Quantity Converter
Translate a count among individual units, dozens, and grosses. Use it when the object being counted stays the same but a stock list, order, or record uses a different grouping.
Inputs, units, and assumptions
Enter a finite, nonnegative amount, select its From grouping, and select the To grouping. The amount is a number of groups, not necessarily a whole number. The supported grouping sizes are exact:
- 1 unit = 1 item
- 1 dozen = 12 items
- 1 gross = 144 items = 12 dozen
The counted item must be defined consistently. A dozen bolts can be converted to units or grosses of bolts, but not to the weight, volume, or package price of those bolts. No score, great gross, pair, case, or other named grouping is assumed.
Exact method and variable definitions
Let q be the entered amount, f_s the number of individual units in the source grouping, and f_t the number in the target grouping. The supported factors are 1, 12, and 144.
Here, u is the plain individual-unit count and r is the amount in the target grouping. The displayed details retain the individual-unit total and both grouping sizes.
Worked inventory example
Suppose an inventory record lists 2 gross of one item and an order sheet asks for dozens. First convert to plain units:
Then divide by the dozen size:
The result is exact. The supporting values are 288 individual units, 144 units per gross, and 12 units per dozen.
Count-group reference table
Use the row as the starting grouping and the column as the destination:
| From \ To | Unit | Dozen | Gross |
|---|---|---|---|
| Unit | q | q/12 | q/144 |
| Dozen | 12q | q | q/12 |
| Gross | 144q | 12q | q |
For example, 3 dozen is 3×12/144=0.25 gross. A fractional group is mathematically valid: it describes part of a dozen or gross. It does not determine whether a supplier sells partial groups.
Precision and limits
These grouping relationships are exact, but an entered decimal may represent an estimate. Conversion does not add precision to that estimate. Results may be shown with limited decimal places, so retain the plain-unit count when reconciling records.
Zero converts to exact zero. Negative, nonnumeric, or unsupported grouping inputs do not produce a result. Very large inputs can also be rejected if the arithmetic would overflow. This tool does not establish package contents, minimum order quantities, sellable quantities, weight, volume, or price.
Practical next step
Write the item name beside both counts, compare the displayed individual-unit total with the source record, and confirm that the destination record permits fractional groups. If it requires whole dozens or grosses, apply that purchasing rule separately rather than silently rounding the converted count.
Sources
- NIST Handbook 44, Appendix C, general tables of units of measurement, including dozen and gross count relationships.