Sequential vs Stacked Discounts: The Math That Costs You Money
"25% off, plus a further 10% off" is one of the most common phrases on a commercial invoice, and almost nobody calculates what it means. Add the percentages and you promise a bigger discount than you intend to give; apply the stack to the gross when you meant the net and your VAT total drifts. Both errors are invisible on the invoice and expensive at year end. This page is the arithmetic, checked.
- Stacked discounts compound — they do not add. 25% then 10% is a 32.5% discount, not 35%. Multiplying retained fractions gets it right every time.
- The order never matters. All six orderings of 25%, 10% and 5% give the same €64.13. "Apply your biggest discount first" is not a pricing tactic.
- For a uniform percentage discount, net or gross makes no difference. The usual warning is wrong in this case — and the page shows the working.
- Fixed-amount discounts are where the base matters. €10 off a €119 gross is not €10 off a €100 net: it overcharges the net by €1.60.
- Rounding is what breaks real invoices. Three lines of €33.33 at 19% give €18.99 or €19.00 depending on where you round. Pick a rule, write it down.
- 1. Why percentages do not add
- 2. The order does not matter
- 3. Net or gross? The advice you have been given is wrong
- 4. Fixed-amount discounts behave differently
- 5. Rounding and the VAT breakdown
- 6. Early-payment discounts are not stacked discounts
- 7. Surcharges push the error the other way
- 8. Four rules that prevent the errors
- Frequently asked questions
1. Why percentages do not add
Each percentage discount multiplies the running price by the fraction you keep. Two discounts therefore multiply, and the effective discount is one minus the product:
Effective discount = 1 − the product of those fractions
Worked on a €100 invoice with 25% then 10%:
The reason addition fails is that the second discount applies to a price that has already been reduced. Ten percent of €100 is €10, but ten percent of €75 is only €7.50. Adding the percentages implicitly assumes both discounts apply to the original price, which is not what "a further 10% off" means.
The gap widens fast, which is where it starts to cost real money:
| Stack | Naive sum | Actual effective | Overstated by |
|---|---|---|---|
| 20% + 20% | 40% | 36.00% | 4.00 pp |
| 25% + 10% | 35% | 32.50% | 2.50 pp |
| 15% + 10% + 10% | 35% | 31.15% | 3.85 pp |
| 10% + 20% + 25% | 55% | 46.00% | 9.00 pp |
| 5% × 4 | 20% | 18.55% | 1.45 pp |
| 50% + 50% | 100% | 75.00% | 25.00 pp |
Look at the last row. Added naively, two 50% discounts promise the goods for nothing. Applied correctly, the customer still pays a quarter of the price. Any pricing schedule built on added percentages is quietly giving away more than intended, and the more tiers you add, the worse it gets.
2. The order does not matter
Because each step is a multiplication, and multiplication is commutative, the sequence is irrelevant. On a €100 invoice, all six orderings of 25%, 10% and 5% produce the same final price:
This matters commercially, because "apply your biggest discount first" is advice you will see repeated. Mathematically it achieves nothing at all. Order only starts to matter if you round at an intermediate step, which is a rounding problem rather than a pricing one — and the honest fix for that is a documented rounding rule, not a chosen order.
3. Net or gross? The advice you have been given is wrong
Almost every guide on stacked discounts includes a warning: never apply a discount to the gross total, always apply it to the net. For a uniform percentage discount at a single VAT rate, that warning is incorrect. Here is the working, on a net €100.00 invoice at 19% VAT:
| Method | Net | VAT at 19% | Gross total |
|---|---|---|---|
| Discount applied to the net (correct) | €67.50 | €12.83 | €80.33 |
| Same two factors applied to the gross €119.00 | €67.50 | €12.83 | €80.33 |
Identical. The reason is that VAT at a flat rate is just a constant multiplier on the net, so scaling the net by 0.675 scales the VAT by 0.675 too, and scaling the gross by 0.675 gives the same answer. The same holds with mixed rates: a €100 line at 19% plus a €100 line at 7% gives a €226.00 gross, and 10% off that gross produces exactly the same result as 10% off each net.
So the rule worth keeping is narrower and more useful: the base only matters when the discount is not a uniform percentage of everything. That covers three real cases — fixed-amount discounts, discounts that apply to selected lines only, and reading a VAT breakdown back out of a gross figure. For a flat percentage across the whole invoice, either base is fine and the total is the same.
4. Fixed-amount discounts behave differently
A fixed-amount discount has to come off a specific base, and the two bases diverge immediately. Same invoice as above — net €100.00, 19% VAT, gross €119.00 — with a €10.00 discount:
| Method | Net | VAT at 19% | Gross total |
|---|---|---|---|
| €10 off the net | €90.00 | €17.10 | €107.10 |
| €10 off the gross | €91.60 | €17.40 | €109.00 |
The second row is €1.90 heavier on the customer and declares €0.30 more output VAT than the first. Nobody intended that, and it is invisible unless you check the arithmetic. If a customer challenges a VAT figure, this is the kind of discrepancy that turns a two-minute email into an argument.
The same trap applies when fixed amounts are stacked. Two €10 discounts on a €100 net invoice are worth €20 off the net, not €20 off the gross — and if the second is computed as "10% of the already-discounted total", you have mixed a fixed and a percentage discount, which is a third case with its own answer.
