How to Calculate Percentage Increase (and Decrease)

Percentage increase and decrease calculations come up constantly — pay raises, price changes, growth rates, and discounts. The formula is simple once you know it, but it is easy to apply incorrectly if you divide by the wrong number.

The Percentage Increase Formula

% Increase = ((New Value − Old Value) ÷ Old Value) × 100. The key rule: always divide by the OLD (original) value, never the new one.

Worked Examples

• •A salary rises from $50,000 to $55,000: % Increase = ((55,000 − 50,000) ÷ 50,000) × 100 = (5,000 ÷ 50,000) × 100 = 10%.
• •A price falls from $200 to $150: % Change = ((150 − 200) ÷ 200) × 100 = (−50 ÷ 200) × 100 = −25%, a 25% decrease.
• •Website traffic grows from 1,200 to 1,800 visitors: % Increase = ((1,800 − 1,200) ÷ 1,200) × 100 = 50%.

Percentage Increase vs Percentage Points

This is the single most common source of confusion. If an interest rate rises from 4% to 6%, that is a 2 percentage point increase (6 − 4 = 2), but it is actually a 50% relative increase (since (6−4)÷4 × 100 = 50%). News headlines often blur this distinction, so always check which one is being reported.

Reversing a Percentage Increase Is Not Symmetric

A common mistake: increasing a number by X% and then decreasing the result by the same X% does NOT return you to the original number. Example: $100 increased by 50% = $150. Now decrease $150 by 50% = $75 — not back to $100. This is because the base value changed between the two calculations (the second decrease is calculated from $150, not $100).

Calculating the Required Increase to "Undo" a Decrease

If a value drops by X%, the percentage increase needed to return to the original value is always larger than X%. Formula: Required % Increase = (X ÷ (100 − X)) × 100. Example: a value drops 20% — to return to the original, you need an increase of (20 ÷ 80) × 100 = 25%, not 20%.