Each Conversion Formulas
Complete formulas for converting between different quantity units including each, dozen, gross, score, and other counting measurements.
๐ข Basic Quantity Unit Conversions
Standard Counting Units
Each โ Dozen
Example: 36 each
36 each = 3 dozen
Dozen โ Gross
Example: 24 dozen
24 dozen = 2 gross
Each โ Gross
Example: 288 each
288 each = 2 gross
Traditional Counting Units
Score and Century
Example: 400 each
400 each = 20 score = 4 century
Great Gross and Million
Example: 3,456 each
For million: Need 1,000,000 each = 1 million
3,456 each = 2 great gross
๐ญ Commercial and Industrial Applications
| Industry | Common Unit | Equivalent (Each) | Usage Example |
|---|---|---|---|
| Bakery | Dozen | 12 each | Eggs, donuts, bagels |
| Wholesale | Gross | 144 each | Pencils, small parts |
| Stationery | Ream | 500 each | Paper sheets |
| Publishing | Quire | 24-25 each | Paper sheets (traditional) |
| Retail | Six-pack | 6 each | Beverages, batteries |
| Agriculture | Bushel Count | ~48,000 each | Corn kernels per bushel |
| Electronics | Thousand (K) | 1,000 each | Resistors, capacitors |
๐ฆ Bulk Quantity Calculations
Packaging and Distribution
Multi-Level Packaging
Shipping calculation
50 cases ร 12 boxes/case ร 24 units/box
In dozens: 14,400 รท 12 = 1,200 dozen
In gross: 14,400 รท 144 = 100 gross
Total shipment: 14,400 units
Inventory Planning
Office supplies planning
Usage: 2,000 pens per month
Package size: 144 each (1 gross)
Planning period: 6 months
Order: 84 gross (12,096 pens)
Cost Analysis
Bulk Pricing Calculations
Wholesale vs retail pricing
Retail: $2.00 per dozen (12 each)
Wholesale: $18.00 per gross (144 each)
Retail unit cost: $2.00 รท 12 = $0.167 each
Wholesale unit cost: $18.00 รท 144 = $0.125 each
Bulk savings: $0.042 per unit (25% less)
Break-Even Analysis
When to buy in bulk
Bulk cost: $18.00 per gross
Retail equivalent: $24.00 per gross
Savings: $24.00 - $18.00 = $6.00 per gross
Usage: 50 each per month
Time to use gross: 144 รท 50 = 2.9 months
ROI: $6.00 savings over 3 months
๐ Historical and Cultural Counting Systems
Traditional Counting Units
Biblical and Ancient
Cubit count: Ancient length-based counting
Myriad: 10,000 each (Greek)
Lakh: 100,000 each (Indian)
Crore: 10,000,000 each (Indian)
These systems still used in modern contexts
Cultural significance in counting
Commercial History
Baker's dozen: 13 each (not 12)
Long hundred: 120 each (6 score)
Timber dozen: 13 pieces
Printer's ream: 516 sheets
Extra units to account for defects/waste
Historical quality assurance
Modern Applications
Digital Systems
Kilobyte: 1,024 bytes each
Not exactly 1,000
Binary vs decimal counting
Creates conversion complexity
1 KB โ 1000 bytes
Scientific Notation
Avogadro's number: 6.022ร10ยฒยณ
Mole concept in chemistry
Extremely large quantities
Standard scientific counting
Universal scientific standard
Manufacturing
Six Sigma: 3.4 defects per million
PPM: Parts per million
Quality control metrics
Statistical process control
Modern quality standards
๐ Quick Conversion Reference
Standard Conversions
1 Dozen:12 Each
1 Gross:144 Each (12 dozen)
1 Great Gross:1,728 Each (12 gross)
1 Score:20 Each
1 Century:100 Each
1 Thousand:1,000 Each
1 Million:1,000,000 Each
Special Units
1 Baker's Dozen:13 Each
1 Ream (Paper):500 Each
1 Quire:24-25 Each
1 Six-pack:6 Each
1 Pair:2 Each
1 Quartet:4 Each
1 Quintet:5 Each