Percentage Formulas Explained

Every percentage question on this site's calculator reduces to one of three formulas. Here they are worked through by hand.

X% of Y

result = (X ÷ 100) × Y

Example: 20% of 150 → (20 ÷ 100) × 150 = 30.

X is what percent of Y?

result = (X ÷ Y) × 100

Example: 30 is what percent of 150? → (30 ÷ 150) × 100 = 20%.

Percentage change from X to Y

result = ((Y − X) ÷ X) × 100

Example: from 50 to 65 → ((65 − 50) ÷ 50) × 100 = +30% (an increase). From 65 back to 50 → ((50 − 65) ÷ 65) × 100 ≈ −23.1% (a decrease) — the two directions aren't symmetric, because the base number changes.

Markup vs margin

Both describe the same profit, measured against a different base:

• Markup = profit ÷ cost. A $50 item sold for $75 has $25 profit on a $50 cost: 25 ÷ 50 = 50% markup.
• Margin = profit ÷ selling price. Same numbers: 25 ÷ 75 ≈ 33.3% margin.

Markup is always the larger number for the same sale — mixing them up is a common (and expensive) pricing mistake.

Percentage points vs percent

If something moves from 20% to 25%, that's a 5 percentage-point increase, but a 25% relative increase (5 ÷ 20 × 100). Headlines often blur the two — always check which one is meant.

Back to the percentage calculator.