A discount is announced as a share of the price, but it is paid entirely out of the contribution — the money left after variable costs. Because the contribution is the smaller of the two, the extra volume a discount must bring is always larger than the discount itself, and past a certain depth no volume repairs it.
A discount comes off the price and out of the contribution
Two numbers move when you put a sign in the window. The price falls by exactly what the sign says, and the money you keep falls by the same number of PLN — but it was a much smaller number to begin with, so in relative terms it falls far further.
Discount rate — the discount as a share of the price it is taken from. Its base — one item or the whole check — is part of the number, and a discount rate quoted without its base is not yet something to calculate with.
The second quantity is defined elsewhere on this site and taken here unchanged: expressed as a share of net sales, contribution margin is the contribution margin ratio — see restaurant break-even point. This page neither redefines it nor calculates a break-even threshold for the venue; it applies the same algebra to one decision about one price.
Everything below runs on one demonstration set, so you can follow the arithmetic and substitute your own two numbers. A menu position sells at 52.00 PLN net of VAT. Its variable cost — ingredients at yield-adjusted prices, packaging if it travels, the card fee, anything that exists only because that plate was sold — is 33.80 PLN. The contribution is 18.20 PLN and the contribution margin ratio is 18.20 ÷ 52.00 = 0.35.
Now cut the price by ten percent. The guest sees 46.80 PLN; your variable cost has not moved. The contribution becomes 46.80 − 33.80 = 13.00 PLN.
Both statements describe the same 5.20 PLN, and the gap between them is why a discount that reads as modest demands a volume response that reads as heroic.
Take the discount off the same price the rest of your reporting uses: net sales, without VAT and after discounts already granted. A percentage taken on a gross figure and compared with a ratio built on a net one produces an error nobody can see — both inputs are real, only their bases disagree.
The required uplift formula
The owner's real question is not "how much do I lose per plate" but "how many more plates make me whole". That has a closed answer.
Required uplift % = d ÷ (m − d) × 100
d— the discount as a decimal share of the price it is taken from, dimensionless, between 0 and 1;m— the contribution margin ratio before the discount, dimensionless, between 0 and 1, measured on the same base asd;- the result is dimensionless as well, and multiplied by 100 it is a percentage increase in unit volume, not in revenue and not in guests.
That last line matters more than it looks: the answer is a percentage of units, so it belongs next to the plates, covers or orders you can physically produce and seat — never next to a percentage of money.
With a discount of twenty percent: d = 0.20 and m = 0.35, so the required uplift is 0.20 ÷ (0.35 − 0.20) = 0.20 ÷ 0.15 = 1.3333, that is 133.3 %. More than twice as many portions, to end the week with the same money in hand.
Check it the long way round, because a formula you have never verified is one you are trusting. One hundred portions produce 100 × 18.20 = 1 820.00 PLN of contribution. After the cut the price is 41.60 PLN and the contribution per portion is 41.60 − 33.80 = 7.80 PLN, so reaching 1 820.00 PLN again takes 1 820.00 ÷ 7.80 = 233.33 portions — an increase of 133.33 %. Formula and count agree.
Discount d | Contribution per portion after | Required uplift in units |
|---|---|---|
| 5 % | 15.60 PLN | 16.7 % |
| 10 % | 13.00 PLN | 40.0 % |
| 15 % | 10.40 PLN | 75.0 % |
| 20 % | 7.80 PLN | 133.3 % |
| 25 % | 5.20 PLN | 250.0 % |
| 30 % | 2.60 PLN | 600.0 % |
Read the right-hand column as a curve, not a list.
The reason sits in the denominator: every point of discount you add is also a point taken from what is left to divide by.
The condition under which this formula has an answer at all
m − d sits in the denominator, so the formula is defined only while d < m — while the discount stays smaller than the ratio it cuts into.
Ignore that and the arithmetic keeps working while the advice stops making sense. Put a forty percent discount against a ratio of 0.35 and you get 0.40 ÷ (0.35 − 0.40) = 0.40 ÷ (−0.05) = −8, which a spreadsheet prints as "−800 %". Nobody sells minus eight hundred percent of anything. The negative sign reports that no volume restores the contribution, because every portion sold at that price subtracts money.
Three cases, differing in kind rather than in degree:
d < m— the formula answers, and the answer is a finite volume you can compare with your capacity;d = m— the contribution per unit is exactly zero, so no volume changes the total, and the exercise stops being about volume at all;d > m— every unit sold at the discounted price deepens the hole, and more volume makes it worse rather than better.
The maximum contributing discount
The boundary between them has a name and a value.
