Help with Xfactor

What's it for?

Dimensional analysis or factor-label method is a process for converting known information into desired units, by multiplying or dividing value+unit terms until all units except the desired ones have canceled out, by appearing in both the numerator and denominator (top and bottom) of the equation. It can be used for simple units conversion (how many minutes in a day?) or complicated word problems (see Examples). It can also verify that a formula is dimensionally correct. Factor-label conversions commonly come up in chemistry, engineering, and programming tasks.

How's it work?

Start by entering the desired units on the left-hand side. Then add known information on the right-hand side as units or value units (separated by a space), so that intermediate units cancel out. To add another term, click on the last (gray) X. To remove an unwanted term, click on the preceding (black) X. If you entered a term upside-down, just click on the divider line to flip it around.

As you enter information, Javascript code scans the formula and checks for any units that cancel out, showing them in green. It also accumulates the numeric terms. Once the remaining units match on the left and right side, the equals signs change from red to green indicating that the final answer has been reached.

How do I...

• ... use compound units? Everything after the last space is considered a unit. We suggest you hyphenate compound units, e.g. "foot-lbs", or use abbreviations, e.g. "Nm", but the important thing is just to be consistent so the automatic matching will work.

• ... include variables? You can include symbolic variables in the terms, with or without numbers, before the last space separating the value from the units. These variables are carried into the final result, to give you a simplified conversion formula rather than a simple number. See example 2.