The Universal Calculation Engine
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The Universal Calculation Engine

Discounts

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

Start this lessonHow to calculate percent off a price

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 this mistake is expensive

Cart math is where small percents turn into real cash. Misreading a stacked promo often means you think you saved more than you did. The same habit shows up in tax on the discounted subtotal, subscription teaser rates, and any fine print where the second discount bites a smaller base than you pictured.

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.