How to Calculate Percentage Increase (and Decrease)

The formula

Percentage change = (New − Old) ÷ Old × 100.

The result is positive for an increase, negative for a decrease. To report a 'decrease of X%', take the absolute value.

Worked example: a raise

Your hourly pay goes from $22.50 to $24.75.

Change = 24.75 − 22.50 = 2.25. Divide by the old value: 2.25 ÷ 22.50 = 0.10. Multiply by 100: a 10% raise.

Applying a percentage directly

To increase a number by p%, multiply by (1 + p/100). To decrease, multiply by (1 − p/100).

Increasing 340 by 15%: 340 × 1.15 = 391. Decreasing 340 by 15%: 340 × 0.85 = 289.

The reversal trap

If a price rises 25% and then falls 25%, it does not return to the start. 100 × 1.25 = 125, then 125 × 0.75 = 93.75 — you're 6.25% below where you began.

To undo a 25% increase you need a 20% decrease (1 ÷ 1.25 = 0.8). The reversal percentage is always smaller than the increase that created it.

Edge cases

• Starting from zero: undefined. There is no meaningful percentage increase from 0 to anything.
• Decreases past −100%: impossible for quantities that can't go negative.
• Repeated changes compound: multiply the (1 + p/100) factors together.