How to Calculate a Discount: Percent Off, Stacked Discounts and the Order of Sales Tax
“30% off,” “an extra 10% off at the register,” “500 off with a coupon.” Try to do the math in your head at the checkout and it's easy to lose track of what to multiply by what. This guide covers the one-step multiplication for the price after a discount, a percent-off chart, which comes first between the discount and sales tax, how stacked discounts really add up, how points back compares, and how to work backward to the discount rate.
Multiply by the share that remains
Discount math trips people up because of the two-step routine of working out the amount off and then subtracting it. Multiply directly by the share that remains after the discount and it takes just one step.
- 20% off → 80% remains → price × 0.8
- 30% off → 70% remains → price × 0.7
- 25% off → 75% remains → price × 0.75
- Half price → 50% remains → price × 0.5
For example, 20% off a price of 3,800 is 3,800 × 0.8 = 3,040. Only when you want the amount off do you multiply by the discount rate itself: 3,800 × 0.2 = 760. To avoid mixing them up, remember: “for the price you pay, multiply by the share that remains.”
Chart: percent off, share paid and multiplier
Japanese price tags mix “X% off” with “X wari-biki,” where 1 wari is one tenth (10%). Multiply the wari number by 10 to get the percentage: “3 wari-biki” is 30% off. The chart below works for both.
| Label | Discount rate | Share paid | Multiplier | On a price of 1,000 |
|---|---|---|---|---|
| 10% off (1 wari-biki) | 10% | 90% | 0.9 | 900 |
| 20% off (2 wari-biki) | 20% | 80% | 0.8 | 800 |
| 30% off (3 wari-biki) | 30% | 70% | 0.7 | 700 |
| 40% off (4 wari-biki) | 40% | 60% | 0.6 | 600 |
| Half price (5 wari-biki) | 50% | 50% | 0.5 | 500 |
| 60% off (6 wari-biki) | 60% | 40% | 0.4 | 400 |
| 70% off (7 wari-biki) | 70% | 30% | 0.3 | 300 |
| 80% off (8 wari-biki) | 80% | 20% | 0.2 | 200 |
Watch out for wording that refers to the share you pay rather than the share taken off. In Japan, “7 wari-biki” means you pay 30%, but “7 kake” (7 tenths of the price) means you pay 70%. In English, “70% of the price” and “70% off” are just as easy to confuse, so check whether the number is what's removed or what remains.
Which comes first: the discount or sales tax?
Sales tax (such as Japan's consumption tax or VAT) is charged on the amount the seller actually receives after the discount. So the correct order is to apply the discount first and then add tax.
| Pre-tax price | After 20% off | 10% tax | Amount paid | |
|---|---|---|---|---|
| Discount → tax | 1,000 | 800 | 80 | 880 |
| Discount on the tax-inclusive price | 1,100 incl. tax | — | — | 880 |
With a percentage discount, the result is the same whether you discount the pre-tax or the tax-inclusive price: 1,100 × 0.8 = 880, matching the table. The order doesn't matter because multiplications give the same answer in any order.
How fractions of a cent or yen are handled (round down, round up or round to nearest) is up to each store. You can try converting between tax-inclusive and pre-tax prices with different rounding in the consumption tax and service charge calculator. The rules for rounding tax on Japanese invoices are covered in Consumption tax on qualified invoices, and Japan's price-display rules in Japan's total price display rule. If food and dining out are taxed at different rates, see also Japan's 8% vs. 10% consumption tax.
Stacked discounts, coupons and points back
“20% off, plus an extra 10% off at the register” is not 30% off. The second discount applies to the price already reduced by the first.
- 1,000 × 0.8 = 800 → 800 × 0.9 = 720. Overall, that's 28% off.
- For the same two percentage discounts, swapping the order gives the same result.
- With three discounts, keep multiplying in the same way, as in 0.8 × 0.9 × 0.95.
- When a fixed-amount coupon is mixed in, applying the percentage discount first gives a smaller total discount. Which order applies is set by the store's rules.
Points back works differently from a discount that lowers the price on the spot. 20% back means “pay 1,000 and receive 200 points,” so you paid 1,000 for 1,200 worth of value. As a discount rate, that's 200 ÷ 1,200 ≒ 16.7%, less than 20% off.
| Offer | Paid now | Value received | Effective discount |
|---|---|---|---|
| 20% off | 800 | 1,000 | 20% |
| 20% back in points | 1,000 | 1,200 | about 16.7% |
| 10% off + 10% back | 900 | 1,090 | about 17.4% |
Points also expire, and any you don't use never become a discount. If you already know what you'll spend them on, you can count points as a real discount, but convert both offers to the same basis before deciding. A chart for converting points rates into discount rates, and the cases where earning caps or pre-tax points shrink the benefit, are covered in Points back vs. discount: which is the better deal?
Working backward to the discount rate, and splitting the bill
To find out what discount a sale tag represents, divide the amount off by the original price. The formula is (original price − sale price) ÷ original price.
- 1
Find the amount off
If an original price of 4,500 is now 3,150, the amount off is 1,350.
- 2
Divide by the original price
1,350 ÷ 4,500 = 0.3, so the discount is 30%.
- 3
Convert to a percentage
Just multiply the decimal by 100: 0.3 → 30%. 0.28 would be 28% off.
- 4
Compare on equal terms
If some prices include tax and some don't, or some include shipping and others don't, the comparison is meaningless. Compare total amounts paid.
If you get a bulk discount and split it among several people on the spot, divide the discounted total by the number of people. Working out each person's original share first and discounting that can change how fractions fall, and the total may not add up, so mind the order. How to split a bill, including who covers the remainder, is covered in How to split a bill, and how to split unevenly in How to decide who pays more.
FAQ
- How do I calculate 20% off?
- Multiply the price by 0.8, because 80% remains after taking 20% off. For a price of 2,480, that's 2,480 × 0.8 = 1,984. Only if you want the amount off should you multiply by the discount rate: 2,480 × 0.2 = 496. For mental math, find 10% (drop a digit: 248), double it and subtract from the price. Sticking to “multiply by what remains” (0.7 for 30% off, 0.6 for 40% off) keeps you from getting confused.
- Should I calculate the discount or sales tax first?
- Sales tax is charged on the amount actually received after the discount, so the correct order is to apply the discount first and then add tax. With a percentage discount, though, the amount paid is the same whether you discount the pre-tax or the tax-inclusive price. 20% off a pre-tax 1,000 is 800 plus 80 tax, or 880; 1,100 including tax × 0.8 is also 880. A fixed amount off, such as “100 off,” does give different totals depending on which price it's taken from.
- Which is better: 20% off or 20% back in points?
- 20% off, which lowers the price on the spot, is better. 20% off turns a 1,000 item into 800, while 20% back means paying 1,000 and receiving 200 points: you paid 1,000 for 1,200 worth of value, an effective discount of about 16.7%. Points also come with expiry dates and limits on where they can be used, and any you don't use never become a discount. Compare offers by lining up what you pay against the value you receive.
- What's the total discount for 30% off and then another 10% off?
- 37% off, not 40%. The second discount applies to the price already reduced by the first: 1,000 × 0.7 = 700, then 700 × 0.9 = 630, which is 37% off the original. Just multiply 0.7 × 0.9 = 0.63; swapping the order gives the same result. If a fixed-amount coupon is involved, though, the order changes the total, so check the order of application on the receipt.
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