Dozenal Weights & Measures:  Proposal for a comprehensive duodecimal system of weights and measures

Originated: Fall Semester 2003
Revised: 25 November 2004

I have made no secret of the fact that I am opposed to compulsory metrication.  I like the metric system just fine; I don’t like the prospect that my government might require me to use it to the exclusion of other measurement systems.  I would urge English-speaking countries to adopt a unified Customary system if they must force a measurement system upon us. 

The metric system does have some advantages, for example the millimeter is useful for very precise measurements; I think that someone should produce a customary ruler that goes down to 1/32 inch.  Additionally, something that has always bugged me about our customary measure is the fact that 1 fluid ounce is 1.805 cubic inches.  In metric, one milliliter is equal to one cubic centimeter.  It is much easier for me to construct a precise 1ml container than it is for me to build a 1 fl. oz. container.   Also, it is easier for me to calculate the volume in cm of 51ml than it would be for me to calculate the volume of 51 fl. oz.   

However, despite the advantages of the metric system, it has a huge disadvantage.  It is decimal.  Ten divides by 2 numbers: 2 & 5.  It is not very versatile; people sometimes need to divide sections into thirds, too.  Portions of the customary measurement system are dozenal; 1 foot is 12 inches and 1 yard is 3 feet.  12 is a much more useful base number for a measuring system -- it can be evenly divided by 2,3,4, & 6; twice as many numbers as 10.  However, despite the usefulness of 12, our pint and cup are 16 and 8 fluid ounces respectively.  I have often needed to measure out 1/3 cup in a recipe, but the number 8 does not divide by three -- unless I have '1/3 cup' marked, I have to guess. 

To add to the confusion, the U.K. also has weights and measures that look like American Customary units, but aren’t.  For example, while the Imperial fluid ounce weighs one ounce, it is smaller than the Customary fluid ounce.  And the Imperial pint is 20 fluid ounces while the Customary pint is 16 fluid ounces.  Now, this has not been a problem in the past.  The United States and the British Empire each had a large enough economy to negate any market pressure from the rest of the industrialized world to switch to the metric system.  However, as the rest of the world becomes more economically important, there will be more and more market pressure to go metric.  Some governments, such as the U.K. government, might think that demand for metric in the rest of the world is good enough reason to require that its own citizens use it whether they want to or not.  This is not an appropriate function of government.  If people choose to use the metric system to bring in more business, that’s one thing, but it is inappropriate for governments to force people to use it at the point of a gun.  I think that we English-speakers should adopt something like the unified system that I present here.  The only way to avoid any future economic pressure from the metric system it to have our own international standard. 

The reason Americans don’t really take to the metric system is that it does not actually resemble customary measure very much.  It would be a mistake for the U.S. government to force its citizens to use such a system.  Even Thomas Jefferson, a proponent of decimal measure, thought that the base units for any such system should resemble existing units of measurement wherever possible.  I agree.  We English-speaking people like our customs and traditions.  We do not destroy our history, we do not throw away something that works perfectly well -- we are not the French.  To that end, I have designed a dozenal measurement system that I think resembles Customary measure closely enough so as not to bother most people if adopted.  The base units are the inch, the ounce, and the fluid ounce.  The other units are powers of 12 (for the most part).  This gives my system the advantage that most all of my units can be divided by 3 as well as by 2.  This greatly increases the utility.

In my system (using the current definition of the second), I have slightly redefined the inch to make its value (defined as the distance light travels in a fraction of a second) compatible with the foot and the yard.  In fact, this inch is almost as long as the old US survey inch.  For common usage, you would not be able to tell the difference, though.  My dozenal inch is only about 0.000 000 000 000 000 169 inches longer than the current international inch.  To the naked eye, it will look like it is exactly 2.54cm.  The base values of my dozenal system are as follows:

1 inch = Length traveled by light in a vacuum during 1/11 802 829 104 of a second. 

1 foot = Length traveled by light in a vacuum during 1/983 569 092 of a second. 

1 yard = Length traveled by light in a vacuum during 1/327 856 364 of a second. 

1 second = the duration of 9 192 631 770 cycles of radiation corresponding to the transition between two hyperfine levels of the ground state of cesium 133. (Approximately Equivalent to 1/86 400 of 1 mean solar day)

If we switched to dozenal time, the second would be of a different duration, and thus the definitions of the inch, foot, and yard would necessarily be different.   But more on that in my time section.

Volume Definitions of Capacity/Mass (Weight)

unit	volume (cubic feet)	metric equivalent	metric volume
1 fluid ounce	1/648 cu. ft.	40.967 66 mL	40.967 66 cm3
1 ounce	1/648 cu. ft.(of distilled water at maximum density)	40.875 962 396 375 302 777 777 777 777 777 8 g	40.967 66 cm3
1 pint	1/54 cu. ft.	491.611 92 mL	491.611 92 cm3
1 pound	1/54 cu. ft. (of distilled water at maximum density)	490.511 548 756 503 633 333 333 333 333 333 g	491.611 92 cm3

Special Volume/Capacity/Mass Relationships

volume (cubic feet)	capacity	mass of distilled water at maximum density
1 cu. ft.	54 pints	54 pounds

