Dimensions, Units, Conversion Factors, and Significant Digits
Primary Dimension 
Symbol 
SI unit 
BG unit 
English unit 
mass 
m (sometimes M) 
kg (kilogram) 
slug 
lbm (poundmass) 
length 
L (sometimes l) 
m (meter) 
ft (foot) 
ft (foot) 
time 
t (sometimes T) 
s (second) 
s (second) 
s (second) 
temperature 
T (sometimes q ) 
K (Kelvin) 
^{oR (degree Rankine)} 
R (Rankine) 
electric current 
I (sometimes i) 
A (ampere) 
A (ampere) 
A (ampere) 
amount of light 
C (sometimes I) 
c (candela) 
c (candela) 
c (candela) 
amount of matter 
n or N (sometimes ) 
mol (mole) 
mol (mole) 
mol (mole) 
Secondary Dimension 
Symbol 
SI unit 
BG unit 
English unit 
force 
F (sometimes f) 
N (Newton = kg× m/s^{2}) 
lbf (poundforce) 
lbf (poundforce) 
acceleration 
a 
m/s^{2} 
ft/s^{2} 
ft/s^{2} 
pressure 
p or P 
N/m^{2}, i.e. Pa (Pascal) 
lbf/ft^{2} (psf) 
lbf/in^{2} (psi) (note: 1 ft = 12 in) 
energy 
E (sometimes e) 
J (Joule = N× m) 
ft× lbf (foot pound) 
ft× lbf (foot pound) 
power 
P 
W (watt = J/s) 
ft× lbf/s 
ft× lbf/s 
Relationship 
Newton’s second law, F = m a. [Note: Bold notation indicates a vector.] By definition of the fundamental units, this yields 1 N = 1 kg× m/s^{2}. 

Conversion 
 
Discussion 
The above expression is dimensionless and has a value of 1. Thus it is the conversion factor with which to multiply or divide any equation to simplify the units. 

Example 
How much force (in Newtons) is required to accelerate a mass of 13.3 kg at a constant acceleration of 1.20 m/s^{2}? 

Terminology 
It is not proper to say that 1.00 kg equals 9.81 N, but it is proper to say that 1.00 kg weighs 9.81 N under standard earth gravity. This is obtained by utilizing Newton’s second law with gravitational acceleration, i.e. 
Relationship 
Newton’s second law, F = m a. [Note: Bold notation indicates a vector.] By definition of the fundamental units, this yields 1 lbf = 1 slug× ft/s^{2}, or 1 lbf = 32.174 lbm× ft/s^{2}. 
Conversion 
or or 
Discussion 
The above expressions are dimensionless and each has a value of 1. Thus any of them can be considered a conversion factor with which to multiply or divide any equation to simplify the units. 
Example 
How much force (in lbf) is required to accelerate a mass of 13.3 lbm at a constant acceleration of 1.20 ft/s^{2}? 
Terminology 
It is not proper to say that one lbm equals one lbf, but it is proper to say that one lbm weighs one lbf under standard earth gravity. This is obtained by utilizing Newton’s second law with gravitational acceleration, i.e. 