How discount maths actually works
A percentage discount is only ever one of two operations: either multiply the price by the share you keep, or subtract the share you lose. sale = price × (1 − discount ÷ 100) and saved = price × discount ÷ 100. On a ¥200 item at 15% off that is 200 × 0.85 = ¥170, saving ¥30. The trick most people use in their head is to build the discount from 10% steps: 15% is 10% (20) plus half of that (10), and 25% is a quarter, and 30% is three lots of 10%.
Stacked discounts: why 30% then 20% is 44%, not 50%
When a shop applies a second discount to an already-reduced price, the two percentages multiply rather than add: 0.70 × 0.80 = 0.56, so you pay 56% and the real discount is 44%. Adding them gives 50% — six points too generous, and on a ¥200 order that is ¥12 of the difference. The same trap appears with three discounts: three 20% discounts leave 0.8³ = 0.512, i.e. 48.8% off, not 60%. The order of the discounts never changes a pure percentage result (multiplication is commutative), but it does change spend-and-save-style fixed reductions, because a fixed amount taken off before a percentage is worth less than the same amount taken off after it.
Chinese zhe pricing
Chinese shops quote the share you pay, not the share you save, so the numbers move in the opposite direction. The unit is the zhe, one tenth of the price, so 8.5折 = pay 85% = 15% off. The conversion is discount% = (10 − zhe) × 10 and zhe = 10 − discount% ÷ 10. Useful anchors: 9.5 zhe is 5% off, 9 zhe is 10% off, 8 zhe is 20% off, 7 zhe is 30% off, 5 zhe is half price, and 1 zhe is 90% off. Beware of a further zhe applied on top of a discount — that is a stacked discount and multiplies.
Spend X, save Y (threshold reductions)
A spend-and-save rule takes a fixed amount off once the basket clears a threshold, so its real discount rate depends on the basket: spend ¥300, save ¥50 works out at 50 ÷ 300 = 16.7% off at exactly ¥300, but only 11.1% at ¥450 and 6.3% at ¥800. The rate always peaks just above the threshold, which is exactly why shops set the threshold where they do — adding a ¥60 item you did not want to reach a ¥50 reduction is a net loss. If a percentage discount is also in play, check which order the shop uses, because the two orders can differ by several yuan.
Working backwards: what was the original price?
To recover the original price from the price you paid, divide instead of add: original = paid ÷ (1 − discount ÷ 100). Paying ¥68 after 15% off means 68 ÷ 0.85 = ¥80. Multiplying by 1.15 instead gives ¥78.20, the single most common discount mistake. The same division tells you whether a "was/now" comparison is real: a ¥399 price against a "¥899 original" is 56% off, which is a genuine deal only if ¥399 is below what you would otherwise have paid.
Frequently asked questions
How do I calculate 20% off a price?
Multiply by 0.8, or take 10% twice. A ¥200 item at 20% off costs 200 × 0.8 = ¥160 and saves ¥40. The percentage you keep and the percentage you lose always add up to 100, so "20% off" is the same as "pay 80%".
Why is 30% off then an extra 20% off not 50% off?
Because the second discount applies to the reduced price, not the original. The multipliers multiply: 0.70 × 0.80 = 0.56, so you pay 56% and the total discount is 44%, not 50%. On a ¥200 order, adding the percentages would overstate the saving by ¥12.
What does 8.5 zhe mean in English?
Pay 85% of the price, i.e. 15% off. Chinese pricing quotes the share you pay, so a smaller number is a bigger discount: 9 zhe is 10% off, 8 zhe is 20% off and 5 zhe is half price. Convert with discount% = (10 − zhe) × 10.
How do I find the original price from the sale price?
Divide: original = sale price ÷ (1 − discount ÷ 100). ¥68 paid after 15% off means 68 ÷ 0.85 = ¥80. Multiplying by 1.15 would give ¥78.20 — close, but wrong, and the error grows with the size of the discount.
Is spend 300 save 50 better than 20% off?
Usually not. A fixed reduction is one amount, so its rate falls as the basket grows: spend 300 save 50 is 16.7% off at exactly ¥300, 11.1% at ¥450 and just 6.3% at ¥800, while 20% off stays flat at any amount. The reduction only wins if you were going to spend close to the threshold anyway.
Does the order of stacked discounts matter?
For pure percentage discounts, no — multiplication is commutative, so 30% then 20% gives exactly the same price as 20% then 30%. Order does matter when a fixed reduction is involved, because money taken off before a percentage is worth less than the same amount taken off afterwards.
How do I quickly work out 15% off in my head?
Take 10% (move the decimal point one place), halve it to get 5%, then add the two. 15% of ¥240 is 24 + 12 = ¥36, so you pay ¥204. For 25%, take a quarter; for 30%, take three lots of 10%.
Do discounts and coupons always stack?
No. Many shops exclude coupons from discounted items, or apply the coupon to the post-discount price. If a ¥50 coupon meets a 20%-off promotion, the coupon is worth ¥50 before the discount and only ¥40 after it — which is why the tool shows both orders when you enter an extra percentage.