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Discount Calculator

Take a percentage off any price, work back from a sale price to the original, and see what stacked discounts are really worth — 20% plus 10% is 28%, not 30%.

Final price
$72.00
You save
$28.00
Effective vs naive discount
28%
effective — what you actually pay
30%
naive — what the signs add up to
savedthe gap stacking hides

You pay $72.00 of $100.00 — an effective 28% off, against 30% on the signs.

Apply several discounts in order, the way a checkout does, and see what they total.

Applied top to bottom — 20 then 10 takes 10% of the already-reduced price. A trailing % is fine.

Results update as you type. Savings are rounded half-up to the cent at every step, and everything runs in your browser.

How it works

  1. 1

    Pick the question you are asking

    Forward answers what an item costs after a discount. Reverse works back from a sale price to the original it implies. Stack applies several discounts in sequence and shows what they are worth together — the mode for '30% off plus an extra 20%' signage.

  2. 2

    Enter the price

    Type it as you would read it off the tag — 49.99 or 1,299 — and the tool reads it to the cent. Results update as you type, and a value the tool cannot read as a price is flagged inline rather than silently treated as zero.

  3. 3

    Enter the percentage, or list the stack

    A single percent for forward and reverse; for stack mode, one percentage per line in the order the checkout would apply them. Each one must sit between 0 and 100, and a trailing % sign is accepted.

  4. 4

    Read the breakdown

    Every mode reports the final price and the saving. Stack mode adds the effective percentage next to the naive one — what the discounts actually total against what they appear to add up to — with the gap drawn on the meter.

The stack that isn't a sum: why 20% + 10% is 28%

The most common discount arithmetic error is treating percentages of the same item as if they were percentages of the same money. They are not, because each discount changes the base the next one works on. Follow $100.00 through a 20%-then-10% stack and the mechanics are visible: the first discount is computed on the full price, the second on what is left of it. Each step is ordinary till arithmetic — a saving rounded half-up to the cent, then the next percentage taken on the new figure.

StepPercent offTaken ofSavingPrice after
120%$100.00$20.00$80.00
210%$80.00$8.00$72.00
Stack total——$28.00$72.00

The total saving is $28.00 on a $100.00 original: an effective discount of 28%, against the 30% the two signs add up to. Equivalently, the price is multiplied by 0.8 and then by 0.9, and 0.8 × 0.9 = 0.72 — you pay 72 cents on the dollar, not 70. The shortfall from the naive sum is not rounding and not a trick of this tool; it is structural, and it grows with the size of the earlier discounts because those are the ones that shrink the base the rest work on. Two 50% discounts leave you at 25% of the original price, a 75% effective discount against the 100% they appear to promise.

Every row above is what the calculator returns for those exact inputs, so the table doubles as a test script: enter 100.00 with 20 and 10 on separate lines in stack mode and the tool reports $72.00 final, $28.00 saved, 28% effective against 30% naive.

Percent off versus amount off: where the two offers cross

Percent-off and flat-amount offers are different shapes of the same discount, and which one serves you depends only on the price. A percentage scales with the ticket, so it is worth little on cheap items and a great deal on expensive ones; a flat amount is indifferent to the ticket and therefore dominates at the low end. Between the two regimes lies a single crossing price where the offers are worth exactly the same — for P percent against a flat F dollars, that price is 100 × F ÷ P, which for 20% against $20 is $100.

Price20% off saves$20 off savesBetter offerGap
$50.00$10.00$20.00$20 off$10.00
$100.00$20.00$20.00identical$0.00
$200.00$40.00$20.0020% off$20.00

The pattern generalizes in a useful way: a flat coupon is beaten by P percent once the price passes 100 × F ÷ P dollars, so a $10 coupon loses to 25% off above $40, and a $50 coupon loses to 10% off only above $500. Retailers pair the two forms deliberately — flat amounts on low-ticket lines where percentages look stingy, percentages on high-ticket lines where they look generous — so the offer form itself is a hint about the margin. Priced on the actual tag rather than on instinct, the comparison usually takes under a minute.

Rounding: half-up, to the cent, at every step

A percentage of a price in dollars and cents rarely lands on a whole cent, and somewhere the penny has to be settled. This tool settles it the way tills do: half-up, at the moment the discount is taken. $9.99 at 15% off earns a saving of $1.4985, which rounds to $1.50, and the item rings up at $8.49 — the price a cash register would show, not the $8.4915 of unrounded arithmetic.

