Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Unit Factor Method

Convert between units with the unit factor or factor-label method

Unit Factor Method

Unit converting from one system to an other can be done with the unit factor method - also called dimensional analysis.

The relationship between two different units can be expressed as

$$1 (u_1) = x (u_2) \tag{1}$$

where

u1 = unit 1

u2 = unit 2

x = converting factor from u2 to u1

Example - inches vs. mm

$$1 (in) = 25.4 (mm)$$

Dividing the relationship (1) with the two sides - two unit factors for the relationship can be expressed as

$$\frac {1 (u_1) }{ x (u_2)} = 1 \tag{2}$$

$$\frac {x (u_2) }{ 1 (u_1)} = 1 \tag{3}$$

Example - inches vs. mm

$$\frac {1 (in) }{ 25.4 (mm)} = 1$$

$$\frac {25.4 (mm) }{ 1 (in)} = 1$$

Converting a value from one unit to an other can then simply by done by multiplying both sides of eq. 2 or 3 with the value.

$$\frac {1 (u_1) \ a (u_2)}{ x (u_2)} = a (u_2) \tag{2a}$$

$$\frac {x (u_2) \ b (u_1)}{ 1 (u_1)} = b (u_1) \tag{3a}$$

Example - Converting 10 mm to inches

$$\frac {1 (in) \ 10 (mm)}{ 25.4 (mm)} = 10 (mm)$$

$$0.39 (in) = 10 (mm)$$

Factor-label Method

The factor-label method is an sequential combination of conversion factors where numerator and denominator of the conversion factor fractions can be cancelled out to achieve a desired set of dimensional units.

$$\frac {1 (u_1) }{ x (u_2)} \ \frac {y (u_2) }{ 1 (u_3)} \ \frac {1 (u_3) }{ z (u_4)} = \frac {y (u_1) }{ x z (u_4)} \tag{4}$$

Example - Converting 2.5 feet to mm

Th unit factor for mm to feet can be calculated using eq. 4 as:

$$\frac {25.4 (mm) }{ 1 (in)} \ \frac {12 (in) }{ 1 (ft)} = 304.8 (\frac {mm}{ft})$$

10 mm can be converted to feet as

$$308.5 (mm/ft) \ 2.5 (ft) = \underline{771.3} (mm)$$

Related Topics

• Basics - The SI-system, unit converters, physical constants, drawing scales and more.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

Translate

Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Citation

• Engineering ToolBox, (2022). Unit Factor Method . [online] Available at: https://www.engineeringtoolbox.com/unit-factor-converting-method-d_2196.html [Accessed Day Mo. Year].

Modify access date.

. .

close

6 24