SOLVETUTORMATH SOLVER

Instrument MI-05-276 · Conversion

Quantity Converter

A dozen is 12, a score is 20, a gross is 144 -- pick the counting unit and enter the count, and this converts straight to individual items.

Instrument MI-05-276
Sheet 1 OF 1
Rev A
Verified
Type 05 — Counting Units SER. 2026-05276

Individual items

36.0000

items = number of units x items-per-unit

The working Every figure verified twice
  1. y = 3·12 = 36.0000
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

Long before decimal counting dominated commerce, several cultures grouped items in other quantities, and a few of those groupings are still in everyday use. The dozen, 12 items, likely survives from ancient duodecimal (base-12) counting systems and remains the standard for eggs, baked goods, and countless retail packs because 12 divides evenly by 2, 3, 4, and 6 -- a genuinely convenient number for splitting a batch. A gross is a dozen dozens, 144 items, a unit that stuck in wholesale trades like stationery, hardware, and printing, where goods are bought and sold by the box rather than one at a time. A great gross, 1,728 items (a dozen gross, or 12 x 144), shows up at an even larger bulk scale -- historically for goods like pins, screws, or pencils ordered by the case. A score, 20 items, is older still and less tied to any particular trade, surviving mainly in a handful of set phrases.

The clearest surviving use of "score" in English is the opening line of Lincoln's Gettysburg Address: "Four score and seven years ago" means 4 x 20 + 7, or 87 years, counting back from 1863 to the Declaration of Independence in 1776. Half a dozen, 6 items, is the smallest unit here and the most everyday -- a carton of eggs, a pack of drink cans, a set of chairs. This page multiplies a count of any of these units by the unit's fixed size to give the total number of individual items, useful anywhere an old trade quantity shows up on an invoice, a recipe, or a historical text and needs converting to a plain count.

items=x×u\text{items} = x \times u
x -- the number of units you enter. unit -- the fixed size of the counting unit selected in the dropdown (6 for half-dozen, 12 for dozen, 20 for score, 144 for gross, 1,728 for great gross). y -- the resulting total of individual items.
  • Enter how many of the unit you have into Number of units; it opens at 3.
  • Pick the Counting unit from the dropdown: Half-dozen, Dozen, Score, Gross, or Great gross.
  • Read the total from Individual items beneath both fields -- it recalculates the instant either field changes.
  • The page opens already showing 3 dozen as 36 individual items, so you can see the multiplication before entering your own figures.

Worked example -- 3 dozen eggs

Enter 3 into Number of units and leave Counting unit on its default, Dozen. Individual items reads 36 -- an egg carton is typically sold by the dozen, so 3 dozen eggs, three standard cartons, comes to 36 individual eggs.

Change Number of units to 2 and Counting unit to Gross, and Individual items reads 288 -- pencils, like many small stationery items, are traditionally ordered wholesale by the gross, so 2 gross of pencils comes to 288 individual pencils, an order size that makes far more sense for a school or office supplier than for a single shopper.

Questions

How many items are in a dozen, a score, and a gross?

A dozen is 12, a score is 20, and a gross is 144 (a dozen dozens, 12 x 12). This page also covers half-dozen (6) and great gross (1,728, a dozen gross). Enter a count and pick the matching unit to get the total number of individual items.

Why is a gross 144 and not some other number?

A gross is defined as a dozen dozens: 12 groups of 12 items, or 12 x 12 = 144. The name and the grouping both come from the same duodecimal (base-12) counting tradition that gave the dozen its 12, just applied one level up for wholesale-scale trade in goods like stationery and hardware.

What does 'four score and seven years' mean?

It means 4 x 20 + 7, or 87 years. The line opens Abraham Lincoln's 1863 Gettysburg Address, and it is the best-known surviving use of "score" as a counting unit (20 items) in English, counting back 87 years from 1863 to the Declaration of Independence in 1776.

Why isn't a baker's dozen (13) included as an option?

Because a baker's dozen is not a fixed multiplier the way a dozen, gross, or score is -- it names the customary practice of adding one extra item as a bonus on top of an even dozen, not a separate counting unit with its own defined size. This page covers units with a fixed, unambiguous items-per-unit figure.

How big is a great gross?

A great gross is 1,728 items -- a dozen gross, or 12 x 144. It is the largest unit this page covers, historically used for ordering small manufactured goods like pins, screws, or pencils at an extreme bulk, case-lot scale rather than by the box.

References