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

Recent math words

  1. What is an abacus? Definition and Chinese Abacus

    Jan 18, 22 08:00 AM

    What is an abacus? Learn quickly and easily to use an abacus to do math.

    Read More

  2. Width of an Object

    Jan 17, 22 09:15 AM

    What is the width of an object? Definition, explanation, and easy to understand real life examples.

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.
Share this page: