Stacked Discounts

Discounts multiply; they do not add

"20% off, plus an extra 15%, plus 10% at the till" is not a 45% discount, though the sentence reads like one. Each cut applies to the already-reduced price, so every percentage acts on a shrinking base. This page stacks up to three discounts in sequence, prints the price after each step, and states the true combined discount — the single figure you can carry to the till, compare against a rival's plain discount, or quote in a price-match squabble.

The same arithmetic settles a myth in passing: order does not matter. Removing 10% first and 20% second lands on the same final price as the reverse, because multiplication is commutative — a multiplication table rearranged is still a multiplication table. What matters is always the set of cuts, never their sequence.

A worked example, step by step

Problem: a 100 jacket with a members' 20%, a weekend extra 15% and a clearance final 10%.

1. After 20%: 100 × 0.80 = 80.00.
2. After 15%: 80 × 0.85 = 68.00 — the "extra 15%" removed 12, not 15.
3. After 10%: 68 × 0.90 = 61.20 — the last 10% removed 6.80.
4. True combined discount: (100 − 61.20) ÷ 100 = 38.8%, against the naive sum of 45%.
5. Pair-only variant: 20% + 15% lands at 68.00 — a real 32% discount, not 35%.

The shrinking base is the entire story: the second cut removed 12 because it worked on 80, and the third removed 6.80 because it worked on 68. Percentages of percentages are exactly why stacked deals pay out less than their arithmetic advertises.

One price, four deal shapes

The last row is the pattern's cleanest lesson: three modest 10% cuts produce 27.1% — the real figure always sits between the largest single cut and the naive sum, never at the sum, and the gap widens as more cuts join.

Where stacking meets the tax line and cash coupons

Two boundaries finish the picture. Fixed-amount coupons are not percentages: 20 off, then 10%, differs from 10%, then 20 off — the flat amount does not shrink with the base, so order begins to matter the moment cash enters the stack. And sales tax applies after every discount, on the final price, while this tool's outputs are pre-tax — which is what shelf labels quote but not what receipts print. Run the stack here, then let the sales tax page add the last line.

Mistakes that quietly overvalue a deal

• Adding the percentages. 20 + 15 + 10 equals 45 only if every cut worked on the full price; none ever does.
• Believing order changes the total. Percentage-only stacks are order-free; only mixed cash-and-percent stacks care.
• Comparing a stack against a plain discount pre-tax. Both sides need the same tax treatment before the comparison is honest.
• Ignoring minimum-spend rules. "Extra 15% over 75" changes the base the arithmetic should use; re-run the tool per bracket.

Keep exploring

• Discount Calculator — one cut at a time, with the saved amount named.
• Unit Price Comparison — comparing pack sizes once the deal price is known.
• Sales Tax Calculator — add the tax line after the stack, on the reduced base.
• Guide: VAT and Sales Tax Explained.