Maximum contributing discount — the discount at which the contribution reaches zero. It equals the contribution margin ratio before the discount.
Maximum contributing discount = m
m— the contribution margin ratio before the discount, dimensionless;- the result is a dimensionless share of the price, directly comparable with any
dmeasured on the same base.
On the demonstration set that is 0.35.
Below that line a discount still leaves something towards the fixed costs; above it, they are not merely unfunded, they are funded backwards.
Two cautions.
Second, m is not a property of your restaurant. The ratio is a blend — one value per dish, per channel, per daypart — so your ceiling differs for the pasta and for the wine, and one house-wide rate applies the same cut to positions whose ceilings are nowhere near each other. Which positions can carry a cut is the subject of menu engineering; this page says how deep, that one says where.
What happens to the contribution margin ratio after the discount
The volume answer is half the picture. The other half is what each remaining PLN of sales is now worth, and it has a denominator that surprises people.
Contribution margin ratio after the discount = (m − d) ÷ (1 − d)
dandmas above, both dimensionless and measured on the same base;- the result is a dimensionless ratio, directly comparable with
m.
The denominator is (1 − d) and not 1, and that is the whole subtlety: after the discount the price changed too. The contribution shrank, but so did the sales figure you express it as a share of. Divide the reduced contribution by the original price and you understate the new ratio, breaking every comparison afterwards.
With a twenty percent discount: (0.35 − 0.20) ÷ (1 − 0.20) = 0.15 ÷ 0.80 = 0.1875. Directly: the new price is 41.60 PLN, the contribution 7.80 PLN, and 7.80 ÷ 41.60 = 0.1875. The two paths meet.
So a twenty percent price cut took the ratio from 0.35 to 0.1875 — nearly half of it, not a fifth. Carry that number downstream. The payback threshold for advertising is built on the ratio, not on revenue, which is why a promotion and a campaign in the same week interact — see restaurant marketing ROI measured on margin. Feed the pre-discount ratio into it and you will conclude the advertising paid for itself when it did not.
Keeping both ratios side by side — before and after, per position and per channel — is a reporting job: see reporting automation, and keep both in the analytics you already have.
The markup that undoes a discount is not the size of the discount
Here is the trap that costs the most money for the least reason, and it has the shape of the one delivery platforms set with their commission: a percentage taken away and a percentage added back are not each other's opposites.
The plan sounds airtight: "we want minus thirty percent, so we put the menu price up thirty percent first and end up where we started." Multiply it out. The position at 52.00 PLN becomes 52.00 × 1.30 = 67.60 PLN on the menu, and the guest takes thirty percent off: 67.60 × 0.70 = 47.32 PLN.
The reason is arithmetic, not marketing: (1 + d) × (1 − d) = 1 − d², and that square never disappears.
The markup that genuinely restores the price after a discount of d is a different number:
Required markup % = d ÷ (1 − d) × 100
d— the discount as a decimal share, dimensionless, strictly below 1;- the result is dimensionless, and multiplied by 100 it is the percentage the menu price must rise by so that the post-discount price equals the original.
For a thirty percent discount that is 0.30 ÷ 0.70 = 0.428571, or 42.857 %. Check it: 52.00 × 1.428571 = 74.2857 PLN on the menu, and 74.2857 × 0.70 = 52.00 PLN at the till — exactly the price, and therefore exactly the contribution, you started from.
| Discount announced | "Add the same percent" gives back | Markup that really restores the price |
|---|---|---|
| 10 % | 99 % of the price | 11.111 % |
| 20 % | 96 % of the price | 25.000 % |
| 30 % | 91 % of the price | 42.857 % |
And the honest version means the guest buying without the discount now pays 74.29 PLN for a plate that cost 52.00 PLN last month: a price rise with a decoration on top, which regulars read correctly.
The same algebra appears where the percentage is taken by a platform rather than offered to a guest: see online orders for restaurants. If your discount runs on a delivery channel both cuts land on the same plate, so calculate m after the commission and only then put d against it.
A discount on one dish and a discount on the whole check sit on different bases
Same word, same percentage, wildly different sums — because the base is half of what a discount rate means.
Take a check of 186.00 PLN net with variable costs of 126.48 PLN: the contribution is 59.52 PLN and the check-level ratio is 0.32.
Twenty percent off the whole check gives up 37.20 PLN — 3.58 times more money for a sign that reads identically.
The required uplift follows the base as well.
