# Convert units by hand using the railroad tracks method

The quickest, most reliable and accurate way to do unit conversions is with a program like Uconeer, but there will be times when you do not have access to your computer, or you need to prepare a conversion factor for a custom unit that you want to add to Uconeer, and then you need to be able to calculate the unit conversion factor manually. This is sometimes confusing, but if it is approached with a logical procedure like the Railroad Tracks Method it becomes very easy. This method of converting units is often called the Factor Label method by scientists - but engineers prefer trains!

Method:

Draw up a set of "Railroad Tracks" with the original value in the top "row" of the first "column" and the original units in the top or bottom row of this column just the way you would normally put them above or below the line. Then write each conversion factor into the following columns in such a way that the units cancel out - leaving the units you want. Note that each time you add a conversion factor you are actually multiplying by 1.0 because the top and bottom are equal - just in different units. Then multiply or divide all the conversion factors depending on whether they are above or below the line. This is best described with a few examples.

Example 1:
Convert 5 ft into inches

Conversion factors available:
12 inch = 1 ft

We put the 5 ft on the top row in the first column, and then enter the "12 inch / 1 ft" in the second column in such a way that the ft cancel each other out. Multiply the 5 by 12 giving the answer of 60 inches.

Example 2:
Convert 42 inches to ft

Conversion factors available:
12 inch = 1 ft

This time the "12 inch / 1 ft" is entered with the "12 inch" on the bottom row so that the inch cancels with the original inch. Answer now is 42 / 12 = 3.50 ft

Example 3:
Convert 42 inches to ft

Conversion factors available:
1 inch = 0.08333 ft

This is identical to Example 2, except that the conversion factor is given for 1 inch rather than 1 ft. The same method is used and the answer is still the same but calculated as 42 x 0.08333 = 3.50 ft

Example 4:
Convert 1.5 Btu/lb.ºF to cal/gram.ºC

Conversion factors available:
1 Btu = 252 calorie
1 lb = 453.6 gram
1 ºC = 1.8 ºF (NB this is a temperature DIFFERENCE)

Answer is 1.5 x 252 x 1.8 / 453.6 = 1.5 calorie / gram. ºC

Example 5:
Convert 5000 ft³/minute to m³/second
(This example demonstrates the use of units raised to a power)

Conversion factors available:
1 ft = 0.3048 m
1 minute = 60 seconds

Answer is 5000 x 0.02832 / 60 = 2.36 m³/s

Generating Conversion Factors:

If you have to convert many values between two sets of units then it is more efficient to generate a new combined conversion factor than to lay out the railroad tracks with the individual conversion factors each time. To do this you simply use 1.0 as your starting number. For example if you had to do many conversions from ft³/minute to m³/second (as in Example 5 above) you would use 1.0 ft³/minute in place of the 5000 to get a new conversion factor of 1.0 ft³/minute = 0.000472 m³/second.

To make it absolutely clear how this works, the combined conversion factor can be illustrated using the same data as in Example 5.

Example 6:
Convert 5000 ft³/minute to m³/second
(This example demonstrates the use of combined conversion factors)

Conversion factors available:
1.0 ft³/minute = 0.000472 m³/second

Answer is 5000 x 0.000472 = 2.36 m³/s

This shows that any value in ft³/minute can be converted to m³/second by multiplying by 0.000472. If you are ever confused by whether you should multiply or divide by the conversion factor a quick sketch of the railroad tracks makes it obvious.

Example 7:
Convert 3.5 yards to mm
(This example demonstrates the use of chained conversion factors)

Conversion factors available:
1.0 yard = 3.0 ft
1.0 ft = 12.0 inch
1.0 inch = 25.4 mm

Answer is 3.5 x 3 x 12 x 25.4 = 3200.4 mm

This technique is useful when you do not have the overall conversion factor required, but you can break the conversion down into steps where you do have the conversion factors for each step. A similar example would be converting days to seconds. In this case you would chain together the conversion factors for days to hours, hours to minutes and finally minutes to seconds.