Discount Math Guide
The single formula for sale price — and the stacking trap that turns "30% plus 20% off" into something less than 50% off.
Compute sale prices correctly, and spot the stacked-discount math that stores use to nudge perceived savings.
A discount is a single subtraction done multiplicatively: sale price = original × (1 − rate). The formula stays tidy until you try to combine two discounts — "30% off plus an extra 20%" is NOT 50% off. This guide covers the basic math, the stacking trap, and the reverse calculation for when only the sale price is quoted.
Part of: Saving & Spending Calculators
Quick answer
Compute sale prices correctly, and spot the stacked-discount math that stores use to nudge perceived savings.
Key points
- ▸ Core formula: sale price = original × (1 − rate/100). For 20% off $49.99 → 49.99 × 0.80 = $39.99. Savings: $10.00.
- ▸ Savings amount: original × (rate/100). 40% off $120 → 0.40 × 120 = $48 saved; $72 paid.
- ▸ Stacked discounts MULTIPLY, not add. 30% off, then 20% off the reduced price: 0.70 × 0.80 = 0.56, i.e. 44% off total. Not 50%.
- ▸ Reverse the math: if a $60 item is now $45, the discount rate is (60 − 45) / 60 = 25%.
- ▸ Tax is applied to the sale price, not the original. "$100 item, 20% off, 7% tax" → $80 × 1.07 = $85.60.
- ▸ Coupon math: a percent coupon stacks with sale price multiplicatively; a dollar-off coupon subtracts after the percent. Store policy decides the order.
How to
- Enter the original price.
- Enter the discount percent.
- The tool shows savings and final price instantly.
- For a second discount, enter the NEW (reduced) price and apply the second percent.
- For tax, apply it to the final sale price — not the original.
Examples
- 20% off $49.99Save $10.00, pay $39.99. (From the tool example.)
- Stacked: 30% then 20%$100 → 0.70 × 100 = $70 → 0.80 × 70 = $56. You save $44, a 44% effective discount — not 50%.
- Reverse: known sale priceTag says "$36 (was $48)." Discount = (48 − 36) / 48 = 25%.
When to use which tool
- CYAN · STABLE — Single percent-off discount — mental math or one tool pass.
- GOLD · GUARDED — Stacked discounts, percent-off plus dollar-off coupon — use the tool for each layer, do not sum percents.
- MAGENTA · CRITICAL — Bundle/BOGO offers with store-policy quirks — compute the effective per-unit price; the percent rarely captures it cleanly.
Related
Frequently asked questions
› Why is "30% + 20% off" not 50% off? Troubleshooting
Because the second discount applies to the already-reduced price. 0.70 × 0.80 = 0.56 (44% off total). The absent 6 percentage points are the second discount being "wasted" on a smaller base.
› Do I include tax in the discount math?
No. Compute the sale price first, then add tax on top. Tax on the pre-discount price is incorrect (and illegal in most jurisdictions).
› What about a "50% off the second item"?
That is 25% off the pair if the items are priced the same. Two items at $40 each = $80; the second is $20 off; total $60, which is 25% off $80.
› How accurate are online calculators and converters? Trust & accuracy
Online calculators are only as accurate as the numbers, units, assumptions, and rounding choices you enter. Recheck the input values first, then compare the formula against your real situation. For legal, tax, medical, financial, or professional decisions, treat the result as a planning estimate, not advice.
› What inputs should I double-check first? Troubleshooting
Double-check units, dates, percentages, decimal placement, and whether the input is before-tax, after-tax, gross, net, original, or final. Most calculator mistakes come from feeding the right formula the wrong base. If the result feels off, rebuild it from a simple worked example.