$9.99 purchaseSavingsFinal priceEffectiveNaive
15% off$1.50$8.4915%15%
50% + 50% off$7.49$2.5074.97%100%

The second row shows where stacking and rounding meet. Half of $9.99 is $4.995, which rounds half-up to $5.00; the second 50% then takes $2.50, landing at $2.50 — one cent above the $2.4975 a single unrounded calculation would suggest. The saving is $7.49, and against the original that is 74.97%, which is the honest answer to 'how much off is 50 plus 50 percent' for this price. The tool reports effective percentages to two decimals for exactly this reason: whole-number percentages would hide the very cents this tool exists to get right.

Frequently asked questions

Is 20% off plus 10% off the same as 30% off?
No — it is 28% off, and the difference is what the second percentage is taken of. On a $100.00 item the first discount removes $20.00, leaving $80.00; the second discount is then computed on that shrunken price, so it removes $8.00 rather than $10.00, and the item rings up at $72.00. The total saving is $28.00, which is 28% of the original — the percentages multiply (0.8 × 0.9 = 0.72) instead of adding. The only case where stacked percentages behave like their sum is the trivial one where the first percentage is zero, because then the second has the full original price to work on.
When is 20% off better than $20 off?
It depends entirely on the price, and the two offers cross at exactly one point. Twenty percent of a price equals a flat $20 when the price is $100, so there the offers are identical: both leave you at $80.00. Below that price the flat amount wins — on a $50.00 item, 20% is only $10.00 while the flat $20 doubles it. Above it the percentage wins — on a $200.00 item, 20% is $40.00 against the same flat $20. The general crossing point for P percent against a flat amount F is a price of 100 × F ÷ P dollars, so a $10 coupon beats 25% off until the price passes $40. Whichever way the signage is spun, the tool's forward and stack modes let you price both offers on the actual tag before you commit.
What does "extra 20% off already-reduced items" actually mean?
It means the extra percentage is applied to the reduced price, never to the original tag — the phrase 'already-reduced' is doing the work. A $100.00 tag at 30% off comes down to $70.00, and the extra 20% is taken of that $70.00, removing $14.00 and landing at $56.00. The total discount is $44.00, or 44% — not the 50% that reading the two numbers side by side suggests. Stores price it this way because the alternative genuinely gives away half the ticket, but the wording survives because 30 + 20 reads as 50 at a glance. Entering 30 and 20 in the stack mode reproduces the $56.00 exactly.
Why do stores stack discounts instead of offering one big one?
Because stacked numbers sound bigger than they are worth. Each successive percentage acts on a smaller base, so its absolute contribution shrinks: on that $100.00 item the 20% takes $20.00 but the following 10% takes only $8.00 — a $2.00 gap on a single item, and a far wider one on a cart. A single '28% off' sign also invites direct comparison with a competitor's '30% off', which the stacked version would lose, while '20% off plus an extra 10%' sounds like 30. None of this makes the final price dishonest — you really do pay $72.00 — but the framing consistently flatters the offer, which is why computing the effective percentage yourself is worth the ten seconds.
How are the results rounded?
Half-up to the cent, at every step, the way a till settles a fraction of a penny: a saving of $1.4985 is charged as $1.50, and $9.99 at 15% off therefore rings up at $8.49. Stacked discounts round after each discount rather than once at the end, because that is how registers apply them — $9.99 cut by 50% twice goes to $5.00 (from $4.995) and then to $2.50, not to $2.4975 rounded once. The consequence is that a stack's final price can differ by a cent from the single-discount equivalent, and the effective percentage can carry two decimals — that second stack saves $7.49, which is 74.97% of the original, not the clean 100% the two signs promise.
How do I find the original price from a sale price?
Use the reverse mode: give it the sale price and the percentage the sign claimed, and it divides the sale price by the fraction of the price you still pay. An $80.00 sale at 20% off means you paid 80% of the original, so the original was $80.00 ÷ 0.80 = $100.00. This is the check worth running when a receipt shows a discount percentage and you want to know what the store says the item normally costs — or when comparing two sales that quote different percentages on different current prices. The one input it refuses is a 100% discount, because a zero price divided by zero leaves nothing to work back from.

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Last updated: October 10, 2026