How Discounts Stack
The compounding math, and why stacked discounts look bigger than they are.
Multiply the "keep" fractions. 30% off + 20% off = 0.70 × 0.80 = 56% of price = 44% off.
Stacked discounts do not add — they compound. Each discount applies to the already-discounted price, not the original. This is why "30% off plus another 20% off" is less than 50% off.
Part of: Saving & Spending Calculators
Quick answer
Multiply the "keep" fractions. 30% off + 20% off = 0.70 × 0.80 = 56% of price = 44% off.
Key points
- ▸ Formula: combined "keep" fraction = (1 − d1) × (1 − d2) × …
- ▸ 30% off then 20% off = 0.70 × 0.80 = 0.56 = pay 56% = 44% off, not 50%.
- ▸ Order does not matter — the math is the same whichever discount applies first.
- ▸ A flat-dollar discount after a percentage is NOT compounding — it subtracts.
- ▸ Tax is usually applied AFTER discounts, so the tax amount goes down with discounts too.
Examples
- 30% + 20%0.70 × 0.80 = 0.56. On a £100 item, pay £56, save £44 (44%).
- 50% + 10%0.50 × 0.90 = 0.45. Pay 45% of original, save 55% — not 60%.
- Flat + percentage£10 off then 20% off: 100 − 10 = 90, then 90 × 0.80 = £72. Order matters here; read store rules.
When to use which tool
- Discount CalculatorMain tool — handles single and stacked discounts, shows the math step by step.Calculate the sale price and savings from any percent-off discount.
- Percentage CalculatorFor ad-hoc percentage operations outside the shopping context.Calculate percentages: what is X% of Y, X is what % of Y, and % change.
Related
- Discount CalculatorCalculate the sale price and savings from any percent-off discount.
- Percentage CalculatorCalculate percentages: what is X% of Y, X is what % of Y, and % change.
- How to Compare Two DiscountsWhen is £20 off better than 20% off? Depends on the price.
- Percentage Mental Math TricksFive shortcuts that cover tips, discounts, tax, and sale prices.
Frequently asked questions
› Is a 50% + 50% off = free? Trust & accuracy
No. 0.50 × 0.50 = 0.25 = pay 25%, save 75%. You only get "free" if the second discount is 100%.
› What if the store lets me choose the order?
The math is the same either way with two percentage discounts. Order only matters when you mix percentage and flat-dollar discounts.
› How should I use this guide with a Kefiw tool? How-to
Use the guide as the plan and the linked Kefiw tool as the check. Read the steps first, try the move manually, then use the tool to compare outputs, catch edge cases, and decide whether the result actually fits your task.
› What mistake do tool guides help avoid? Troubleshooting
Tool guides help avoid using a utility mechanically without understanding what you are trying to accomplish. Most word, writing, and text utilities are fast, but speed can hide context mistakes. Know whether you are solving a puzzle, cleaning copy, drafting a line, or checking a rule.
› Can a tool guide help me learn the skill? How-to
A tool guide can help you learn if you pause before accepting the output and ask why it worked. Compare your first guess with the tool result, look for the rule or pattern, and repeat that review. Passive copying solves one task; active review builds the skill.