Interactive Calculator
BY: Statistics Fundamentals Team

Percentage Change Calculator (Increase & Decrease)

Enter an original value and a new value to calculate the percentage increase or decrease between them. The calculator also shows the numerical change, absolute difference, and the calculation steps. Zero and negative starting values are handled separately so the result is not presented as a normal percentage change when the baseline makes that interpretation unclear.

Percentage Change Calculator

Enter the two values
The starting or baseline value.
The later, updated, or comparison value.
Result settings
Intermediate calculations keep full JavaScript numeric precision. Rounding is applied to the displayed result.

Apply a Percentage Change

Use this secondary calculator when you know the starting value and the percentage to apply.

How to Calculate Percentage Change

To calculate percentage change, subtract the original value from the new value, divide that change by the original value, and multiply by 100. This standard formula works directly when the original value is positive. If the original value is zero, the percentage change is undefined because division by zero is not defined.

Percentage change formula
Percentage change = ((New − Original) / Original) × 100%
Change in value
Change = New − Original

The denominator matters. Percentage change compares the change with the starting value, not the ending value. If a value rises from 80 to 100, the change is 20. Dividing 20 by 80 gives 0.25, so the percentage increase is 25%.

Percentage Increase and Percentage Decrease Examples

Increase: 100 to 125

Change = 125 − 100 = 25. Percentage change = 25 / 100 × 100 = 25%. The value increased by 25%.

Decrease: 200 to 150

Change = 150 − 200 = −50. Percentage change = −50 / 200 × 100 = −25%. The value decreased by 25%.

No change: 80 to 80

Change = 0. Since the original value is not zero, percentage change = 0 / 80 × 100 = 0%. There was no change.

Zero baseline: 0 to 100

Change = 100. Standard percentage change is undefined because the formula requires 100 / 0. The calculator reports the numerical change without inventing a percentage.

What Happens When the Original Value Is Zero?

Percentage change uses the original value as its baseline. When that baseline is zero, the calculation would divide by zero. For 0 to 50, the change in value is +50, but the standard percentage change is undefined. It is not a normal 50%, 100%, or infinite percentage increase.

The same issue applies to 0 to 0. There is no numerical change, but the percentage-change formula still contains 0 / 0. This page therefore reports no numerical change and states that the percentage formula is undefined.

Percentage Change With Negative Values

Negative starting values need an explicit convention. For example, moving from −10 to −5 is a numerical increase of 5. Dividing by the original value gives 5 / −10 = −50%, which has a sign opposite to the numerical direction. Dividing by the magnitude of the original value gives 5 / 10 = +50%.

This calculator’s convention: when the original value is negative, the displayed relative change uses the absolute magnitude of the original value in the denominator: (New − Original) / |Original| × 100. The page also reports the ordinary original-denominator arithmetic in its warning. This keeps the direction visible while making the convention explicit.

If values cross zero, such as 10 to −10 or −10 to 10, the arithmetic can be computed, but the percentage can be hard to interpret in ordinary business or scientific language. In those cases, the signed numerical change and absolute difference should be read alongside the percentage result.

Percentage Change vs Percentage Difference

Percentage change assumes an ordered relationship: an original value changes into a new value. The original value is the baseline. Percentage difference is used when two values are being compared without a natural “before” and “after” order. A common percentage-difference formula divides the absolute difference by the average magnitude of the two values.

Common percentage difference formula
|A − B| / ((|A| + |B|) / 2) × 100%

Do not switch these formulas just because the same two numbers are involved. If one value is clearly the starting point, percentage change is usually the relevant calculation.

Percentage Change vs Percentage Points

Percentage points are used when the values themselves are percentages. Suppose a conversion rate rises from 20% to 25%. The percentage-point change is 25% − 20% = 5 percentage points. The relative percentage increase is (25 − 20) / 20 × 100 = 25%.

Those are different statements. “Up 5 percentage points” describes the direct gap between two percentages. “Up 25%” describes the change relative to the original 20% baseline.

Applying an Increase or Decrease to a Number

The secondary calculator above answers a different question: what is a number after a stated percentage increase or decrease? To increase a value by p%, multiply it by 1 + p/100. To decrease it by p%, multiply it by 1 − p/100.

Increase a value by p%
New value = Original × (1 + p/100)
Decrease a value by p%
New value = Original × (1 − p/100)

For example, 200 increased by 15% is 200 × 1.15 = 230. A 15% decrease from 200 is 200 × 0.85 = 170.

Common Percentage Change Mistakes

  1. Dividing by the new value instead of the original value.
  2. Forgetting to multiply the decimal ratio by 100.
  3. Treating a zero starting value as if it were a normal percentage baseline.
  4. Confusing percentage change with percentage difference.
  5. Confusing a percentage change with a percentage-point change.
  6. Assuming a 20% increase followed by a 20% decrease returns to the starting value. Starting at 100 gives 100 → 120 → 96.
  7. Ignoring the ambiguity created by a negative original value.
  8. Rounding intermediate values too early instead of rounding only the displayed result.
  9. Saying “increased by 125%” when the intended meaning is “increased to 125% of the original.”
  10. Treating percentage change as evidence of statistical significance. Percentage change is descriptive arithmetic, not a significance test.

Related Calculators and Statistics Guides

Statistics Calculators Percentage Calculator Weighted Average Calculator Mean Calculator Descriptive Statistics Calculator Descriptive Statistics Guide Coefficient of Variation Statistical Interpretation

Frequently Asked Questions

For a positive original value, percentage change = ((new value − original value) / original value) × 100. The sign shows direction: positive for an increase, negative for a decrease, and zero for no change.

Subtract the original value from the new value, divide that increase by the original value, and multiply by 100. For 80 to 100, the increase is 20 and 20 / 80 × 100 = 25%.

Subtract the original value from the new value and divide by the original value. A fall from 200 to 150 gives −50 / 200 × 100 = −25%, which is normally stated as a 25% decrease.

Yes. If a positive value more than doubles, the percentage increase exceeds 100%. For example, 100 to 250 is an increase of 150, so the percentage increase is 150%.

Not with the standard formula. The original value is the denominator, so an original value of zero would require division by zero. The numerical change can still be reported, but the standard percentage change is undefined.

When the original value is positive, a negative percentage change means the new value is lower than the original value. If the original value itself is negative, the sign becomes convention-dependent, which is why this calculator gives an explicit warning.

The baseline changes. A 50% decrease takes 100 down to 50. To return from 50 to 100, the increase is 50 relative to a new baseline of 50, so 50 / 50 × 100 = 100%.

For one interval, percent change may be described as a growth or decline rate in some contexts. Multi-period annualized growth is different because compounding matters, so a total percentage change should not automatically be divided by the number of years.