Comparing amounts measured in different units

Two amounts can be compared fairly only when they use the same unit, cover the same period and measure the same thing. Converting to one unit handles the first requirement, lining up time periods handles the second, and a check on definitions handles the third. Most comparison errors come from skipping one of the three. Unit mix-ups in particular can produce errors far larger than rounding, sometimes by a factor of a thousand.

Convert both figures to one unit

Choose one unit before doing anything else, usually the unit the question is asked in. To convert, multiply or divide by a known factor. A mile is about 1.609 kilometers, so 10 miles is about 16.1 kilometers. A kilogram is about 2.2 pounds, so a 10-kilogram parcel weighs about 22 pounds. Volumes need care too. A US gallon is about 3.785 liters, while the UK imperial gallon is about 4.546 liters, so the same word can mean different amounts depending on where a figure was produced.

Temperatures need more care than the other units, because they need an offset as well as a factor. Zero degrees Celsius equals 32 degrees Fahrenheit, so simply multiplying a Celsius reading by 1.8 gives the wrong Fahrenheit figure. The correct conversion is to multiply a Celsius reading by 9/5 and then add 32. Before converting any figure, check whether the unit needs an offset as well as a factor, because a single multiplication will not do for temperature.

A direction check catches many slips. A kilometer is shorter than a mile, so a distance given in kilometers should produce a larger number than the same distance in miles. A pound is lighter than a kilogram, so a weight in pounds should be the bigger number. If your converted figure moves the wrong way, you probably multiplied when you should have divided, or the other way around.

Line up the time periods

A figure for one month cannot be compared directly with a figure for one year, or with one for a single week. Convert both to a common period, usually per day or per year, and state the assumption. Suppose one site records 3,100 visits in a 31-day month and another records 2,800 visits in a 28-day month. Both work out to 100 visits per day. The raw totals suggest a large gap that the calendar alone explains.

Weeks and months need extra care. A month is not four weeks. A year has 52 weeks and 12 months, so an average month is about 4.3 weeks long. Multiplying a weekly figure by 4 produces a monthly total that is about 8 percent too short. Partial periods also mislead. A year-to-date figure covers fewer months than a full-year figure, so setting the two side by side says little about the trend. Compare like with like, such as the same months in two different years.

Check that both figures measure the same thing

Matching units is not enough when the quantities differ. Power and energy are easy to confuse because both appear on appliance labels and energy bills. A kilowatt measures power, which is a rate. A kilowatt-hour measures energy, which is an amount: running a 1-kilowatt appliance for one hour uses one kilowatt-hour. Comparing a power rating with an energy total gives a meaningless answer.

Bits and bytes are another common source of confusion. There are 8 bits in a byte, so a connection rated at 100 megabits per second can move at most about 12.5 megabytes per second. To compare a file size given in megabytes with a speed given in megabits per second, multiply the file size by 8 first.

The word ton also varies. A metric tonne is 1,000 kilograms, about 2,205 pounds. A US short ton is 2,000 pounds, and a UK long ton is 2,240 pounds. A figure given in tons can differ by roughly 10 to 12 percent depending on which system is meant. Finally, check whether figures are gross or net, before or after tax, or include and exclude a category. Those differences can be bigger than any conversion error, and they are usually stated in a footnote that is easy to miss.

Test the converted comparison before you use it

A converted figure should pass a rough check. Round the conversion factor and see whether the answer lands in the right range. Ten miles is roughly 16 kilometers, so a result of 160 or 1.6 kilometers points to a slipped decimal point, and about 6.2 kilometers means you divided instead of multiplied. Estimates like these take seconds and catch most slips. Write the conversion factor down beside the result as well, so that anyone checking the work can repeat the step without guessing which factor was used.

Conversion also preserves order. If you convert two figures using the same factor, the larger one stays larger. If the figure that was bigger before conversion becomes the smaller one after, go back and check each step. When you write up a comparison, state the unit and the period beside each figure. A reader who can see the units can check the comparison without redoing your arithmetic, and that is the best protection against an error that nobody notices.