Discount Calculator

How to use the discount calculator

Enter the original price and the discount percentage and you get what you save and what you would pay. The defaults, $80.00 at 25 percent off, save $20.00 for a $60.00 price. The slider runs from 0 to 90 percent so you can match any tag and watch the final figure move as you drag.

Leave the sales-tax field at zero and tax stays out of the arithmetic completely; fill it in with your combined local rate and the tool adds tax to the discounted price, which is exactly the order a register uses. That order is not cosmetic: the discount shrinks the taxable amount, so a bigger reduction saves you a little tax as well as a little price.

A percent-off tag means the percentage comes off the original price, never off some already-lowered figure. Twenty-five percent off an $80.00 item is $20.00 off, leaving $60.00, and that stays true no matter how the sign is worded.

That is also why the tool now runs backwards. Given only the $60.00 you paid, the ticket price is 60 ÷ 0.75 = $80.00, not the $75.00 that adding 25 percent back on suggests. The percentage was a share of the larger number, so undoing it divides rather than adds, and the gap widens as the discount does.

The distinction only starts to matter when a second discount appears, because two percentages do not combine the way the signs make them look. Stacked discounts are sequential: each one applies to whatever price is left after the one before it, so the second reduction is working on a smaller number and therefore takes fewer dollars off than its headline rate suggests. The gap is small at low rates and large at high ones.

Sales tax goes on last because you are taxed on what you actually pay, not on the sticker. On the $60.00 discounted price, an 8 percent rate adds $4.80 for a $64.80 total; applying that same 8 percent to the original $80.00 would have added $6.40 and overstated the bill by $1.60.

US prices are generally displayed without tax and it is added at the register, so the discounted price on the shelf is not the number you hand over. In most of Europe and much of the rest of the world, value-added tax is already inside the displayed price, which means a percent-off tag there is reducing a figure that already contains the tax and no further addition happens at the till.

Why stacked discounts never add up

Work through the standard case. Twenty percent off a $100.00 item takes you to $80.00, and an extra 10 percent comes off that $80.00 rather than the original $100.00, landing at $72.00. That is 28 percent off in total, not 30. Two 50 percent reductions do not make an item free; they leave you paying $25.00, an effective 75 percent off.

The shortcut for any pair of rates is to multiply what remains rather than add what comes off: 0.80 times 0.90 is 0.72, so 28 percent came off. To check a stacked offer in this tool, run the first discount, then enter the after-discount figure as a new original price and apply the second rate to it.

The formula, worked line by line

A discount is a percentage of the original price taken off, and sales tax, when it applies, is charged on what is left. Those two steps happen in that order because the tax is levied on the price you actually pay, so writing the expression in the wrong sequence overstates the bill.

The second line is the one that repays attention. Because the final price is the original multiplied by one minus the rate, stacking two offers multiplies those remaining fractions together rather than adding the rates. That single fact explains every stacked-discount surprise anyone has ever had at a till.

saved = price × (discount% ÷ 100)
after discount = price − saved = price × (1 − discount% ÷ 100)
final = after discount × (1 + tax% ÷ 100)
stacked: remaining = (1 − r₁) × (1 − r₂)

Worked example with the defaults, $80.00 at 25 percent off: saved = 80 × (25 ÷ 100) = $20.00, so the price after the discount is 80 − 20 = $60.00. Add an 8 percent sales tax and the final is 60 × 1.08 = $64.80, of which $4.80 is tax.

With the tax field left at zero the final is simply the discounted price, $60.00. The one-step version multiplies by one minus the rate, so 80 × 0.75 = $60.00 directly, and the tax then scales that figure by 1.08.

Now stack two offers on a $100.00 item. Twenty percent off leaves $80.00, and an extra 10 percent off that leaves $72.00, so $28.00 came off in total rather than the $30.00 the signs imply. The general rule is that the remaining fraction is the product: 0.80 × 0.90 = 0.72.

Two 50 percent reductions leave 0.50 × 0.50 = 0.25, so an item still costs a quarter of its original price rather than being free. Three offers multiply the same way: 0.80 × 0.90 × 0.90 = 0.648, an effective 35.2 percent off, not 40. This page describes retail arithmetic for general information; it is not advice about what to buy or when a sale is worth acting on.

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