Unit Analysis - Definition and Examples


Unit analysis, also called dimensional analysis, is the process of converting from one unit to another, such as converting minutes to hours, feet to miles, meters to centimeters, and so forth.

A couple of examples showing how to perform unit analysis

mile = mi, seconds = s, feet = ft, minutes = min, kilometers = km, and hours = h

Example #1:

Convert 8 miles per 8 minutes to kilometers per hours

We need to convert minutes to hours and miles to kilometers.

(8 mi / 8 min) × (60 min / 1 h ) × (1.61 km / 1 mi) 

We mark in green units that will cancel or disappear. Each unit disappears because the unit is in the numerator and in the denominator at the same time.

(8 mi / 8 min) × (60 min / 1 h ) × (1.61 km / 1 mi

We get (8 × 60 × 1.61 km) / ( 8 × 1 h × 1)

Finally, we get (772.8 km) / (8 h) = 96.6 km / h 


Example #2:

A cheetah ran 400 feet in 3.90 seconds. What was the cheetah's average speed in miles per hour?

We need to convert feet to miles and seconds to hours.

(400 ft / 3.90 s) × (1 mi / 5280 ft) × (60 s / 1 min) × (60 min / 1 h) 

We mark in green units that will cancel or disappear. Again, each unit disappears because the unit is in the numerator and in the denominator at the same time.

(400 ft / 3.90 s) × (1 mi / 5280 ft) × (60 s / 1 min) × (60 min / 1 h) 

We get (400 × 1 mi × 60 × 60) / (3.90 × 5280 × 1 × 1 h)

The average speed in miles per hours is 1440000 mi / 20592 h = 69.9 m/h

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