Beware that other symbols are sometimes used. Concentrations may be expressed as either moles per unit of volume or masses per unit of volume; to avoid confusion and ambiguity, only the former are used at this website. Quantities followed by an arrow ( ) are vectors. Where no symbol is given, there is no standard, and symbols will be defined when used. Loosely, a static variable lacks a time dimension; kinematic variables contain a time dimension and are sufficient to describe patterns of change over time but not the forces underlying them; dynamic variables complete this spectrum and are sufficient to characterize underlying forces. |
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Fundamental and Derived Quantities, Their Dimensions and Units |
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Quantity |
Symbol |
Dimensions |
SI Units |
SI Name,
|
cgs Units |
cgs Name |
Conversion Factors |
|
| Static
variables |
length | L | meter | meter, m | cm | centimeter, cm | 1 cm = 10-2 m | |
| area | S | L2 | square meter (m2) | N/A | cm2 | N/A | 1 cm2 = 10-4 m2 | |
| volume | V | L3 | cubic meter (m3) | stere, st (rare) | cm3 | N/A | 1 cm3 = 10-6 m3 | |
| mass | M | kg | kilogram, kg | g | gram | 1 g = 10-3 kg | ||
| density |  |
M L-3 | kg m-3 | N/A | g cm-3 | N/A | 1 g cm-3 = 103 kg m-3 | |
| concentration | C | N L-3 | mol m-3 | N/A | mol cm-3 | N/A | 1 mol cm-3 = 106 mol m-3 | |
| Kinematic
variables |
time | t | T | s | second, s | s | second, s | 1 s = 1 s |
| frequency | 1/t | T-1 | s-1 | Hertz, Hz | s-1 | Hertz, Hz | 1 Hz = 1 Hz | |
| velocity |
u, v, w | L T-1 | m s-1 | N/A | cm s-1 | N/A | 1 cm s-1 = 10-2 m s-1 | |
| acceleration |
L T-2 | m s-2 | N/A | cm s-2 | galileo, Gal (rare) | 1 cm s-2 = 10-2 m s-2 | ||
| kinematic viscosity |  |
L2 T-1 | m2 s-1 | N/A | cm2 s-1 | stokes, St | 1 St = 10-4 m2 s-1 | |
| diffusion coefficient | D | L2 T-1 | m2 s-1 | N/A | cm2 s-1 | NA | 1 cm2 s-1 = 10-4 m2 s-1 | |
| flux density |
J | mol T-1 L-2 | mol s-1 m-2 | N/A | mol s-1 cm-2 | N/A | 1 mol s-1 cm-2 = 104 mol s-1 m-2 | |
| Dynamic
variables |
momentum |
M L T-1 | kg m s-1 | N/A | g cm s-1 | N/A | 1 g cm s-1 = 10-5 kg m s-1 | |
| force |
F | M L T-2 | kg m s-2 | newton, N | g cm s-2 | dyne, dyn | 1 dyn = 10-5 N | |
| surface tension |  |
M T-2 | kg m-2 | N m-1 | g cm-2 | dyn cm-1 | 1 dyn cm-1 = 0.1 N m-1 | |
| dynamic viscosity |  (or  ) |
M L-1 T-1 | kg m-1 s-1 = Pa s = N s m-2 | poiseuille, Pl | g cm-1 s-1 | poise, P | 1 P = 0.1 Pa s = 1 Pl | |
| shear stress |
 |
M L-1 T-2 | kg m-1 s-2 | pascal, Pa | g cm-1 s-2 | barye, ba | 1 ba = 0.1 Pa | |
| pressure |
p,  |
M L-1 T-2 | kg m-1 s-2 | pascal, Pa | g cm-1 s-2 | barye, ba | 1 ba = 0.1 Pa | |
| work or energy | M L2 T-2 | kg m2 s-2 = N m | joule, J | g cm2 s-2 | erg | 1 erg = 10-7 J | ||
| power | M L2 T-3 | kg m2 s-3 = J s-1 | watt, W | g cm2 s-3 | N/A | 1 g cm2 s-3 = 10-7 W | ||