## Units Conversions

You might want to review **how I write numbers** if some of these don’t make sense to you.

One of the fascinating (and archaic) aspects of Imperial measurements is the wide range of them from different sources. Here we will focus on the units that are most commonly encountered in antenna work, particularly those regarding length / distance, and ignore most of the others, including the furlong, fathom, perch, chain, link, and nautical mile. (Of historical interest, the US officially adopted the SI / Metric system around 1893, but allowed the continued use of “customary units” in commerce, which continues to this day.)

### Distance units

The basic Imperial Units for distance are:

- 1 foot = 12 inches
- 1 (statute) mile = 5280 feet (there are other types of miles)
- 1 yard = 3 feet

Fractions of inches were measured by dividing units in half repeatedly until the result was close enough. Thus we find increments like 1/2, 1/8, 1/32 inch, etc. Very small sizes are measured in “mils”, ( 0.001 inch, or about 25 microns ) as the binary fractions are far too awkward at that level.

With that introduction, let’s look at the standard units for distance. First, the exact definition of the relationship between the two systems, standardized in the mid-1900s because the British and American inches were very slightly different sizes:

1 inch = 2.54 cm = 25.4 mm

From that, we can derive the other units:

1 cm = 0.3937 inches

1 foot = 0.3048 meter (or metre, for those who prefer).

1 meter / metre = 3.2808 feet = 39.37 inches

1 (statute) mile = 1.609 km

1 km = 0.6215 (statute) miles

Those should handle most required conversions, but there are some convenient short cuts that make day-to-day use more convenient when precision isn’t required. Here are some that I find handy, along with an estimate of the actual error of the result.

10 feet = 3 m or 1 m = 40 inches ( 1.6% error )

1 inch = 25 mm or 4 inches = 10 cm ( 1.6% error )

3 feet ( 1 yard ) = 1 meter ( 10% error )

30 miles = 50 km ( 3.6% error ) 50 miles = 80 km ( 0.6% error )

Of course, one of the aspects that makes conversions more difficult is that, in many cases, **fractional inches** are used instead of decimal values. For example, an antenna for the 10m band might be specified as, ” eight feet, nine and three quarters inches” long. To convert this, start by **translating 3/4 inch to a decimal** (0.75) and adding that to the number of inches, giving us “8 feet 9.75 inches”. Then there are two ways to proceed: one is to divide the inches by 12 to get decimal feet (“0.8125 feet”) and adding that to the integer feet (“8.8125 feet”), then dividing that by 3.2808 feet/meter to get 2.686 meters. The other is to multiply the 8 feet by 12 to convert it to inches, and add the 9.75 inches to that for “105.75 inches”. Then this can be converted to cm by multiplying by 2.54 cm/inch, or to meters by dividing by 39.37 inches/meter, again giving 2.686 m.

This is one reason why I am trying to provide all measurements in both metric and Imperial units, so readers don’t need to do conversions. But readers should understand that many American tape measures are marked in feet, inches, and **binary fractional inches** (often 1/16 or 1/32 inch increments), so measuring decimal fractions of feet or inches requires some conversion, and they may encounter such measurements from other sources. (Fortunately, newer tape measures often have a metric scale in addition to feet and inches.)

Or, of course, you could use an online calculator, like one of these:

- https://www.calculator.net/conversion-calculator.html
- https://www.metric-conversions.org/length/meters-to-feet.htm
- https://www.conversion-metric.org/
- https://www.calculatorsoup.com/calculators/conversions/metricunits.php
- https://www.metriccalculator.com/length.html
- or many others…

A grammatical note: the plural of foot, of course, is feet, both abbreviated “ft”. But when the term is used as an adjective, the singular form is used. So it is correct to say, “This four-foot board is four feet long.”

### Weight units

Since I address weights, particularly in regards to antennas for backpacking, I’ll include those conversions also.

The basic Imperial Units for weight / mass are:

- 1 ounce (avoirdupois) = 28.35 grams
- 1 pound (avoirdupois) = 16 ounces = 453.6 grams
- 1 kg = 2.205 pounds = 35.27 ounces

It is common to see weights given in the form “3 pounds 7 ounces” rather than in decimal pounds.

Common conversions of 1 ounce = 28 grams and 1 kg = 2.2 pounds are generally close enough. (For rough estimates, 1 ounce = 30 grams and 1 kg = 2 pounds may be adequate.)

The abbreviation for pound is “lb”, just to confuse people. For ounce it is “oz”.

Note that the pound is also a unit of force:

- 1 pound (avoirdupois) = 4.45 Newtons

You can convert a value in pounds to either kg or N, depending on your application. For common use on the surface of the Earth, when variations in the acceleration of gravity are not significant, the values are often used interchangeably.

Not to be confused, of course with “pounds sterling”, the British unit of currency, which was initially the value of one pound of silver.

For simplicity I will stick with these units for weight. Of course, there are other variants: troy units also use the ounce and pound, but the sizes differ (and 1 troy pound = 20 troy ounces, just to confuse matters further). The “stone” = 14 pounds isn’t used in the US, and the larger units (“hundredweight” and “ton”) vary in value between the US and British systems. I’ll just observe that the US “short ton” = 2000 pounds and the British “long ton” = 2240 pounds are both relatively close to the “metric tonne” = 2205 pounds, if you need an approximate conversion of large weights.