Gross — Definition, Formula & Examples
A gross is a counting unit equal to 144 items. It is the same as 12 dozen, since one dozen equals 12.
A gross is a unit of quantity defined as individual items. It belongs to the duodecimal (base-12) family of counting units, where one dozen = 12 and one gross = 12 dozen = 144.
Key Formula
Where:
- = 12 individual units
- = 12 dozen, or 144 individual units
How It Works
To convert from gross to individual units, multiply the number of gross by 144. To convert from individual units to gross, divide by 144. The term comes from historical trade, where goods like pencils, buttons, and eggs were sold by the dozen or gross. A "great gross" goes one step further: it equals 12 gross, or items.
Worked Example
Problem: A school orders 3 gross of pencils. How many individual pencils is that?
Step 1: Recall that 1 gross = 144 pencils.
Step 2: Multiply the number of gross by 144.
Answer: The school ordered 432 pencils.
Why It Matters
The gross shows up in word problems involving bulk quantities and unit conversions. Understanding it also introduces the idea that not all counting systems are base-10 — the dozen and gross are remnants of base-12 counting, which appears again in topics like time (12 hours, 60 minutes) and angle measurement.
Common Mistakes
Mistake: Confusing a gross (144) with a dozen (12) or thinking a gross means 100.
Correction: The word "gross" can mean "total" in everyday English, but in mathematics it specifically means 144. Remember: a gross is a dozen dozens, so .