Pascal
SI derived unit · quantity: pressure, mechanical stress
01 · Definition
The pressure produced by a force of one newton spread evenly over a square metre. The unit is tiny: the atmosphere around us is a hundred thousand pascals.
The smallness of the pascal is not a flaw but a consequence of building the system honestly: it is assembled from the newton and the metre with no fudge factors. Practice gets by with prefixes — hectopascals in the weather report, kilopascals in ventilation, megapascals in hydraulics, gigapascals in materials science. The essential property of the quantity lies elsewhere: pressure depends not on the force but on the area that force lands on. The same woman dents a parquet floor in stilettos and leaves no mark in trainers, because the bearing area differs two hundredfold.
In a liquid at rest, pressure is transmitted equally in every direction — this is what Pascal himself discovered. Hence the hydraulic press: a hand pushes the small piston, and on the large one the same pressure, multiplied by the greater area, yields a force tens of times larger. The car jack, the brakes and every press live by this rule, which also explains why the pressure at the bottom of a vessel depends only on the height of the column and not on whether the vessel is narrow or wide.
02 · Conversion
Pascals, bars, atmospheres, millimetres of mercury
No trade uses the bare pascal: meteorology counts in hectopascals, tyre people in bars, doctors in millimetres of mercury, American engineering in pounds per square inch.
The standard atmosphere is defined as exactly a hundred and one thousand three hundred and twenty-five pascals — the pressure of a mercury column seven hundred and sixty millimetres high at zero degrees and standard gravitational acceleration. The technical atmosphere is another thing: the kilogram-force per square centimetre, ninety-eight thousand and sixty-six and a half pascals. The difference is three per cent, and old Soviet equipment data plates carry both.
| Unit | Name | Value | Where it is met |
|---|---|---|---|
| Pa | pascal, the SI unit | 101325 | physics calculations |
| hPa | hectopascal | 1013 | weather report |
| kPa | kilopascal | 101.33 | ventilation, medicine |
| MPa | megapascal | 0.1013 | hydraulics, strength |
| GPa | gigapascal | 1.013·10⁻⁴ | elastic modulus of materials |
| N/m² | newton per square metre | 101325 | the same as the pascal |
| bar | bar | 1.01 | engineering, meteorology before the SI |
| atm | standard atmosphere | 1 | chemistry, reference conditions |
| at | technical atmosphere, kgf/cm² | 1.03 | Soviet equipment data plates |
| mmHg | millimetre of mercury, the torr | 760 | medicine, vacuum technology |
| psi | pound per square inch | 14.7 | English-language engineering |
| Ba | barye, the CGS system | 1013250 | acoustics and physics before the SI |
The newton per square metre and the pascal are one and the same, differing only in notation. The hectopascal is numerically equal to the millibar, so the switch of meteorologists to the SI required no change to the familiar figures
03 · Orders of magnitude
from accelerator vacuum to the interior of the SunA hundred and one thousand three hundred and twenty-five — the atmosphere at sea level
04 · Measuring instruments
What pressure is measured with
A hollow tube of oval section, coiled into an arc, tends to straighten under pressure, and that movement is passed to the needle through a linkage. Invented in 1849 and hardly changed since: it is exactly what sits on every compressor and gas cylinder.
A corrugated capsule with the air pumped out contracts and expands with the atmosphere; a spring keeps it from collapsing. An instrument without a single drop of mercury — hence the name aneroid, meaning without liquid.
A diaphragm etched in silicon deflects by microns, and the resistors built into it change their resistance. Such sensors sit in a phone, a car and a weather station, and they cost less than a dial gauge.
At low pressures a diaphragm can no longer be deflected, so the measurement goes another way: by the heat carried off a hot filament. The thinner the gas, the worse it removes heat, and the heating power tells the pressure down to thousandths of a pascal.
05 · Writing rules
Capital P, lowercase a
The symbol comes from a surname and therefore starts with a capital, with a lowercase second letter: Pa. The prefix is written closed up without a space, kilo in lowercase, mega and giga in capitals: kPa, MPa, GPa. The Russian symbol is Па.
A lowercase m means milli, so megapascals written as mPa turn into millipascals — an error by a factor of a billion. The third example is incomplete: engineering almost always quotes gauge pressure, counted from the atmosphere, and without a note the figure is ambiguous. Absolute pressure is marked with the letter a and gauge pressure with g, which in English-language documentation looks like psia and psig.
06 · Neighbouring units
The bar is handy for being close to the atmosphere, the atmosphere is tied to a mercury column, and the pascal is the only one derived from the system without adjustment.
a hundred thousand pascals
newton per metre²
760 mm of mercury
In the neighbouring Simetrium passports: newton, out of which the pascal is built, bar and atmosphere as non-SI units serving the same purpose, psi for English-language engineering, and millimetre of mercury for medicine.
07 · Historical section
How air was found to have weight
A pupil of Galileo sealed a tube of mercury and upended it into a dish: the column fell to seven hundred and sixty millimetres and stopped. Above it remained a void that science had until then held to be impossible.
Blaise Pascal asked his brother-in-law to carry a barometer to the summit of a volcano in Auvergne. The mercury column fell by eight centimetres: the air above the mountain presses less than above the valley, and so the atmosphere has weight.
Engineers counted in kilograms-force per square centimetre, meteorologists brought in the bar and the millibar, doctors stayed with millimetres of mercury. The same gauge carried different scales in different countries.
The Fourteenth General Conference gave the unit a name of its own, although it had existed in the system since 1960. Meteorologists moved to hectopascals painlessly: the hectopascal is numerically equal to the millibar.
Absolute, gauge, and what the instrument actually shows
Almost every gauge measures not pressure but a difference: inside the tube against outside. That is why a flat tyre reads zero although there is air in it, and a household blood-pressure monitor gives a hundred and twenty millimetres on top of the atmospheric seven hundred and sixty. Absolute pressure is obtained by adding the atmospheric value, and it is absolute pressure that enters the gas equations — confusing the two references remains the commonest error in thermal calculations. A separate subtlety concerns the mercury column: its height depends on the density of mercury, and that depends on temperature, so the definition stipulates zero degrees and standard gravitational acceleration. Medicine neglects this correction; metrology does not, and primary pressure standards today are built not on mercury but on deadweight testers, where the pressure is set by weights of known mass on a piston of precisely measured area.
Catalogue · units of measurement
A passport for every quantity
Seven SI base units, twenty-two derived units with names of their own, and the non-SI units without which neither engineering nor everyday life gets by. Each has its own sheet: definition, conversion, instruments, writing rules. In 19 languages.
SI derived units with names of their own
the pascal passport is openSI base units
in terracotta — the kilogram, metre and second, out of which the pascal is assembledNon-SI units
in terracotta — pressure units of other systemsPassport language
19 languages. The symbol Pa is international, but the everyday unit differs: hectopascals in the European weather report, inches of mercury in the American one, millimetres of mercury in the Russian.