Unit Conversions

Basic Units
Derived Units
Worked Examples
Approximate Conversions to Memorize
Getting the Feel of Conversions
Online Conversion Calculator

Basic Units

In mechanics there are only three basic units:  length, mass and time.  US Customary units are based on feet (or inches), pounds, and seconds (or hours).  MKS, or SI units are based on meters (m), kilograms (kg) , and seconds (s).  Pounds are used for both mass (a basic quantity, sometimes written as lbm) and force (a derived quantity, sometimes written as lbf).  Under earth gravity 1 lbm weighs 1 lbf


U.S. Customary Units

MKS Unit Equivalent


1 lbm

2.204 lbm

0.4536 kg

1 kg


1 in.

39.37 in.

1 ft.

3.281 ft.

0.0254 m

1 m

0.3048 m

1 m

Back to top

Derived Units

Derived units include force, velocity, stress or pressure, energy, power, volume and others.  Here are just a few that you will need for the torsion lab.  You can find further examples in standard mechanics textbooks. 


U.S. Customary Units

MKS Unit Equivalent


1 lbf

0.2248 lbf

4.448 N

1 N

Stress or Pressure

1 lb/in2 = 1 psi

0.0001450 psi

1000 lb/in2 = 1 ksi

0.1450 ksi

6895. N/m2 = 6895. Pa

1 Pa

6 895 000 Pa = 6.895 MPa

1 MPa


1 lbf-in

8.850 lbf-in

0.1130 N-m

1 N-m

Back to top

Worked Examples

Elastic Modulus

The elastic modulus, E, of 2024 aluminum alloy is approximately .  What is E in MKS units? 

Using the basic units and expressing the unit MKS values in terms of their US equivalents:

This example could also be done using the derived units,


What is the weight, in lbf of a circular PMMA (plexiglass) cylinder, 15 mm diameter and 130 mm long?

You need to know the density of PMMA.  It is approximately 1.2 g/cm3. 

Mass=volume x density=

Mass in US units=

Weight in US units equals the mass in US units, so the weight is 0.068 lbf.

Back to top

Approximate Conversions to Memorize

You can approximate most unit conversions in your head if you can recall a few basic results.  Here are a few numbers you should know:

1 kg approx.2 lbm

1 kg mass weighs about 10 N, thus 2 lbf approx. 10 N, or 1 lbf approx. 5 N.

1 inch approx. 25 mm

1 m approx. 40 inches

1 ksi approx. 7 MPa

1 N-m approx. 10 lbf-in

Back to top

Getting the Feel of Conversions

Knowing the approximate value of important engineering constants and material properties will also help you become more comfortable with working with both US and MKS units.  Here are some commonly used quantities:


Value in U.S. Customary Units

Value in MKS Units

Elastic Modulus of Aluminum

Elastic Modulus of Steel

Elastic Modulus of PMMA

420 ksi

2.9 GPa

Yield stress of low strength steel

345 MPa

Yield stress of very high strength steel

A pencil diameter

0.3 in

7.6 mm=.0076 m

Paper clip diameter

.032 in (or 32/1000 in)

.8 mm

Weight of a small car

2250 lbf

10 000 N = 10 kN

Back to top