Easy how to calculate percentage: the two sums behind every deal badge

Two sums cover almost every shopping question

The first sum is a part expressed against a whole. You have two numbers and you want to know what share the smaller one is of the larger. Divide the part by the whole, then move the decimal point two places to the right. Eighteen out of 72 becomes 0.25, which becomes 25 percent. Nothing else is happening, however it is dressed up.

The second sum is a change expressed against a starting number. Subtract to get the difference, divide the difference by the number you started from, then move the decimal point two places again. A figure falling from 80 to 60 is a difference of 20, divided by 80 gives 0.25, so a 25 percent reduction. The only trap here is which number goes on the bottom. The starting figure always does. Dividing by the ending figure gives a different and wrong answer, and it is the single most common slip.

The reverse direction matters just as much, because deal pages usually show you the percentage and the final figure and leave the starting figure implicit. To go backwards, divide the amount you pay by one minus the discount expressed as a decimal. Pay 60 after a 25 percent reduction and the original was 60 divided by 0.75, which is 80. Being able to run that in reverse is what lets you check whether the advertised starting figure is the one the arithmetic implies.

Doing it in your head with a 10 percent anchor

Ten percent of any number is that number with the decimal point moved one place left. That single move is the whole technique. Once you have 10 percent, you have 5 percent by halving it, 20 percent by doubling it, 1 percent by moving the point one more place, and almost any other figure by adding those pieces together.

Take 35 percent of 240. Ten percent is 24, so 30 percent is 72. Five percent is half of 24, which is 12. Add them and you have 84. No long division, no calculator, and the error bars are tight enough for a shelf decision. The same anchor works for the awkward numbers: 15 percent is 10 plus 5, 45 percent is 50 minus 5, and 12 percent is 10 plus 1 plus 1.

Two shortcuts are worth keeping alongside the anchor. First, a percentage of a number equals the same percentage the other way around, so 8 percent of 50 and 50 percent of 8 are both 4, and one of those is far easier. Second, when you want to know what you pay rather than what you save, work with the remainder directly: a 30 percent reduction means paying 70 percent, so take 10 percent and multiply by 7 in one step instead of subtracting at the end.

• 10 percent: move the decimal point one place left.
• 5 percent: halve the 10 percent figure.
• 1 percent: move the decimal point two places left.
• What you pay after a reduction: use the remainder, not the discount.
• Swap the two numbers when one of them is easier to halve or double.

The same two numbers, worked three ways

The table sets out each form of the sum with the setup and a worked example, so you can match the question you are facing to the arithmetic that answers it. Read the middle column as the pattern and the right-hand column as proof that the pattern produces a sane answer.

The third row is the one most often skipped and most often needed, because it is how you audit a badge rather than accept it.

The starting number is chosen for you, and the rules say what it must be

Every reduction percentage has a denominator, and on a retail page that denominator is a former price selected by the seller. This is where a correct calculation can still mislead, and it is also the part the federal pricing guides address directly.

The Guides Against Deceptive Pricing, at 16 CFR 233.1, state that a former price gives a legitimate basis for a comparison only where it is the actual, bona fide price at which the article was offered to the public on a regular basis for a reasonably substantial period of time. Where the former price is not genuine but artificial and inflated, established so that a large reduction can be advertised afterwards, the guides describe the bargain being advertised as a false one. The same section cautions sellers against implying that a former figure was a selling price rather than an asking price unless substantial sales were actually made at it.

The worked illustration in the guides is instructive about the arithmetic as well as the ethics. It describes a retailer whose usual markup is 50 percent over cost, which sets his ordinary retail figure, and who then begins advertising at a raised figure purely so that a later reduction looks dramatic. The percentage in that advertisement is arithmetically correct and informationally worthless. The guides also note that a reduction can be too small to match the impression it creates, so that calling something reduced when the change is merely nominal misleads a reader who expected a meaningful saving.

The practical move is to stop treating the badge as data and treat the denominator as the thing to verify. Ask whether the former figure was charged on a regular basis and for how long. If you cannot establish that, the percentage is a claim about the seller's own previous asking figure and nothing more.

A percentage of a total that is not final yet

The second structural problem is that a reduction is almost always applied to a subtotal, while what leaves your account is a total. Mandatory fees added after the percentage is calculated dilute it, sometimes heavily on small orders, and they do so invisibly if you only read the badge.

