Discounts, Margins and the Percentage Mistake Almost Everyone Makes

By Tom Ashcroft · July 21, 2026

Stacked discounts, reversed increases and the gap between margin and markup cost people real money. Here is the arithmetic behind each, in plain language.

Percentages are taught early and then quietly misapplied for the rest of our lives. The mistakes are consistent enough that you can predict them: people add discounts that should be multiplied, they reverse an increase by subtracting the same percentage, and they use margin and markup interchangeably when the two produce very different numbers. None of this is about being bad at mathematics. It is about a set of operations that look symmetrical and are not.

Stacked discounts do not add up

A shop advertises 40 percent off, and at the checkout there is a further 20 percent off the sale price. Most people, including most shop staff, will say that is 60 percent off. It is not. The first discount leaves you paying 60 percent of the original price. The second leaves you paying 80 percent of that, and 0.6 multiplied by 0.8 is 0.48. You pay 48 percent of the original, so the true discount is 52 percent.

Eight percentage points may not sound dramatic on a jacket, but the same error applied to a wholesale order, a rebate schedule or a contract with tiered discounts becomes a serious sum. The rule to remember is that discounts multiply. Convert each one into the fraction you still pay, multiply those fractions together, and subtract from one.

A decrease and an increase of the same percentage do not cancel

Suppose an investment falls 20 percent and then rises 20 percent. Starting at 1,000, the fall takes it to 800, and a 20 percent rise on 800 is 160, leaving 960. You are four percent down despite the two moves appearing to cancel. The asymmetry exists because each percentage is applied to a different base, and it is why a portfolio that halves needs to double to recover, not rise by fifty percent.

The same trap appears in payroll discussions. A ten percent pay cut followed by a ten percent restoration leaves an employee one percent below where they started, which is a conversation worth having explicitly rather than discovering on a payslip.

Reversing an increase requires division

This is the one that costs small businesses money. A price including 20 percent tax is 120. To find the price before tax, people subtract 20 percent of 120, which is 24, and arrive at 96. The correct answer is 100, obtained by dividing 120 by 1.2. Subtracting the percentage applies it to the larger, post-increase figure, which is the wrong base.

Whenever you are working backwards from a figure that already includes an addition, divide by one plus the rate. To remove a 15 percent service charge from 92, divide by 1.15. To find the list price behind a 30 percent discount, divide the sale price by 0.7.

Margin and markup are not the same thing

An item costs 100 and sells for 150. The markup is 50 percent, because profit is half the cost. The margin is 33 percent, because profit is a third of the selling price. Both describe the same transaction, and confusing them systematically understates profitability targets. A business that intends to run a 40 percent margin and instead applies a 40 percent markup ends up with a margin of about 29 percent, which across a year can be the difference between viable and not.

To convert a target margin into a markup, divide the margin by one minus the margin. A 40 percent margin requires a markup of about 67 percent. Write the formula down somewhere near your pricing sheet, because this is the mistake people make repeatedly even after having it explained.

Percentage points versus percentages

When an interest rate moves from 5 percent to 7 percent, that is a rise of two percentage points and a relative increase of 40 percent. Both statements are true and they invite very different reactions, which is exactly why reporting sometimes chooses whichever sounds more dramatic. If you are reading a claim about a change in a rate, check which of the two is being described before drawing a conclusion.

A checklist for getting it right

1. Identify the base. Ask which number the percentage is being applied to, because most errors come from applying it to the wrong one.
2. For sequential changes, convert each into a multiplier and multiply them together rather than adding the percentages.
3. To reverse a change, divide by the multiplier instead of subtracting the percentage.
4. Decide explicitly whether you mean margin or markup, and state which one in any document that others will read.
5. Sanity check the result against a rough estimate. Ten percent of a number is easy to find mentally, and it catches most decimal place errors.
6. Use the Percentage Calculator for the arithmetic so that the only thing you have to get right is the question.

Where these calculations show up

• Retail promotions with a headline discount and a voucher applied at checkout.
• Freelance invoicing where tax is added, a platform fee is deducted, and an early payment discount is offered.
• Salary negotiations involving a percentage rise against a different base than the one you assumed.
• Exam and assessment marks where components carry different weightings, so a percentage in one paper is not equivalent to the same percentage in another.
• Loan and savings comparisons where a rate difference of half a percentage point compounds into a large absolute figure over years.
• Business reporting where a change is described relatively in one place and in percentage points in another.

One habit that prevents most errors

Before calculating anything, say the question out loud in full: "what is 15 percent of the pre-tax total" rather than "what is 15 percent". Half of all percentage errors are not arithmetic failures at all; they are the result of answering a slightly different question from the one that was asked. Naming the base explicitly forces the ambiguity into the open, where it is easy to resolve.

The second habit is to keep the intermediate figures. When a calculation runs through three steps, writing down each result means that a wrong answer can be traced to the step that caused it rather than repeated from scratch. That is particularly valuable when someone else questions your number, which in commercial contexts they eventually will.

Wrapping up

Percentages reward a small amount of care. Multiply sequential changes, divide to reverse them, keep margin and markup separate, and always name the base. Get those four right and you will avoid nearly every percentage error that shows up in shops, invoices and spreadsheets.

Run the numbers yourself with our free calculator.

Try the Percentage Calculator tool.

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