Pascals to Atmospheres

Depth, Density and the Weight of the Rock Above

Every rock sample carries a pressure story. Lithostatic pressure is simply the weight of the column standing on it — density times gravity times depth — and it comes out of that calculation in pascals, because those are the units the density and the gravity were in. Turning the result into atmospheres is what makes it human: a number you can compare to sea-level air pressure, to a laboratory cell, or to the bar and kilobar figures printed in older papers.

Conversion factor: 1 Pa = 9.8692327 × 10⁻⁶ atm, which is the same as dividing by 101 325. One kilometre of average continental crust (ρ ≈ 2 700 kg/m³, g = 9.81 m/s²) presses down with 26 487 000 Pa — that is 26.5 MPa, or roughly 261 atm.

Why Earth Scientists Keep Both Units in View

The lithostatic gradient

Crustal rock adds roughly 26 to 27 MPa for every kilometre of burial, so depth and pressure are effectively the same axis once you fix a density for the column.

Metamorphic pressure–temperature paths

Facies diagrams put GPa on the vertical axis and degrees on the horizontal, because a mineral assemblage records the pressure the rock passed through, not the depth it was mapped at.

A planet-wide pressure ladder

From the base of the crust to the centre of the core the figure climbs by five and a half orders of magnitude, which is why seismic reference models tabulate it depth by depth.

Reproducing it in the laboratory

Piston-cylinder rigs reach a few GPa, multi-anvil presses tens of GPa, and a diamond anvil cell can push past the pressure at Earth's centre — all quoted in GPa, all convertible to atmospheres.

From a Field Number to a Pressure You Can Plot

The calculation stays in SI from start to finish, and the conversion happens only at the moment you need to talk to someone using a different unit.

Work out ρgh and keep it in pascals

Multiply the column density in kg/m³ by 9.81 and by depth in metres. Nothing needs rescaling along the way — the answer is already in pascals, however awkwardly long it looks.

Paste the figure into the pascal field

The atmosphere value builds up beside it while you type. Long strings are forgiving here: a decimal comma is accepted like a dot, and spaces used as digit grouping are simply ignored.

Take the clean number into your notes

Copying from either field puts the bare digits on the clipboard, without a unit tagged on the end and without the thousands spacing — the form a spreadsheet column or a plotting script will read without complaint.

Reverse it for a value quoted in atmospheres

Older experimental petrology is full of pressures in atmospheres and bars. The swap control (↔) turns the page into atm → Pa, where the multiplier is 101 325: 5 000 atm becomes 506 625 000 Pa, just over half a gigapascal.

Say which density you assumed: the same depth gives noticeably different pressures for a sedimentary pile at 2 400 kg/m³ and a mafic lower crust at 2 950 kg/m³. Depth converted to pressure is only as good as the column model behind it.

Pressure at Depth Inside the Earth

Reference points from the deepest workings humans have cut to the centre of the planet, with each pressure written in pascals (using the convenient prefix) and in standard atmospheres.

Level	Depth	Pressure (Pa)	Pressure (atm)
Deepest working mine level	≈ 4 km	106 MPa	≈ 1 046 atm
Kola Superdeep Borehole, bottom	12.26 km	325 MPa	≈ 3 207 atm
Base of continental crust (Moho)	≈ 35 km	1.0 GPa	≈ 9 869 atm
Diamond stability field, cratonic root	≈ 150 km	5.0 GPa	≈ 49 346 atm
410 km seismic discontinuity	410 km	13.4 GPa	≈ 132 250 atm
660 km discontinuity, base of the transition zone	660 km	23.8 GPa	≈ 234 890 atm
Core–mantle boundary	2 891 km	136 GPa	≈ 1 342 000 atm
Inner-core boundary	5 150 km	329 GPa	≈ 3 247 000 atm
Centre of the Earth	6 371 km	364 GPa	≈ 3 592 000 atm

The shallow rows come straight from ρgh; the deep ones come from seismic reference models, where density is derived from wave speeds rather than assumed. Notice how quickly the atmosphere column loses its usefulness — by the core–mantle boundary the number runs to seven digits, which is precisely why the deep-Earth literature settled on gigapascals.

Handling Numbers of This Size

Feed it the raw ρgh product

There is no need to round to a tidy MPa first — enter the full pascal figure your calculation produced and let the atmosphere value follow it digit for digit.

Mantle-scale figures stay readable

Thousands are separated by a space, and anything from ten billion pascals upward is shown in scientific notation, so 136 GPa does not arrive as an unbroken wall of zeros.

Kilobars are one dropdown away

The searchable unit lists on both sides cover 26 pressure units in eight groups, so a pressure from an older paper can be restated in bar or in modern SI without a second tool.

Run the pair either way round

The swap control reverses the direction whenever the source quotes atmospheres, which is common in experimental work published before SI became standard.

Questions About Pressure in the Crust and Mantle

How much does pressure increase for each kilometre of burial?

For average continental crust at about 2 700 kg/m³, roughly 26.5 MPa per kilometre, or a little over 260 atm per kilometre. The rule of thumb most petrologists carry is that 1 GPa corresponds to something near 35 km of crustal burial. Denser lower crust and mantle rock steepen the gradient, so the relationship is not a straight line all the way down.

What is the difference between lithostatic and pore-fluid pressure at the same depth?

Lithostatic pressure counts the whole rock column; pore-fluid pressure counts only the connected water in the pore space, so it climbs at roughly 9.8 MPa per kilometre — about 97 atm per kilometre — against the rock's 26.5. Where fluid cannot escape as fast as burial compacts the sediment, pore pressure drifts above that fluid line towards the lithostatic value. That gap is what drilling engineers call overpressure, and it is why the two gradients are always plotted together.

Why do petrologists plot metamorphic conditions in GPa instead of atmospheres?

Because the interesting range fits neatly into single digits. Blueschist assemblages sit near 0.6 to 1.2 GPa, eclogite above roughly 1.5, and ultrahigh-pressure rocks that carry coesite start around 2.7 GPa. In atmospheres those become 6 000, 15 000 and 27 000 — harder to read and harder to compare with the thermodynamic data the phase diagrams are built from, which is tabulated in SI.

What pressure does diamond need in order to be stable?

The graphite–diamond boundary depends on temperature, but at the 900 to 1 300 °C of a cratonic mantle root it lies somewhere above about 4.5 GPa — around 44 000 atm — which corresponds to depths beyond roughly 140 to 150 km. That is why natural diamonds are carried up in kimberlite from the deep lithospheric keel of old continents rather than formed in the crust.

Older papers give pressures in kilobars — how do those map onto Pa and atm?

One kilobar is 10⁸ Pa, so 10 kbar equals 1 GPa exactly and 1 kbar is 986.9 atm — near enough to a thousand atmospheres that the two were often treated as interchangeable in text. A 1970s paper describing an experiment at 30 kbar is describing 3 GPa. The atmosphere and the bar differ by about 1.3 percent, which is negligible next to the uncertainty on a geobarometer but not something to carry into a calculation as if it were zero.