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Unit Price: Comparing Two Sizes Without a Calculator

You rarely need the price per unit. Scale the smaller pack up to the larger one and compare two totals — one multiplication instead of two awkward divisions.

By Published Updated 6 min read

Reign Creative LLC makes IQ Test & Brain Training Games, which this article links to, so we have a commercial interest in it. How we write and check articles.

Key takeaways

  • Most size comparisons can be settled by scaling the smaller pack up to the larger one, which replaces two divisions with a single multiplication.
  • When the sizes are not exact multiples of one another, scale both to a shared size — usually their lowest common multiple — and compare two totals.
  • If you do want a unit price, choose a friendly unit such as price per 100 grams rather than price per gram, because the division then lands on numbers you can hold.
  • A unit price label is a regulated artefact in some places and absent in others: NIST records unit pricing as mandatory in ten US jurisdictions, voluntary in nine more, and covered by no provision in the remaining states.
  • The larger size is not automatically cheaper, and the lowest unit price is not automatically the best buy once waste, storage and actual use are counted.

You almost never need the price per unit to decide which pack is better value. Scale the smaller pack up to the larger one and compare two totals — one multiplication instead of two awkward divisions. A 250 gram pack at 1.80 against a 750 gram pack at 4.95 is settled the moment you notice that three small packs would cost 5.40, which is more than 4.95. The large pack wins by 0.45 and you never touched a decimal.

The unit price is the thing the shelf label computes for you. Where it exists and where both labels use the same unit, the work is done. Where it does not, the scaling method is faster than reconstructing it.

What a unit price actually is

NIST defines unit pricing as the pricing of goods based on the cost per unit of measure, with a label typically carrying the product name, the size, the price, and the price per unit — per gram, litre or ounce.

It is not universal. NIST's guide to US retail pricing laws records unit pricing provisions as mandatory in ten jurisdictions — Connecticut, Maryland, Massachusetts, New Hampshire, New Jersey, New York, Oregon, Rhode Island, Vermont and the District of Columbia — voluntary in nine more, and absent in the remaining thirty-three states. Where the NIST Handbook 130 regulation applies, it permits either metric or customary units, and requires the unit of measure to be consistent across like items within a category.

NIST also frames the label as a defence against package downsizing: it describes shrinkflation as a product sold at the same price with its net contents reduced, states that approximately 30% of consumer goods have been downsized, and cites research finding that 82% of consumers use unit pricing where it is available. That is the case for reading the label. The case for being able to do the arithmetic is that the label is missing, inconsistent or absent a third of the time.

The scale-up method

When one size is a multiple of the other. 250 g at 1.80 against 750 g at 4.95. Three small packs make 750 g and cost 5.40, against 4.95 for the large. The large pack is cheaper by 0.45 on the same quantity. As unit prices those are 0.72 and 0.66 per 100 g, which agrees — but computing them was unnecessary.

When neither is a multiple. 400 g at 3.20 against 600 g at 4.50. The lowest common multiple of 400 and 600 is 1,200, so scale both to that: three of the 400 g packs cost 9.60, and two of the 600 g packs cost 9.00. The 600 g pack wins. Unit prices confirm it at 0.80 and 0.75 per 100 g.

The scaling method has a real advantage beyond speed: it is exact. Nothing has been rounded, so the comparison cannot be reversed by a rounding error, which is a genuine hazard when two unit prices are close.

When you do want a unit price, pick a friendly unit

Price per gram produces numbers like 0.0075, which nobody can hold. Price per 100 grams produces 0.75, which everyone can. Choose the unit that keeps the result between about 0.10 and 100, and use the same unit on both sides.

4.50 for 600 g. Six hundred grams is six lots of 100 g, so divide 4.50 by 6: 0.75 per 100 g. One small division.

5.94 for 780 g is uglier. Round to friendly numbers: call it 6.00 for 800 g, which is 6.00 ÷ 8 = 0.75 per 100 g. The true figure is 5.94 ÷ 7.8 = 0.7615, so the estimate is about a penny and a bit low per 100 g.

That direction is worth understanding rather than memorising. Rounding the price up multiplied it by about 1.010, but rounding the weight up multiplied it by about 1.026 — the denominator grew proportionally more, so the estimated unit price came out below the true one. Whenever you round both parts of a division, the side you inflated more decides the direction of your error.

This is the move the app's techniques library calls compatible numbers: swap an awkward number for a nearby one that pairs cleanly, the way 638 ÷ 9 becomes 630 ÷ 9 = 70. The general method set is in how to divide in your head, and the neutral-rounding discipline behind it in estimation techniques that make mental math useful.

When the bigger size is not cheaper

It happens often enough to be worth a check rather than an assumption.

500 ml at 2.00 against 1.2 L at 5.40. Per 100 ml those are 0.40 and 0.45. The small bottle is cheaper per unit, and anyone reaching automatically for the large one pays more.

