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Percentage Change Calculator

Change (%): -
Visual representation

Percentage Change Calculator diagram

The diagram updates with your entries and is illustrative, not necessarily drawn to scale.

Calculation explained

How this result was calculated

The formula, your substituted values, and the evaluated result are shown below.

Visual analysis

How the result changes when the first input changes

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This calculator applies the percentage change relationship. Enter values in the stated units and review the result. Check assumptions and use appropriate professional guidance for safety-critical decisions.
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About this calculator

Calculate percentage change using clearly labelled inputs.

Calculator guide

How the percentage change calculator works

Percentage change measures how much a value has grown or shrunk relative to where it started:

Change (%) = (new value − original value) ÷ original value × 100

A positive answer is an increase and a negative answer is a decrease.

Worked examples

  1. Rent goes from $480 to $520 a week: (520 − 480) ÷ 480 × 100 = +8.33%
  2. A share falls from $92 to $80: (80 − 92) ÷ 92 × 100 = −13.04%
  3. Sales rise from 80 units to 92: (92 − 80) ÷ 80 × 100 = +15%

Examples 2 and 3 use the same two numbers but give different answers, because the starting point (the base) is different.

Why gains and losses aren't symmetrical

If something falls 50%, it must then rise 100% to get back to where it started. A $100 investment that drops 20% to $80 needs a 25% gain to return to $100. That asymmetry is why large losses are so hard to recover from.

Percentage change vs percentage points

If an unemployment rate moves from 4% to 5%: - the change is 1 percentage point - the percentage change is 25%

Both are correct, but they mean different things. Say which one you mean.

Annual growth over several years

For growth across several years, the compound annual growth rate is often more useful:

CAGR = (end ÷ start)^(1 ÷ years) − 1

A house bought for $600,000 and sold for $840,000 six years later grew 40% in total, which is about 5.8% a year.

Common mistakes

How do I calculate a percentage increase?

Subtract the old value from the new value, divide by the old value and multiply by 100.

How do I calculate a percentage decrease?

Use the same formula. The result will be negative. From 50 to 40 is −20%.

If a price drops 20% then rises 20%, is it back where it started?

No. $100 drops to $80, then rises 20% to $96, which is still 4% below the start.

Written by Sam Alex, civil engineer. About the author