5. Rounding and the VAT breakdown
Once an invoice has more than one line, the question is no longer which total is right but where you round. Three lines of €33.33 at 19% VAT:
One cent is trivial on its own. The reason it matters is the audit question: a customer checking your invoice will add up the VAT figures on each line and compare the result with the VAT total you have printed. If they disagree, the invoice does not add up, and you have a conversation about a cent that turns into a conversation about your arithmetic generally.
So: choose one rule, apply it everywhere, and make sure the per-line figures sum to the invoice totals. Many accounting packages let you select this; if yours does, set it deliberately rather than accepting the default.
6. Early-payment discounts are not stacked discounts
A term like 2/10 net 30 is a different mechanism and is easy to miscalculate because it looks like a discount. It is conditional: the customer gets 2% off only if they pay within 10 days. On a €1,000.00 net invoice at 19% VAT:
| Scenario | Net | VAT at 19% | Total payable |
|---|---|---|---|
| Paid on time — discount applies | €980.00 | €186.20 | €1,166.20 |
| Paid late — discount lost | €1,000.00 | €190.00 | €1,190.00 |
| Customer's saving for paying early | €20.00 | €3.80 | €23.80 (exactly 2% of the full total) |
Two things follow. The customer's incentive is 2% of the gross, not of the net — on a large invoice that is a meaningful return for paying a fortnight early. And because the discount is conditional, the amount owed genuinely differs depending on when payment arrives, which is why the payment term belongs on the invoice rather than buried in a contract. Our payment terms guide covers how to word that.
How the discount should be treated for VAT accounting is a separate question that depends on its nature and on national rules. This page deliberately stops at the arithmetic — check the disclosure requirements in the EU invoice requirements guide and confirm the treatment with your tax adviser.
7. Surcharges push the error the other way
Add a surcharge and the naive calculation fails in the opposite direction — it now understates your discount. A 10% surcharge followed by a 20% discount:
The mechanism is the same: the second adjustment applies to a price the first one already moved. This is the version that produces an awkward conversation, because the customer believes they were given a bigger discount than the invoice shows.
8. Four rules that prevent the errors
- Multiply, never add. Use the retained-fraction formula for every stack. If a schedule is written as percentages that sum to more than 100, the schedule is wrong.
- Ignore order for percentages. Only fixed amounts and rounding make order meaningful.
- Decide the base once, per discount type. Uniform percentage → either base gives the same total. Fixed amount → take it off the net.
- Fix the rounding rule and document it. Make sure per-line VAT sums to the invoice VAT total, every time.
For anything beyond two discounts, or where the rates differ by line, do the arithmetic in a tool rather than in a spreadsheet cell. The free Discount Calculator applies up to two stacked percentage discounts, computes tax on the discounted net, and shows the effective rate so you can check it against what you intended. It runs entirely in your browser — no account, nothing uploaded.
Frequently asked questions
Is 25% off plus 10% off a 35% discount?
No. Sequential discounts compound, so the effective discount is 1 minus the product of the retained fractions: 1 − (0.75 × 0.90) = 32.5%. On a €100 invoice that is €67.50, not €65.00. The gap widens with every extra discount — 50% plus 50% is a 75% discount, not 100%.
Does the order in which stacked discounts are applied matter?
No, not for percentage discounts. Each discount multiplies the running price by a fixed factor, and multiplication is commutative, so 25% then 10% gives the same result as 10% then 25%. All six orderings of 25%, 10% and 5% give the same €64.13 on a €100 invoice. Order only matters once rounding is applied at an intermediate step.
Should a percentage discount be applied to the net price or the gross total?
For a uniform percentage discount at a single VAT rate, it makes no difference to the total. On a net €100.00 invoice at 19% VAT, discounting the net gives €67.50 plus €12.83 VAT for €80.33, and discounting the €119.00 gross by the same two factors also gives €80.33, because both net and VAT scale by the same proportion. The base only starts to matter for fixed-amount discounts.
When does a fixed-amount discount differ from a percentage discount?
A fixed-amount discount has to be taken from a specific base, and the bases give different answers. On a net €100.00 invoice at 19% VAT with a €10.00 discount, deducting from the net gives €90.00 net, €17.10 VAT and €107.10 total. Deducting €10.00 from the €119.00 gross gives €109.00 total, implying €91.60 net and €17.40 VAT — overcharging the net by €1.60 and the VAT by €0.30.
How should rounding be handled on an invoice with multiple lines?
Decide where the rounding happens and apply it consistently. Three lines of €33.33 at 19% VAT give €18.99 if each line is rounded and summed, but €19.00 if the VAT is calculated on the €99.99 total. Either is defensible, but the per-line VAT figures should sum to the VAT total printed on the invoice — so pick one rule and document it.
How these figures were produced
Every number on this page comes from the two formulas in section 1, evaluated in exact decimal arithmetic and rounded to two places only at the point of display. The reference table in section 1, the ordering test in section 2, the net-versus-gross comparison in section 3, the fixed-amount comparison in section 4 and the rounding case in section 5 are all direct outputs of those calculations, so any of them can be re-derived from the stated inputs. The Discount Calculator uses the same method as its default calculation.
Disclaimer: Arithmetic guidance only, not tax or legal advice. The VAT accounting treatment of a discount depends on its nature and on national rules and is outside the scope of this page. Corrections are logged in the changelog.