Promotions invert the usual relationship routinely — a multibuy on the small size, a temporary price cut, a pack size that exists only to look like a bargain. The scaling method catches all of them in one multiplication, which is why it is worth having as a reflex rather than a procedure.

And the lowest unit price is not automatically the best buy. If half of the larger pack goes to waste, its effective unit price doubles. Storage, shelf life and whether you will actually use the quantity all sit outside the arithmetic, and the arithmetic cannot see them.

The label traps

Three things reverse a comparison without changing any price.

  • Different units on adjacent labels. Per 100 g beside per kilogram beside per item. NIST's consistency requirement exists precisely because of this, and it applies only where the regulation has been adopted. NIST's own illustration of the intended behaviour compares a 32-ounce ketchup bottle at 0.16 per ounce against a 14-ounce bottle at 0.23 per ounce — same unit, immediate comparison.
  • Per-item pricing across different counts. A price per item tells you nothing when the items differ in size.
  • Drained weight against net weight. For anything packed in liquid, the number on the front and the number you eat are different quantities.

The reasoning underneath

A unit price is a rate, and choosing between two rates is proportional reasoning rather than calculation. The What Works Clearinghouse practice guide on fractions instruction recommends developing conceptual understanding of strategies for ratio, rate and proportion problems before introducing cross-multiplication as a procedure — which is exactly the difference between scaling two packs to a common size and mechanically dividing both prices. The scaling route generalises to recipes, map scales and mixing problems, and those are worked through in ratios and proportions without cross-multiplying.

For the in-aisle version of the same skill — holding a running total, and rounding so the error never runs against you — see running a budget in your head. The full method set sits in the mental math training guide, the rest of this hub under mental math, and the wider subject under education and brain training.

Practising the comparison

IQ Test & Brain Training Games — our own app, built by Reign Creative — ships a Unit Price Challenge, a 75-second timed mode on the "Per unit" difficulty. Two neighbouring modes drill the halves the comparison rests on: Ratio Trainer, also on 75 seconds with Easy, Medium and Hard settings, for the scaling reflex; and Division Dash, a 60-second mode whose difficulty settings run from Small numbers through Exact division and Multiples to Larger dividend and Mixed division, for the divisions you cannot avoid.

The compatible-numbers technique above is one of the 49 entries in the app's techniques library, each carrying steps, a worked example, a "best for" note, a named common mistake and a two-question mini quiz, with a practice link into a specific mode at a specific difficulty.

The app is an educational game and a practice tool. It does also include an IQ-style test, a memory test and a reaction time test, and its Google Play listing describes their results as estimates based on app activities, not clinical or professional assessments. What it records on the drills — score, accuracy, streak, response time and personal bests — describes how you did on the drills you played.

Good to know

Frequently asked questions

What is the fastest way to compare two pack sizes?
Scale rather than divide. If the large pack is three times the small one, work out what three small packs would cost and compare that single figure against the large pack's price. One multiplication replaces two divisions, and the comparison is exact rather than approximate because you never round anything.
Is the bigger size always cheaper per unit?
No. It is usually cheaper, which is why people stop checking, and that habit is exactly what a promotion on the small size exploits. A 500 millilitre bottle at 2.00 works out at 0.40 per 100 millilitres, while a 1.2 litre bottle at 5.40 works out at 0.45 — the small one wins, and only the arithmetic reveals it.
Which unit should you compare in?
Whichever makes the division land on numbers you can hold. Price per 100 grams is usually better than price per gram, because the result is a number with a sensible number of digits rather than a string of decimals. The one rule is that both products must be expressed in the same unit before you compare them.
Do shelf labels always show a unit price?
No. NIST records that unit pricing provisions are mandatory in ten US jurisdictions, voluntary in nine more, and absent in the remaining thirty-three states. Where the NIST Handbook 130 regulation applies, it requires the unit of measure to be consistent across like items within a category, but that consistency requirement does not reach everywhere.

Sources

  1. A Guide to U.S. Retail Pricing Laws and Regulations (opens in a new tab)National Institute of Standards and Technology (NIST), Office of Weights and Measures — accessed
  2. Uniform Unit Pricing: Tools for Consumers to Fight Shrinkflation (opens in a new tab)National Institute of Standards and Technology (NIST) — accessed
  3. Best Practices for Uniform Unit Pricing: An Update to NIST SP 1181 and NIST Handbook 130 Regulations (opens in a new tab)National Institute of Standards and Technology (NIST) — accessed
  4. Developing Effective Fractions Instruction for Kindergarten Through 8th Grade (WWC Practice Guide) (opens in a new tab)What Works Clearinghouse, Institute of Education Sciences, U.S. Department of Education — accessed

About the author

— The independent app studio that builds the apps covered on this site and publishes every article here. On Google Play it publishes as Reign Collective Apps.

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