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Math calculator

Percentage Change Calculator

Find a percent increase, decrease, or unsigned difference from an original value to a new value.

Increase25%
Absolute change20

FormulaIncrease % = ((New − Original) ÷ Original) × 100
Calculation steps
  1. 100 − 80 = 20
  2. (20 ÷ 80) × 100 = 25%

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How it works

How to use this percentage change calculator

  1. Choose Increase, Decrease, or Difference. These are three views of the same pair of numbers, not separate pages.
  2. Enter the original value (the divisor) and the new value.
  3. Read the percent, the absolute change, and the substituted steps.

Formula

The calculation formula

Change % = ((New − Original) ÷ Original) × 100
01

Subtract the original value from the new value to get the absolute change.

02

Divide that change by the original value.

03

Multiply by 100. Difference mode uses absolute values so the result stays non-negative.

Worked examples

Example calculations

Percent increase

A reading moves from 80 to 100. ((100 − 80) ÷ 80) × 100 = 25% increase.

Percent decrease and difference

From 80 to 60 the decrease is ((80 − 60) ÷ 80) × 100 = 25%. The unsigned difference is also 25%.

When to use it

Common use cases

  • Compare a price, score, or measurement across two periods
  • Report a raise or a markdown as a percent
  • Show how far two values sit apart without a signed direction

Limits

Assumptions and limits

  • Increase uses (new − original) ÷ original. Decrease uses (original − new) ÷ original.
  • Difference uses |new − original| ÷ |original| and is never negative.
  • The original value cannot be 0 because it is the divisor.
  • A negative original is allowed; the signed modes keep the sign of the original in the denominator.

Questions

Frequently asked questions

What is the difference between percent change and percent difference?

Percent increase and decrease keep a direction. Percent difference takes absolute values so 80→60 and 80→100 both report 25% apart.

Why can I not start from zero?

Relative change divides by the original amount. Starting from 0 would require dividing by zero, which is undefined.

Is this the same as a percentage of a number?

No. A percentage of a number answers “what is p% of n.” Percentage change answers “how far did a value move relative to where it started.”

Sources

Sources and review