value 1 + Value 2) / 2)) x 100

Use percentage difference when comparing two independent values, such as the price of the same product at two different stores.

This calculator computes percentage change (with a defined original and new value). If you need percentage difference, enter the average of the two values as the reference instead.

Percentage Point vs Percentage Change

A percentage point describes the arithmetic difference between two percentages. A percentage change describes the relative change.

If an interest rate goes from 4% to 5%, it increased by:

1 percentage point (5% – 4% = 1 percentage point)
25% in percentage change terms ((5 – 4) / 4 x 100 = 25%)

This distinction matters in finance, economics, and statistics where small changes in percentages can represent large relative shifts. Unemployment rising from 3% to 4% is a 1 percentage point increase but a 33% relative increase in the unemployment rate.

Compounding Percentage Changes

When percentage changes happen sequentially, they do not simply add together. Each change applies to the result of the previous one.

A stock that gains 20% and then loses 20% does not return to its original price:

Start: $100
After +20%: $120
After -20%: $120 x 0.80 = $96

The net result is a 4% loss, not zero. This happens because the 20% gain is calculated on $100, but the 20% loss is calculated on the larger $120.

Similarly, a price that increases 10% per year for 3 years does not increase by 30%:

Year 1: $100 x 1.10 = $110
Year 2: $110 x 1.10 = $121
Year 3: $121 x 1.10 = $133.10

The total increase is 33.1%, not 30%. This is the effect of compounding.

Real-World Applications

Business and finance. Year-over-year revenue growth, quarterly profit margins, stock price movements, and return on investment are all expressed as percentage changes. These metrics allow comparison across companies of different sizes. A 15% revenue increase means the same thing whether the company earns $1 million or $1 billion.

Economics. Inflation rates, GDP growth, unemployment changes, and consumer price index movements are reported as percentage changes. These figures inform monetary policy, investment decisions, and public understanding of economic health.

Personal finance. Salary increases, investment returns, expense tracking, and debt reduction are all tracked as percentages. A 3% raise on a $50,000 salary is $1,500, while a 3% raise on $100,000 is $3,000. The percentage is the same, but the dollar impact differs.

Science and research. Experimental results often report percentage changes from a control group. A treatment that reduces tumor size by 45% or a fertilizer that increases crop yield by 12% communicates the effect relative to the baseline.

Retail and pricing. Markups, markdowns, and discount percentages are percentage changes applied to cost or original price. A 30% markup on a $50 cost gives a $65 selling price. A 20% discount on a $65 price gives a $52 sale price.

Common Percentage Mistakes

Reversing the direction. Going from 80 to 100 is a 25% increase, but going from 100 to 80 is only a 20% decrease. The reference point matters because the denominator changes.

Adding percentages directly. A 10% increase followed by a 10% decrease does not return to the original value. As shown above, sequential percentage changes must be compounded.

Confusing percentage and percentage point. A tax rate moving from 20% to 25% is a 5 percentage point increase but a 25% relative increase. Using the wrong measure can significantly misrepresent the change.

Using the wrong base value. Percentage change is always calculated relative to the original (starting) value. Using the new value as the denominator gives a different and incorrect result.

Use the Fraction Calculator if your values are expressed as fractions, or the Average (Mean) Calculator to compute averages across multiple percentage changes. The Standard Deviation Calculator can help analyze the variability of percentage changes over time.

Frequently Asked Questions

How do I calculate percentage increase?

Subtract the original value from the new value, divide the result by the original value, and multiply by 100. For example, an increase from 200 to 250: ((250-200)/200) x 100 = 25% increase.

How do I calculate percentage decrease?

Use the same formula as percentage increase. A negative result indicates a decrease. From 250 to 200: ((200-250)/250) x 100 = -20% decrease. Note that a 25% increase and a 20% decrease are not symmetric because the base value differs.

What is the percentage change from 0?

Percentage change from zero is mathematically undefined because division by zero is not possible. If the original value is zero, you cannot express the change as a percentage. In practice, report the absolute change or use a different metric.

What is the difference between percentage change and percentage difference?

Percentage change compares a new value to an original value and has a direction (increase or decrease). Percentage difference compares two values without a designated starting point, using the average as the base. Use change for before/after comparisons and difference for side-by-side comparisons.

Why does a 50% gain followed by a 50% loss not break even?

Because each change applies to a different base. A 50% gain on $100 gives $150. A 50% loss on $150 gives $75, which is a net 25% loss. Sequential percentage changes compound rather than cancel.

How do I reverse a percentage change?

To reverse a P% increase, the required decrease is (P / (100 + P)) x 100. To reverse a 25% increase, you need a (25/125) x 100 = 20% decrease. To reverse a P% decrease, the required increase is (P / (100 – P)) x 100.

How do I calculate year-over-year percentage change?

Use this year’s value as the new value and last year’s value as the original value in the standard formula. For example, revenue of $1.2M this year vs $1.0M last year: ((1.2-1.0)/1.0) x 100 = 20% year-over-year growth.

Data accurate as of: March 2026