How Discounts Work: Percent Off vs Dollars Off

Every discount is one of two things: a percent off, or a flat number of dollars off. Stores mix them freely — "25% off," "$20 off," "extra 10% at checkout" — and the mixing is where money leaks. The math is elementary school arithmetic; the discipline is knowing which deal is better before you're standing at the register.

Percent off: the basic math

A percent discount multiplies the price by what you keep, not what you save. "25% off" means you pay 75%, so multiply by 0.75:

sale price = price × (1 − discount)

A jacket marked $80 at 25% off sells for $80 × 0.75 = $60.00, and you saved $20. The multiply-by-what's-left form avoids the two-step error people make when they compute the discount and then subtract — same answer, but one operation instead of two, and it extends cleanly to stacking (below).

Percent off vs dollars off

Flat-dollar and percentage discounts aren't comparable until you apply both to the actual price. Take "$50 off" against "30% off":

• On a $150 item: $50 off gives $100; 30% off gives $105 — the flat $50 wins
• On a $200 item: $50 off gives $150; 30% off gives $140 — the percent wins

There's a switch point, and you can find it by asking what price makes the two equal: 30% of that price must equal $50, so the price is $50 / 0.30 = $166.67. Below that price, the flat $50 is the better deal; above it, 30% wins. The general rule: compare the discount to the price it's applied to — a flat amount is worth more on cheap items, a percentage scales up on expensive ones.

Where tax enters the picture

Discounts apply to the merchandise price; sales tax is then computed on what you actually pay. A $80 jacket at 25% off with an 8% tax rate costs $60.00 at the register plus $4.80 tax = $64.80 — not 8% of the original $80. The sequence is always discount first, then tax, which is good news: tax is never charged on money the discount removed. The mechanics of the tax step itself are covered in how sales tax works. (Coupons behave the same way — a $10-off coupon shrinks the taxable base in most states, though a few tax the pre-coupon price, which is why two identical receipts can differ.)

Stacking: why 20% + 10% is 28%, not 30%

Stacked discounts apply sequentially, each one on the already-reduced price. A $100 item with 20% off, then an extra 10% coupon:

100 × 0.80 = 80.00   (first discount)
 80 × 0.90 = 72.00   (second discount on the sale price)

You paid 72% of full price — a combined 28% off, not 30%. The percentages multiply: 0.80 × 0.90 = 0.72. Order doesn't matter (you get $72 either way), but the store's framing does: "20% + 10%!" reads like 30% and delivers 28%. On a $500 order, that gap is $10.

Two traps worth naming

The round-trip trap. A price that rises 25% and then falls 25% does not return to where it started: $100 → $125 → $93.75. A +x% followed by −x% always lands below the start, because the second percentage applies to a different base — the same asymmetry explained in how percent change works. This is why "prices dropped back 25%" after a markup can still mean you're paying more than before.

The invented-original trap. A tag reading "$150, now $45 — 70% off" can be verified with division: if $45 is 30% of the original, the original is $45 / 0.30 = $150. When the math checks out, the discount is real. When a store's "original" price is suspiciously convenient, the discount may be anchoring rather than arithmetic — the sale price is the only price that ever mattered.

Try it yourself

The Discount Calculator handles percent-off and dollars-off deals, double discounts, and the final price after tax. The Percentage Calculator answers the surrounding questions — what percent one number is of another, percent increase or decrease. And the Sales Tax Calculator adds the correct tax to your discounted price so the total at the register holds no surprises.