Percentage Change Calculator: Increase, Decrease, and Difference

Percentage change measures how much a value has increased or decreased relative to its starting point, expressed as a percentage. It is different from the absolute change (which is just the raw difference) and from the percentage point difference (which compares two percentages directly). Percentage change is the most common way to communicate growth rates, price changes, and statistical trends.

The formula: percentage change = ((new value − old value) ÷ old value) × 100. A positive result means an increase. A negative result means a decrease. The sign tells you the direction; the number tells you the magnitude relative to where you started.

Percentage increase applies when the new value is higher than the original. Formula: ((new − old) ÷ old) × 100. For a price that rose from $40 to $50: ((50 − 40) ÷ 40) × 100 = (10 ÷ 40) × 100 = 25% increase. The result means the new price is 25% higher than the original.

A common application is calculating year-over-year revenue growth. If annual revenue was $800,000 and rose to $1,000,000: ((1,000,000 − 800,000) ÷ 800,000) × 100 = (200,000 ÷ 800,000) × 100 = 25% growth. The same formula applies regardless of the scale of the values.

Percentage decrease applies when the new value is lower. The formula is identical: ((new − old) ÷ old) × 100. The result will be negative, indicating a decrease. For a stock price that fell from $80 to $60: ((60 − 80) ÷ 80) × 100 = (−20 ÷ 80) × 100 = −25%. The price decreased by 25%.

Note that a 25% increase followed by a 25% decrease does not return to the original value. From $100: a 25% increase gives $125. A 25% decrease on $125 gives $93.75 — not $100. The asymmetry exists because the percentage is applied to a different base each time.

This is one of the most common quantitative mistakes in reporting. A percentage point is the arithmetic difference between two percentages. Percentage change is the relative change. If an interest rate rises from 4% to 6%, that is a 2 percentage point increase — but a 50% change in the rate.

Financial and political reporting frequently confuses these. When a market share rises from 20% to 25%, saying 'it increased by 5%' is ambiguous — it could mean 5 percentage points (the arithmetic difference) or it could mean a 25% increase in the share itself. Specifying 'percentage points' versus 'percent change' removes the ambiguity.

When a value changes across multiple periods — like annual price increases or monthly growth rates — the periods compound, not add. A 10% increase in year one followed by a 10% increase in year two is not a 20% total increase. It is a 21% total increase: (1.10 × 1.10 = 1.21).

For compound change over n periods at a consistent rate r: total change = (1 + r)^n − 1. For 5% annual growth over 3 years: (1.05)^3 − 1 = 1.1576 − 1 = 0.1576 = 15.76% total growth. This is the foundation of compound interest calculations.

Use these benchmark pairs for fast sanity checks.