Guides/Original price before discount

Find the original price before a discount

A “reverse percentage” asks: if this is the price after an X% discount, what was the full price? You cannot add the discount percent back onto the sale price — that understates the original.

Reverse discount formula

Original = sale price ÷ (1 − discount% ÷ 100)

Example structure: after 20% off, you pay 80% of the original, so divide the sale price by 0.80. The discount percent must be less than 100%.

Related reverse: “X is what % of Y”

Another reverse question is: 30 is what percent of 150? → (30 ÷ 150) × 100 = 20%. That answers “what share,” not “what was the pre-discount sticker.”

Worked examples

20% off, sale $40: original = 40 ÷ 0.80 = $50. Check: 20% of 50 = $10; 50 − 10 = $40.
25% off, sale $75: 75 ÷ 0.75 = $100.
15% off, sale $42.50: 42.50 ÷ 0.85 ≈ $50.00.
Wrong method: $40 + 20% of $40 = $48 — not the true $50 original. Always divide by the remaining fraction, not add percent of the sale price.
Why +20% ≠ undo −20%: 100 → 80 needs +25% to return (80 × 1.25 = 100), matching 80 ÷ 0.80 = 100.

Common mistakes

Adding the discount % to the sale price instead of dividing by (1 − rate).
Confusing “sale is 20% of original” with “20% off” (which leaves 80%).
Ignoring tax or fees that were added after the discount.

Verify with the free calculator

Use thePercentage CalculatorDiscount tab: enter your guessed original and the off-% — the sale price should match the ticket. For forward discounts, seedecrease & discount math.