Atmospheric Pressure (P_atm):

It is pressure exerted by atmospheric air on any surface. It can be measured by a barometer. The standard values of it are;

1 P_atm = 760 mm of Hg that is column or height of mercury

=   .g.h. = 13.6 × 10³  × 9.81 × 760/1000

= 101.325 kN/m²  = 101.325 kPa

= 1.01325 bar

when density of mercury is taken as 13.595 kg/m3  and acceleration because of gravity as 9.8066 m/s²

Gauge Pressure (P_gauge):

It is the pressure of fluid contained in closed vessel. It is always greater than atmospheric pressure. It is measured by an instrument called as pressure gauge (like Bourden's pressure gauge). The gauge measures pressure of fluid (liquid and gas) flowing through pipe or duct, boiler etc. irrespective of atmospheric pressure.