The Universal Calculation Engine
The Universal Calculation Engine

Discounts

Sale tags describe one price path; the receipt shows the multiplied result.

The “half off” that isn’t

A coat lists for $200: 30% off, then an extra 20% off the reduced price. Your brain wants to add 30 + 20 and call it 50% off. The register multiplies: you keep 70% of the price, then 80% of that. You pay 0.70 × 0.80 = 56% of $200: $112, not $100. The $12 gap is what you get when you add the two discount percents (30% + 20%) instead of multiplying the shares you still pay (70% × 80%).

Why stacked discounts mislead

Misreading a stacked promo usually means overstating the discount. The same issue shows up in tax on the discounted subtotal, subscription teaser rates, and any offer where the second percentage applies to a smaller base.

What one “percent off” does

“p% off” means: pay (100 − p)% of the current sticker. In one step: multiply the price by (1 − p/100).

Price after one discount = list × (1 − p/100)
Example: 25% off $80 → $80 × 0.75 = $60

Stacking: multiply the “still paying” factors

Each new percent-off applies to the new lower number, not the original tag. Chain discounts by multiplying what you still pay after each step:

Final = L × (1 − p₁/100) × (1 − p₂/100) × …

If you add the percents instead, you invent a fake single-step discount. That is how “30 + 20” becomes a phantom 50% when reality is 44% off total.

Try it yourself

Add tax on the true subtotal before you compare merchants; “saved 40%” means nothing if shipping and fees erase it.

Expected vs guessed

Honest stack: 30% then 20%  →  pay 56% of list  →  44% off in one breath
Additive fantasy: 30 + 20 = 50  →  implies pay 50% of list
On $200: $112 vs $100, small until it repeats every checkout

Where you actually see this

  • Clearance “extra % off”: the second cut hits the already-reduced price.
  • “$15 off your first 3 months” subscriptions: annualize the dollars and compare to a plan you will keep.
  • Checkout coupons on top of member pricing: sequence matters; read the receipt, not the poster.

Traps people actually fall for

  • Treating the strikethrough “original” as truth; it is a reference, not an appraisal.
  • Confusing “20% off the original” with “an extra 20% off the sale price”: different bases, different money.
  • Letting “today only” replace a 30-second Discount calculator check. Urgency is optional; wrong bases are not.

Use the calculator

FAQ

Is 30% off twice the same as 60% off?

No. Two successive 30%-off steps multiply: 0.7 × 0.7 = 0.49 of the original price (51% off total), not 60% off in one step.

How do I compare two sales fast?

Convert each offer to one final multiplier on the same list price, then add tax and fees for an out-the-door total.

Should I trust the “original price” on the tag?

Use it as context. Compare final prices on items you would actually buy, not the display price alone.