Federal rules now speak to this directly. The Rule on Unfair or Deceptive Fees, at 16 CFR Part 464, defines total price as the maximum total of all fees or charges a consumer must pay for the goods or services and any mandatory ancillary good or service, excluding government charges, shipping charges and charges for genuinely optional extras. The rule makes it unlawful for a covered business to offer, display or advertise a price without clearly and conspicuously disclosing that total price, and requires the total to be disclosed more prominently than other pricing information. Where a final amount of payment is shown, that final amount must be at least as prominent.

Two things follow. First, the figure you should be running your arithmetic against is the total price, not the line item the badge was calculated from. Second, if a page shows you a percentage prominently and a total only at the final step, the ordering itself is informative. Recalculate the reduction against the total and you will frequently find the real figure is several points lower than advertised.

Delivery timing belongs in the same audit, because a reduction you have to wait an indefinite time to receive is a different offer. The Mail, Internet, or Telephone Order Merchandise Rule, at 16 CFR Part 435, provides that where no shipping time is clearly and conspicuously stated, the seller must ship within 30 days of receiving a properly completed order, extended to 50 days where the buyer applies for credit to pay for the merchandise at the time of ordering. A page that states no date is therefore not making an open-ended promise.

A 2 minute routine for any badge you meet

Run the arithmetic first, because it is quick and it catches the simplest errors. Use the 10 percent anchor to confirm the reduction shown is consistent with the two figures displayed, and reverse the sum to see what starting figure the percentage implies. Mismatches between the implied and advertised starting figures are worth noticing.

Then move to the denominator and the total. Establish what evidence there is that the former figure was charged regularly and for a substantial period, recalculate the reduction against the total including mandatory fees, and check whether a shipping date is actually stated. Those three checks take about 2 minutes and they dispose of most of the gap between a percentage and a saving. What they cannot do is tell you whether the item is worth owning, which stays a judgement no arithmetic will make for you.

Before you buy

• Identify whether the question is a part of a whole or a change from a starting figure.
• Confirm you are dividing by the starting figure, not the ending one.
• Use 10 percent as your anchor and build the rest by halving and doubling.
• Reverse the sum to see what starting figure the advertised percentage implies.
• Ask what evidence exists that the former figure was charged on a regular basis.
• Recalculate the reduction against the total price including mandatory fees.
• Multiply remainders rather than adding percentages when two reductions stack.
• Check whether a shipping date is stated, and note the default period if it is not.

Questions readers ask

What is the quickest way to work out a percentage without a calculator?

Find 10 percent by moving the decimal point one place to the left, then build the figure you need from it. Halve it for 5 percent, double it for 20 percent, move the point one place further for 1 percent, and add the pieces. For 35 percent of 240, that is 24 times 3 plus 12, which is 84.

Which number do I divide by when working out a reduction?

Always the number you started from. Divide the difference between the two figures by the starting figure, then move the decimal point two places right. Dividing by the ending figure gives a larger and incorrect answer, and it is the most common mistake in this sum.

How do I find the original figure from a discount percentage?

Divide the amount you pay by one minus the discount written as a decimal. Paying 60 after a 25 percent reduction means dividing 60 by 0.75, which gives 80. Running the sum in this direction is how you check whether an advertised former figure is consistent with the badge.

Do two reductions of 20 percent add up to 40 percent?

No. The second is taken against the figure left after the first, so the combined effect is 36 percent, not 40 percent. Multiply the remainders instead: 0.8 times 0.8 is 0.64, meaning you pay 64 percent of the original.

Does a percentage have to be calculated on a genuine former price?

The Guides Against Deceptive Pricing say a former price supports a comparison only where it was the actual, bona fide price offered to the public on a regular basis for a reasonably substantial period. A former figure set artificially high so that a large reduction can be advertised later is described in the guides as the basis of a false bargain.

Should I calculate the percentage before or after fees?

For your own purposes, after. The Rule on Unfair or Deceptive Fees defines a total price covering all mandatory charges and requires it to be disclosed clearly and prominently. Recalculating the reduction against that total is the only way to see what share of what you actually pay was taken off.

Sources

1. 16 CFR Part 233 - Guides Against Deceptive Pricing (eCFR, current) — checked 2026-11-06
2. 16 CFR 233.1 - Former price comparisons — checked 2026-11-06
3. 16 CFR Part 464 - Rule on Unfair or Deceptive Fees — checked 2026-11-06
4. 16 CFR Part 435 - Mail, Internet, or Telephone Order Merchandise — checked 2026-11-06