How to Solve Problems Using Dimensional Analysis
Dimensional analysis is a process that uses conversions to solve problems. There are several points to remember
when solving problems using this method:
1. The conversion ratios must equal one, and can be written with either value on top:
Example: 1 km = 1000 m 1 km = 1 or 1000 m = 1
1000 m 1 km
2. Conversions are often written using the word per. These can be re-written as ratios:
Example: 1000 m per km 1 km = 1 or 1000 m = 1
1000 m 1 km
3. Most important rules to remember:
Set up your conversion ratio to cancel out the original unit and convert to the desired unit. This means if
the unit you are converting from is in the numerator, the conversion ratio should be set up with this unit in the
denominator. This will cancel out the unit you are converting. Keep doing this until you get to units you want for
your answer.
Always label units for each step. This will help ensure you do not make mistakes.
Cross out units that have been canceled out and make sure that your final answer has been correctly
converted to the new unit.
4. Solve by multiplying all the numbers in the numerators of the ratios and then dividing by all the numbers in the
denominator of the ratios.
Example: How many miles has a person run if he runs a 5 km race?
Conversion factors: 1 km = 0.62 mi
Answer: 5 km x 0.62 mi = 3.1 mi
1 km
Example: How many kilometers per liter will a car get if it gets 30 mi/gal?
Conversion factors: 1 km = 0.62 mi , 1 liter = 0.26 gallons
Answer: 30 mi x 1 km x 0.26 gal = 12.6 km
gal 0.62 mi 1 L L
Continued
