5.0 Conversion of units

  Unit and Dimensions

A particular physical quantity can be represented in the different system of units. Thus it is important to know their interconversion from one system to another.

Conversion of length

The SI unit of length is metre.

$1\,m = 100\,cm$
$1\,km = 1000\,m$
$1\,km = 0.6215\,mi$
$1\,mi = 1.609\,km$
$1\,m = 1.0936\,yd = 3.281\,ft = 39.37\,in$
$1\,in = 2.54\,cm$
$1\,ft = 12\,in = 30.48\,cm$
$1\,yd = 3\,ft = 91.44\,cm$
$1\,\mathop {\rm A}\limits^{\text{o}} =10^{-10}\ m$

Conversion of mass

The SI unit of mass is kilogram.

$1$ quintal $=\ 10^2\ kg\ =\ 100\ kg$
$1$ Tonne $(t)\ =\ 10^3\ kg\ =\ 1000\ kg$
Milligram $(mg)\ =\ 10^{-6}\ kg\ =\ 10^{-3}\ g$
Microgram $(\mu g)\ =\ 10^{-9}\ kg\ =\ 10^{-6}\ g$
$1$ slug $=\ 14.59\ kg$
$1$ u $=\ 931.50\ MeV/c^2$

Conversion of time

The SI unit of time is second.

$1$ min $=\ 60\ s$
$1\ h=\ 60\ min\ =\ 3.6\ ks$
$1$ d $=\ 24\ h\ =\ 1440\ min\ =\ 86.4\ ks$
$1$ y $=\ 365.25\ d$
$1$ decisecond $=\ 10^{-1}\ s\ =\ 0.1\ s$
$1$ centisecond $=\ 10^{-2}\ s\ =\ 0.01\ s$
$1$ millisecond $=\ 10^{-3}\ s\ =\ 0.001\ s$
$1$ microsecond $=\ 10^{-6}\ s\ =\ 0.000001\ s$

Conversion of pressure

$1$ Pa $=\ 1\ N \ m^{-2}$
$1$ bar $=\ 100\ kPa$
$1$ atm $=\ 101.325\ kPa\ =\ 1.01325\ bar$
$1$ atm $=\ 14.7\ lbf\ in^{-2}\ =\ 760\ mm\ Hg$
$1\ lbf\ in^{-2}\ =\ 6.895\ kPa$
$1$ torr $=\ 1\ mm\ Hg\ =\ 133.32\ Pa$

Conversion of energy

$1\ kWh\ =\ 3.6\ MJ$
$1\ cal\ =\ 4.186\ J$
$1\ ft\ lbf\ =\ 1.356\ J\ =\ 1.286 \times 10^{-3}\ Btu$
$1\ L\ atm\ =\ 101.325\ J$
$1\ L\ atm\ =\ 24.217\ cal$
$1\ Btu\ =\ 252\ cal\ =\ 1054.35\ J$
$1\ eV\ =\ 1.602 \times 10^{-19}\ J$
$1\ u\ c\ =\ 931.50\ MeV$
$1\ erg\ =\ 10^{-7}\ J$

Note: $1\ Btu:$ British thermal unit

Conversion of force

$1\ N\ =\ 0.2248\ lbf\ =\ 10^5\ dyn$
$1\ lbf\ =\ 4.4482\ N$
$1\ kgf\ =\ 2.2046\ lbf$

Conversion of power

$1\ W\ =\ 1\ J/s$
$1\ hp\ =\ 745.7\ W$
$1\ Btu\ \min ^{-1}\ =\ 17.58\ W$
$1\ W\ =\ 1.341 \times \ 10^{-3}\ hp$

Conversion of magnetic field

$1\ G\ =\ 10^{-4}\ T$
$1\ T\ =\ 1\ Wb\ m^{-2}\ =\ 10^4\ G$