Percentage Change Calculator

A percentage change calculator measures how much a value moved relative to where it started. Enter an original value and a new value to see the size of the increase or decrease, plus the absolute change in the same units as your inputs. This is the right tool for prices, revenue, measurements, scores, inventory, or any before-and-after comparison with a clear starting baseline.

How it works

The calculator reads two numbers: Original value and New value. It subtracts the original from the new value to find the signed change. Then it divides that change by the absolute value of the original and multiplies by 100 to express the result as a percent. For negative baselines, this calculator explicitly uses magnitude so the direction matches whether the new value is higher or lower; other conventions may give a different sign. The result card displays the absolute magnitude, so a calculation of negative 20% appears as a 20.00% decrease. The supporting note shows the signed subtraction, and the details list the original value, new value, and absolute change.

The original value cannot be zero because division by zero is undefined. The calculator returns an invalid state for a zero baseline. Values that produce nonfinite intermediate changes are also rejected; very small representable results may round to 0.00% on the result card. If neither number should be treated as the baseline, use the percentage difference calculator, which compares two values against their average instead.

Formula

Define the variables this way:

• Original value is the baseline or starting number.
• New value is the later or comparison number.
• Change is the new value minus the original value.
• Percentage change is the change divided by the absolute value of the original, multiplied by 100.

$\text{change} = \text{new value} - \text{original value}$

$\text{percentage change} = \frac{\text{change}}{|\text{original value}|} \times 100$

If the percentage change is greater than zero, the movement is an increase. If it is less than zero, the movement is a decrease. If it equals zero, the result is labeled No change.

Retain the baseline when explaining a change

Keep the original value and new value beside the signed percentage. If comparing two periods, use a consistent baseline definition and reporting basis. A large percentage from a small original value can coexist with a small absolute change, so report both where it matters. For a symmetric comparison without a designated baseline, use a percentage-difference task instead.

Example: calculating percentage change

Suppose the original value is 80 and the new value is 100. The signed change is 100 minus 80, or 20. The percentage change is 20 divided by 80, multiplied by 100.

$\text{percentage change} = \frac{100 - 80}{80} \times 100 = 25$

The calculator displays Increase, 25.00%, original value 80.00, new value 100.00, and absolute change 20.00. The copy text reads that 80.00 to 100.00 equals a 25.00% increase.

Now reverse the values. If the original value is 100 and the new value is 80, the signed change is negative 20. Dividing by the original value gives negative 0.20, or a 20% decrease.

$\text{percentage change} = \frac{80 - 100}{100} \times 100 = -20$

The calculator displays Decrease, 20.00%, original value 100.00, new value 80.00, and absolute change 20.00. These two examples have the same absolute unit change but different percentages because the baseline changed. That is the central idea behind percentage change.

For a negative baseline, consider a change from −80 to −100. The signed change is −20; dividing by the baseline magnitude of 80 gives −25%, so the result is a 25.00% decrease. A change from −80 to −60 gives +20 divided by 80, or a 25.00% increase. This magnitude convention preserves numerical direction; it is not a claim that a negative financial balance improved or worsened in practical terms.

Percentage change vs percent off

Percentage change and percent off often use similar words, but they answer different questions. Percentage change starts with two observed values and asks, “How much did the second value move relative to the first?” It can describe growth, decline, inflation, test score movement, traffic changes, or a stock price move. The output may be positive, negative, or zero.

Percent off starts with an original price and an advertised discount rate. The discount percentage is already known, and the job is to find savings and final price. A shirt marked 25% off an 80-dollar list price saves 20 dollars and costs 60 dollars before tax. That is not the same situation as observing a price drop from 80 dollars to 60 dollars and calculating that the new price is 25% lower than the old one, even though the arithmetic aligns in that particular example. Use the percent off calculator when the sale percentage is the input; use this page when the before and after values are the inputs.

For adding a known rate to a starting amount, the percentage increase calculator is more direct. For finding a fraction of a whole, use the percentage calculator.

Interpretation and applications

Percentage change is powerful because it normalizes movement. A 5,000-unit sales increase is huge for a small shop but modest for a national chain. Converting the change into a percentage lets you compare the movement relative to each starting point. It is widely used for revenue growth, price inflation, population change, web traffic, error rates, lab measurements, and personal finance.

The sign matters. A positive percentage change means the new value is greater than the original. A negative percentage change means the new value is lower. The absolute change shown by the calculator is useful for units, but it intentionally removes direction. When reporting the result, include both the direction and the percent: “revenue increased by 12.5%” or “defects decreased by 8.0%.” That wording is clearer than simply saying “a 12.5% change.”

Edge cases and common mistakes

Do not divide by the new value unless you intentionally want a different baseline. Doing so answers a different question and will not match standard percentage change. Do not ignore the sign; a negative result is not an error. Do not use this calculation when the original value is zero, because the formula is undefined. For a zero baseline, report the absolute movement or use domain-specific language such as “increased from none to 25 units.” For a negative original value, this tool uses its magnitude; state that convention when comparing results from other methods.

Relative percentage change is different from percentage points: a rate moving from 10% to 15% rises by 5 percentage points and by 50% relative to its original value.

Another common mistake is assuming decreases and increases of the same percentage cancel. They do not when they are applied sequentially to changing baselines. A 20% decrease from 100 gives 80. A 20% increase from 80 gives 96, not 100. The correct recovery increase is 25%, because 20 divided by 80 equals 25%.

Sources

• OpenStax, Solve General Applications of Percent — percent equations and positive-baseline increase and decrease examples.
• Wolfram MathWorld, Percentage — mathematical definition of percentages as parts per hundred.
• Microsoft Support, Calculate percentages — practical percentage formulas and spreadsheet examples.