Capacity

base (pints)	unit name	customary measure	imperial measure	metric
1/6 912 pt.	1 minim	1 & 107/693 minims	1 & 11/54 minims	0.07 mL
1/1 728 pt.	1 cor (4 minims)	20/2 079 fl. oz.	13/1 296 fl. oz.	0.28 mL
1/144 pt.	1 fluid twelons (12 cor)	80/693 fl. oz.	13/108 fl. oz.	3.41 mL
1/24 pt.	1 fluid hafons (6 twelons)	160/231 fl. oz.	13/18 fl. oz.	20.48 mL
1/12 pt.	1 fluid ounce	1 & 89/231 fl. oz.	1 & 4/9 fl. oz.	40.97 mL
1/2 pt.	1 cup	1 & 3/77 cups	1 & 11/15 gills	245.81 mL
1 pt.	1 pint (2 cups)	1 & 3/77 pints	13/15 pints	491.61 mL
3 pt.	1 quart (3 pints)	1 & 43/77 quarts	1 & 3/10 quarts	1.47 L
12 pt.	1 gallon (3 pints or 4 quarts)	1 & 43/77 gallons (exactly)	1 & 3/10 gallons (closer to 1.297 671 428 gal.)	5.90 L
72 pt.	1 bushel (6 gallons)	9 & 27/77 gallons	39/40 bushels	35.40 L
144 pt.	1 dogall (12 gallons)	18 & 54/77 gallons	1 & 19/20 bushels	70.79 L
576 pt.	1 barrel			283.168 465 92 L
1 728 pt.	1 fluid ton (12 dogalls)	224 & 32/77 gallons	187 & 1/5 gallons	849.51 L
20 736 pt.	1 chaldron (12 fl. tons)	2 692 & 76/77 gallons	7 & 4/5 chaldrons	10 194.06 L

Kitchen Measure

base (fluid ounces)	unit	customary	imperial	metric
1/432 fl. oz.	1 drop	1 & 151/342 small drops	1 & 85/162 small drops	0.09 mL
1/432 fl. oz.	1 drop	1 & 17/108 large drops	1 & 11/54 large drops	0.09 mL
1/72 fl. oz.	1 dash (6 drops)	1 & 23/27 dash	1 & 25/27 dash	0.57 mL
1/6 fl. oz.	1 teaspoon (12 dash)(72 drops)	1 & 7/18 tsp.	1 & 4/9 tsp.	6.83 mL
1/2 fl. oz.	1 tablespoon (3 tsp.)	1 & 7/18 tbsp.	1 & 4/9 tbsp.	20.48 mL
1 fl. oz.	1 fluid ounce	1 & 7/18 fl. oz.	1 & 4/9 fl. oz.	40.97 mL
6 fl. oz.	1 cup	1 & 1/24 cups	1 & 11/15 gills	245.81 mL
12 fl. oz.	1 pint (2 cups)	1 & 1/24 pints	13/15 pints	491.61 mL
36 fl. oz.	1 quart (3 pints)	1 & 9/16 quarts	1 & 3/10 quarts	1.47 L
144 fl. oz.	1 gallon (4 quarts)	1 & 9/16 gallons	1 & 3/10 gallons	5.90 L

Mass (Colloquial Weight)

base (pounds)	unit name	approximate Customary/Imperial value	approximate metric value
1/248 832 lb.	1 smal	23/756 gr.	0.002 g
1/20 736 lb.	1 spec (12 smals)	23/63 gr.	0.024 g
1/6 912 lb.	1 grain (3 specs)	1 & 2/21 gr.	0.071 g
1/1 728 lb.	1 carat (4 gr.)	1 & 21/50 carats	0.284 g
1/288 lb.	1 pennyweight/ scruple (6 carats)	1 & 1/10 pennyweights/ 1 & 4/13 scruples	1.703 g
1/144 lb.	1 twelons (2 pennyweights/ scruples)	3/25 oz.	3.406 g
1/24 lb.	1 hafons (6 twelons)	18/25 oz.	20.438 g
1/12 lb.	1 ounce	1 & 11/25 oz.	40.876 g
1 lb.	1 pound	1 & 2/25 lbs.	490.512 g
6 lbs.	1 clove (6 pounds)	162/175 clove	2.943 kg
12 lbs.	1 stone (2 cloves)	162/175 stone.	5.886 kg
36 lbs	1 quarterweight (3 stones)	38 & 22/25 lbs.	17.658 kg
144  lbs.	1 grossweight (12 stones or 4 quarterweights)	155 & 13/25 lbs.	70.634 kg
1 728 lbs.	1 ton (12 grossweights)	1 866 & 6/25 lbs.	847.604 kg

Jewelers’ Mass*

base (grains)	unit name	dozenal mass	troy equivalent (not exact)	metric equivalent (grams)
1 gr.	1 jewelers’ grain (1/480 j. oz.)	1 gr.	1 & 2/21 gr.	0.071 g
4 gr.	1 carat (1/120 j. oz.)	1 ct.	1 & 21/50 carats	0.284 g
24 gr.	1 jeweler’s pennyweight (1/20 j. oz.)	1 d. wt.	1 & 1/10 pennyweights	1.703 g
480 gr.	1 jewelers’ ounce (20 j. dwt.)	5/6 oz.	1 & 1/10 oz. tr. (1.2 oz. avdp.)	34.08 g
5 760 gr.	1 jewelers’ pound (240 j. dwt.)	5/6 lbs. (10 oz.)	1 & 1/10 lbs. tr. (.9 lb. avdp.)	408.96 g

* Used in weighing gold, silver, other precious metals, and precious stones.  These measures are particularly important for precisely weighing money in the Pound-Shilling-Penny system.

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For more suggestions, check out this page on the British Dozenal Society proposing a sort of dozenal metric system.

Return to ‘Toward a New Metric-Based Customary’

Return to Nearly Everything You Need to Know About Weights and Measures

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Weights & Measures