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

This is an AMP page - Open full page! for all features.

Unit Factor Method

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

Sponsored Links

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

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

Sponsored Links

Related Topics

Related Documents

Sponsored Links

Share

Search Engineering ToolBox

  • the most efficient way to navigate the 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 Extension Warehouse!

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.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.

Topics

Unit Converters

Temperature

oC
oF


Load Calculator!

Length

m
km
in
ft
yards
miles
naut miles


Load Calculator!

Area

m2
km2
in2
ft2
miles2
acres


Load Calculator!

Volume

m3
liters
in3
ft3
us gal


Load Calculator!

Weight

kgf
N
lbf


Load Calculator!

Velocity

m/s
km/h
ft/min
ft/s
mph
knots


Load Calculator!

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O


Load Calculator!

Flow

m3/s
m3/h
US gpm
cfm


Load Calculator!

6 24

This website use cookies. By continuing to browse you are agreeing to our use of cookies! Learn more