That is the distance between a workable promotion and one nothing can reach.
| Form | Base it is taken from | What leaves the contribution | What the guest sees |
|---|---|---|---|
| Percent off one position | The price of that position | The contribution of that position only | A cheaper dish |
| Percent off the whole check | Every position on the check | The contribution of all of them, strongest included | A cheaper evening |
| Fixed sum off the check | The check, as a share that falls as the check grows | A constant sum, so a heavier share of small checks | A gift with a number on it |
| Second item at half price | The price of the cheaper item | Half of one position, if the second item is genuinely additional | Two dishes for less |
| A dish given free | The check it was given on, at plate cost | The plate cost in full, with no change to the price | A present |
| Loyalty points redeemed | The value of the points at redemption | Spread across visits, not concentrated in one | A reward earned earlier |
The last row belongs to a different page: an accrual programme spreads its cost across visits, expires part of it and is measured in visits rather than percent of volume. That arithmetic lives in the economics of a restaurant loyalty programme; mixing it with a one-off discount produces a number that describes neither.
A free dish as a discount: priced at plate cost, not at menu price
A gift is a discount that does not look like one, and the one form where the obvious number overstates the damage by nearly three times.
Effective discount of a gift — the plate cost of a free item as a share of the check it was given on.
Effective discount of a gift = Plate cost of the free item ÷ Value of the check it was given on
Plate cost— the costed sum of every recipe component at yield-adjusted prices, for one portion exactly as it is served; defined on our food cost percentage page and used here unchanged, PLN;Value of the check it was given on— the net value of the check the gift accompanied, PLN;- the result is PLN ÷ PLN, a dimensionless share of that check.
The dish you give away has a plate cost of 14.60 PLN and a menu price of 39.00 PLN.
Now the part worth knowing.
The formula holds for a gift as for a price cut, because the same money left the contribution either way.
But the ratio afterwards is not the same, and this is where the two forms part company. With a price cut the check itself shrinks, so the new ratio is (0.32 − 0.078495) ÷ (1 − 0.078495) = 0.2621. With a gift the check does not shrink — the guest still pays 186.00 PLN and only the cost side moved — so the new ratio is simply m − d = 0.2415.
| Price cut of 7.85 % | Free dish worth 7.85 % of the check | |
|---|---|---|
| Contribution on the check afterwards | 44.92 PLN | 44.92 PLN |
| Required uplift in checks | 32.5 % | 32.5 % |
| Sales value of the check | 171.40 PLN | 186.00 PLN |
| Contribution margin ratio afterwards | 26.21 % | 24.15 % |
Identical money, identical volume requirement, two different ratios — because the denominator moved in one case and stood still in the other. A month of gifts and a month of price cuts are not comparable unless you know which was which.
Uplift has to be uplift: the guest who would have come anyway
Everything above assumes the discount reaches every unit sold. That assumption does enormous work — it is the difference between a promotion that pays and one that does not.
Suppose the offer sits on the shelf for everyone, the dish sells 160 portions instead of 100, and every one carries the twenty percent cut. Contribution: 160 × 7.80 = 1 248.00 PLN against 1 820.00 PLN in a normal week. Volume rose sixty percent and you are 572.00 PLN worse off, because the requirement was 133.3 % and you delivered 60 %.
Now run the identical offer as a targeted one reaching only guests who would not otherwise have come — a lapsed-guest message, a Tuesday-only code. The hundred baseline portions sell at full price for 1 820.00 PLN; the sixty incremental ones sell at the discount for 60 × 7.80 = 468.00 PLN. Total 2 288.00 PLN — 468.00 PLN better off.
Same discount, same sixty percent more units, a swing of 1 040.00 PLN. The only variable is who got the coupon — which is why "sales were up sixty percent" is not a finding: it is compatible with both outcomes above.
Knowing which of the two you ran is a measurement problem, and it needs a comparison group rather than a before-and-after: how to tell whether the promotion worked. Knowing who received the offer needs guests you can recognise, which is the job of a guest database rather than a till — see CRM, and, if you are choosing which layer of system to add next, CRM or ERP.
What to reach for when the required uplift is out of reach
Sometimes the honest answer is that the number cannot be delivered. A 133.3 % uplift means the kitchen produces more than twice as many portions in the same hours and the room seats the guests who eat them. Put it next to your physical capacity — covers per service, portions per station per hour, orders per courier window. If capacity binds, no discount depth fixes it, and the discount simply costs you the difference.
Four directions are worth arithmetic rather than opinion, each pulling a different lever in the same formula.
d without lowering the perceived gift. A free dish at 14.60 PLN plate cost on a 186.00 PLN check is an effective 7.85 % and needs 32.5 % more checks; twenty percent off the same check needs 166.7 %.To the guest "a dish on the house" is not five times smaller than "twenty percent off" — to your contribution it is.
