mmHg to Bar: Mercury Column as a Pressure Standard

Reading a Mercury Column as a Pressure Standard

Long before electronics, pressure was realised as a height: a column of mercury balanced against whatever you were measuring. That heritage is why calibration certificates, barometer logs and older reference instruments still carry figures in millimetres of mercury, while the digital gauge you are checking them against is almost always scaled in bar. Getting from one to the other is routine arithmetic — but only after you know exactly which mercury the millimetre refers to.

Conversion factor: 1 mmHg = 0.001333224 bar. A 500 mm column therefore stands for 0.6666118 bar, and the classic 760 mm barometric column comes out at exactly 1.01325 bar, because 760 mmHg and one standard atmosphere are the same defined quantity.

What the Millimetre Actually Assumes

A fixed mercury density

The conventional millimetre of mercury is tied to a density of 13 595.1 kg/m³ — mercury at 0 °C. Warmer mercury is less dense, so a real column has to be corrected back to that reference.

A fixed gravitational field

It also assumes standard gravity, 9.806 65 m/s². Your laboratory is not standard: g runs from about 9.7803 m/s² near the equator to 9.8322 m/s² at the poles.

Two routes to the same figure

Density × gravity × 1 mm gives 133.322 387 Pa; dividing 101 325 Pa by 760 gives 133.322 368 Pa. The two agree to about 0.14 parts per million — invisible below six significant figures.

A place in the traceability chain

Mercury manometers were once the top of the chain. Today a working gauge in bar is usually referred to a piston-gauge or a national-laboratory realisation, and the mmHg figure survives as a historical scale marking.

Working a Calibration Point Through the Fields

A calibration sheet usually gives nominal test points in one unit and the instrument under test reads in the other. The two boxes let you walk the whole point list without retyping anything.

Enter the column figure

Put the corrected mmHg value in the left box — 250, 500, 749.6 — and the bar equivalent builds up digit by digit. Continental keyboards are fine here: a comma is read as a decimal point, and spaces inside the number are discarded.

Keep the resolution you need

Results run to eight decimal places, which matters when the deviation you are recording sits in the fifth. A 1 mmHg offset is only 0.00133 bar, so truncating early can hide the very error you are hunting.

Lift the digits into the record

Each field has its own copy button, and it hands over the number alone — no unit text, no separators — so it drops straight into a certificate template or a deviation column. Ctrl + C from inside the field behaves identically.

Turn the pair around

When the reference is in bar and the legacy instrument is in mercury, the ↔ button reverses the direction. Done longhand, 1 bar is 750.061683 mmHg — a number worth memorising if you read barometers often.

Correct before you convert: arithmetic here assumes the mmHg value has already been reduced to 0 °C and standard gravity. Feeding in a raw column height taken at room temperature carries that error straight into the bar figure.

Column Height, Temperature and Local Gravity

The table below pairs a mercury column with its pressure in both units, then shows the two corrections that separate a raw reading from a defensible one. The temperature column is the error left in an uncorrected reading taken at 20 °C on a brass scale (mercury expands about 1.818 × 10⁻⁴ per °C, the scale about 1.84 × 10⁻⁵). The gravity column is the error at an equatorial sea-level site where g is 9.7803 m/s², about 0.269 % below standard.

Column at 0 °C, standard g	Pressure (mmHg)	Pressure (bar)	Uncorrected at 20 °C	At equatorial g
100 mm	100 mmHg	0.133322 bar	+0.33 mmHg	−0.27 mmHg
250 mm	250 mmHg	0.333306 bar	+0.82 mmHg	−0.67 mmHg
500 mm	500 mmHg	0.666612 bar	+1.63 mmHg	−1.34 mmHg
750 mm	750 mmHg	0.999918 bar	+2.45 mmHg	−2.02 mmHg
760 mm	760 mmHg	1.013250 bar	+2.48 mmHg	−2.04 mmHg
1000 mm	1000 mmHg	1.333224 bar	+3.27 mmHg	−2.69 mmHg

Notice the size of those corrections against the resolution of a decent digital reference: near a barometric point the temperature term is about 3.3 mbar and the gravity term about 2.7 mbar, and at a warm tropical site they push in opposite directions and partly cancel. That is exactly why a column height on its own is not yet a pressure value.

What the Two Fields Give a Calibration Job

A whole point list without reloading

Overtype the mmHg box for each nominal point in turn — the bar column of your sheet fills in as fast as you can read the next line.

Either instrument can be the reference

One press of ↔ makes bar the input, which is the direction you want when the standard is modern and the unit under test is the old one.

Every scale a gauge might carry

The searchable lists on both sides hold all 26 units in the app, so a torr specification, an inHg barometer or a mmH₂O micromanometer lands on the same page.

Small deviations stay visible

Very small residuals drop into scientific notation rather than rounding away to zero, so a few micro-bar of difference is still something you can read and log.

Questions from the Calibration Bench

Why does an identical mercury column stand for less pressure near the equator?

Because the pressure a column exerts is ρgh, and g is a local quantity. At an equatorial sea-level site of 9.7803 m/s² the field is 0.269 % weaker than the 9.806 65 m/s² the unit assumes, so a 760 mm column is really worth about 758 mmHg. Altitude adds to it: free-air g falls roughly 3.1 µm/s² per metre climbed, another 0.36 mmHg off a barometric column at 1500 m.

How large is the temperature correction on a mercury barometer at room temperature?

Around −2.5 mmHg near 760 mm when the instrument sits at 20 °C. The net coefficient is the mercury expansion minus the scale expansion, near 1.63 × 10⁻⁴ per °C, so the correction scales with both the reading and the departure from 0 °C. In bar that is roughly 3.3 mbar — far larger than the uncertainty of any reference gauge you would be checking.

Is the conventional mmHg identical to the value derived from 101 325 Pa ÷ 760?

Not to the last digit. The density-based definition gives 133.322 387 Pa, the atmosphere-based one 133.322 368 Pa — a gap of 0.14 ppm. On a 1 bar point that is under 0.15 µbar, which no field instrument resolves, so calculators (this one included) use a single factor and the distinction only surfaces in national-laboratory budgets.

If mercury manometers are being retired, what carries the unit now?

Piston gauges — pressure balances — realise pressure from mass, local gravity and an effective piston area, and optical methods that infer gas density from refractive index have taken over the low-pressure end at several national institutes. Restrictions on mercury instruments accelerated the change. The unit itself did not move: it is now a defined multiple of the pascal rather than a physical column somebody has to level and read.

How does a digital gauge marked in bar stay traceable to a mercury-based scale?

Through the pascal. Both scales are fixed multiples of it — 1 bar is 100 000 Pa, 1 mmHg is 133.322 Pa — so a certificate issued in bar against a traceable standard is equally a statement about the mercury scale. Convert the certificate points rather than the instrument's own display, and quote the calibration uncertainty in whichever unit the record is kept, converted with the same factor.

mmHg to Bar