Conversion from Micropascals to Decipascals

Information about the Micropascal (µPa)

The micropascal is a unit of pressure equal to one millionth of a pascal. Its symbol is µPa. It is one of the smallest pressure units in practical use, and it owes its place to a single number: 20 micropascals, the reference pressure against which every sound level in air is measured.

That figure is the threshold of hearing — roughly the quietest sound a healthy young ear can detect at a frequency of about 1,000 hertz. When acousticians defined the decibel scale for airborne sound they needed a fixed pressure to compare against, and they chose that threshold. Zero decibels means a sound pressure of 20 micropascals; every decibel figure quoted for a road, a machine or a concert is a ratio to that number.

The scale that follows is steep. Twenty decibels is ten times the reference pressure, 200 micropascals. Sixty decibels, ordinary conversation, is a thousand times it, or 20 millipascals. A hundred and twenty decibels, the threshold of pain, is a million times it: 20 pascals. The ear covers a range of a million to one in pressure, and the micropascal sits at the bottom of it.

Underwater acoustics uses the same unit but a different reference. Sound in water is referred to 1 micropascal rather than 20, because the threshold of human hearing is meaningless in the sea. That difference matters enormously: a level quoted in decibels underwater is not comparable to one in air, and the gap between the two conventions is about 26 decibels before any other correction. Sonar figures, whale-song measurements and shipping-noise studies all carry the re 1 µPa qualifier for that reason.

Outside acoustics the micropascal appears in vacuum science. A good high vacuum is around 100 micropascals, and ultra-high vacuum, the regime used for surface physics and particle accelerators, runs from a few micropascals down to nanopascals. Pumping a chamber to that level takes hours of baking to drive adsorbed gas off the walls.

The unit also shows up in radiation pressure and in the very small pressure differences that laboratory instruments resolve. Anything measured in micropascals is a measurement rather than a force anyone would feel, which is exactly what makes the reference-level convention so useful.

One micropascal equals 0.000001 pascals, 0.001 millipascals, 1,000 nanopascals, or about 0.000000000145 pounds per square inch.

Information about the Decipascal (dPa)

The decipascal is a unit of pressure equal to one tenth of a pascal. Its symbol is dPa. It belongs to the group of metric prefixes that exist because the system is regular rather than because anyone asked for them: deci, centi, deca and hecto fill the gaps between the thousand-step prefixes, and of those four only hecto found a permanent home in pressure, in the hectopascal of weather reports.

That regularity is the point of the metric system rather than an accident of it. Every prefix from yocto to yotta applies to every unit, so the decipascal is defined whether or not anyone writes it. The alternative would be a system in which some combinations are legal and others are not, and users would then have to memorise a table of exceptions instead of a single rule.

In practice pressure work skips from the pascal to the hectopascal or kilopascal, and the four intermediate prefixes go unused. There is a reason for that beyond habit. The thousand-step prefixes — milli, kilo, mega — line up with how numbers are grouped in writing, so a value in kilopascals is read off a value in pascals by moving the digit grouping, not by counting decimal places. Deci and centi break that alignment.

The decipascal does have a natural size, though. A tenth of a pascal is roughly the pressure of a single sheet of thin paper laid on a table, or the difference in air pressure over about a centimetre of height. It is the pressure a moth exerts on a windowpane, and about a hundredth of the pressure difference across a closed interior door in a ventilated building.

Where such pressures need writing down, the convention is to use the pascal with a decimal: an anemometer calibration might record 0.4 pascals rather than 4 decipascals, and a ventilation specification 50 pascals rather than 500 decipascals. The number is the same and the pascal keeps the page consistent with every other reading.

The unit is still perfectly valid, and a converter has to handle it, because it turns up in older instrument manuals, in occasional national standards, and wherever an author has decided that a figure reads better with one digit before the point than with three after it.

One decipascal equals 0.1 pascals, 100 millipascals, 0.001 hectopascals, or about 0.0000145 pounds per square inch.