Raise m before you cut into it. At m = 0.35 a twenty percent discount needs 133.3 % more units; at m = 0.45 the same discount needs 0.20 ÷ 0.25 = 80 %. Yield, portioning and purchase price are the levers, and they belong to food cost percentage.
Move the offer to the hours that stand empty
The formula is indifferent to when the extra units happen; your fixed costs are not. Filling a dead Tuesday adds contribution against costs paid anyway, while discounting a Friday that was full is a straight transfer of money to guests who had already decided to come.
Check that the discount is fixing the right fault. A quiet week is not always a price problem. If enquiries go unanswered, if the phone rings out during service, if the booking is never confirmed, price was never the obstacle — see why customers do not leave enquiries and restaurant automation.
Where AI is involved here, and where it is not
Nothing here is done by a model. d ÷ (m − d) is arithmetic and works on paper; every answer above was produced by counting. Software helps at the two edges rather than in the middle: assembling m per position and per channel out of the till and the invoices — analytics and dashboards — and replaying the formula across a range of inputs before you commit, which is what a what-if model and an on-site calculator are for. The judgement stays with you.
Why no benchmark appears on this page
There is no published norm for how deep a restaurant discount should be, or how much volume one typically returns. We looked. The Eurostat dissemination catalogue, read in full, holds no dataset whose title carries "discount", "promotion", "rebate", "elasticity" or "contribution margin"; the only entry matching "restaurant" is the harmonised price index for hotels and restaurants, which measures prices charged, not discounts granted. The trade section of the Polish national statistics office lists seventeen documents — retail sales, foreign trade turnover, the internal market report, a methodological handbook on trade and catering activity — and none publishes discount depth or promotional uplift for catering. So this page names no norm.
Frequently asked questions
How much extra volume does a 20 % discount need to break even?
It depends entirely on your contribution margin ratio before the discount, and the relationship is steep. With a ratio of 0.35 a twenty percent discount needs 0.20 ÷ (0.35 − 0.20) = 133.3 % more units — more than twice as many. With 0.45 it needs 80 %; with 0.25 it needs 400 %. There is no single answer to quote: measure m on the position you intend to discount, put your d against it, and read the result as a percentage of units, not of money.
Why does a discount cost more than the percentage suggests?
Because it is calculated on the price and paid out of the contribution, and the contribution is much smaller. On a position at 52.00 PLN with a variable cost of 33.80 PLN, a ten percent cut is 5.20 PLN — ten percent of the price, but 28.6 % of the 18.20 PLN you were keeping. Your variable cost does not fall when the price does.
What is the largest discount that still leaves something?
The contribution margin ratio itself. At a ratio of 0.35 a thirty-five percent discount takes the price down to the variable cost exactly and leaves zero per portion; anything deeper means every extra sale removes money. Two cautions: "leaves something" is not "worth doing" — at 30 % against 0.35 you keep 2.60 PLN per portion — and the ratio differs per dish, per channel and per daypart, so a single house-wide ceiling does not exist.
Is a discount on one dish the same as a discount on the whole check?
No, and the gap is large. On a check of 186.00 PLN, twenty percent off a single 52.00 PLN dish gives up 10.40 PLN — 5.59 % of the check; twenty percent off the whole check gives up 37.20 PLN, 3.58 times more for a sign that reads the same. The uplift follows: about 21.2 % more checks against 166.7 %, at a check-level ratio of 0.32. Always state the base with the percentage.
How do I price a free dish as a discount?
At its plate cost, divided by the check it was given on — never at its menu price. A dish costing 14.60 PLN to plate, given on a 186.00 PLN check, is an effective discount of 7.85 %. The 39.00 PLN menu price would give 20.97 %, which is 2.67 times too large, because it contains a contribution you never paid out. The required uplift is then the same as for a price cut of that size, but the ratio afterwards is not: a gift leaves the check value untouched.
What if the required uplift is impossible to reach?
Then this discount at this depth is not a promotion but a cost, and the answer is to change an input rather than to hope: reduce d by choosing a form the guest values more than it costs you, raise m first through yield and purchase price, move the offer to hours that stand empty, or target it so that it reaches only guests who would not otherwise have come. On the same numbers, sixty percent more units cost 572.00 PLN when everyone got the discount and earned 468.00 PLN when only the incremental guests did.
Work out your own two numbers before you announce anything: the contribution margin ratio of the position you intend to discount, and the depth you have in mind. Put the required uplift next to the covers your room physically holds, and the decision usually makes itself. The rest of the figures a restaurant owner is expected to defend live on the restaurant guides hub.