About

Retail math is often deceptive. A common misconception is that a "50% off plus 20% off" sale results in a 70% total reduction. In reality, discounts are typically applied sequentially, not addictively. This tool provides the exact calculation for both single and stacked (double) discounts, ensuring shoppers understand the true final cost and total savings before reaching the register.

Additionally, the reverse calculation feature solves the "what was the original price?" problem. This is particularly useful when auditing receipts or evaluating the value of a final sale item where only the reduced price is visible. Accurate to two decimal places, it handles the rounding logic used in most point-of-sale systems.

Formulas

The formula for a single percentage discount is straightforward multiplication by the complement of the rate.

Price_final = Price_orig × (1 − rate100)

For stacked discounts (Double Discount), the second discount applies to the intermediate price, not the original.

Price_final = Price_orig × (1 − d₁) × (1 − d₂)

Reference Data

Original	Discount	Math Logic	Final Price
$100	20%	100 × 0.80	$80.00
$100	50% + 20%	(100 × 0.50) × 0.80	$40.00
$50	10%	50 × 0.90	$45.00
$200	25%	200 × 0.75	$150.00
$80	5$ off	80 - 5	$75.00

Frequently Asked Questions

No. In retail, discounts are usually compounded. Taking 50% off $100 gives $50. Taking another 50% off that $50 leaves $25. The total effective discount is 75%, not 100%.

This tool focuses strictly on price reductions. Sales tax is applied to the final price after all discounts are calculated, depending on local laws.

Reverse mode allows you to enter the amount you actually paid and the discount percentage that was applied to find out what the item cost originally. It rearranges the formula: Original = Final / (1 - rate).

Currently, the primary logic focuses on percentage savings, as these are more computationally complex to estimate mentally than simple subtraction of a fixed dollar amount.