Pressure Converter

Every conversion goes through the pascal

Pressure is force spread over area, and the SI unit is the pascal — one newton per square metre. Each unit here is stored as a single number, how many pascals it is, and every conversion is two steps through that base. Eleven units connected by direct factors would be 121 numbers to keep consistent; one column of eleven cannot disagree with itself.

Most of these factors are definitions rather than measurements, which is what makes the arithmetic exact:

• 1 bar = 100,000 Pa exactly, and a millibar is exactly 100 Pa — identical to the hectopascal used on modern weather charts.
• 1 standard atmosphere = 101,325 Pa exactly. Fixed by Resolution 4 of the 10th General Conference on Weights and Measures in 1954. It is a defined reference level, not the pressure outside your window.
• 1 torr = 101325/760 Pa exactly, because the torr is defined as one 760th of that atmosphere.
• 1 psi = 6,894.757293168 Pa, which follows from the pound-force being exactly 4.4482216152605 N and the square inch exactly 0.00064516 m².
• Two units are conventional, not decreed. The millimetre of mercury is 133.322387415 Pa — mercury at 13,595.1 kg/m³ under standard gravity — and the inch of water is 249.08891 Pa, taking water as 1,000 kg/m³. Real fluids change density with temperature, so an inch of water quoted at 60 °F, as North American gas and HVAC work often does, is about 0.1% smaller at roughly 248.84 Pa.

Results are rounded to twelve significant figures rather than to a fixed number of decimal places. A tool spanning the pascal to the megapascal has no single sensible decimal place, and significant figures are what make one atmosphere come back as exactly 760 torr instead of 759.9999999999999.

Gauge pressure versus absolute pressure

This is the part almost no converter mentions, and it changes answers by about 14.7 psi.

Absolute pressure is measured from a perfect vacuum. Gauge pressure is measured from whatever the atmosphere is doing around the instrument. Nearly every dial you will ever read — tyre gauge, tank regulator, blood pressure cuff, boiler gauge — reads gauge pressure, because it works by comparing the inside to the outside. A tyre gauge sitting on a bench reads zero, and that tyre gauge is not claiming the bench is in a vacuum.

This tool converts magnitudes. It never adds or removes the atmospheric offset behind your back. Convert 32 psi to bar and you get 2.206 bar: the same reading in different units, still gauge if the input was gauge. The absolute equivalent is printed as its own separate figure in the results, labelled as such, because only the person holding the instrument knows which kind of reading it is.

Getting it wrong runs both ways. Adding an atmosphere to a reading that was already absolute inflates it just as badly as omitting it from a gauge one. In the US the units are often marked — psig for gauge, psia for absolute — but a bare “psi” in everyday use means psig, and bar, kPa and inH₂O usually carry no marking at all.

A tyre inflated to 32 psi

Step one: 32 × 6,894.757293168 = 220,632.2334 Pa. Step two: 220,632.2334 ÷ 100,000 = 2.206322334 bar. In kilopascals, the unit most European and Asian tyre placards use, that is 220.6 kPa.

Now the part the number alone does not tell you. That 32 psi came off a gauge, so it means 32 psi above the surrounding air. Standard atmospheric pressure is 101,325 Pa, which is 14.69594878 psi, so the absolute pressure inside the tyre is 32 + 14.696 = 46.69594878 psi, or 3.219572334 bar. The air inside is at a little over three times the pressure of the air outside — a fact the gauge reading conceals and a converter that only changes units cannot tell you unless it says so.

A second one, in a unit people rarely think of as pressure: blood pressure of 120/80 mmHg. At 133.322387415 Pa per mmHg, that is 16.0 kPa over 10.7 kPa — and it is emphatically a gauge pressure, measured against the atmosphere pressing on the arm. Absolute systolic would be about 117 kPa, a number no clinician has ever needed.

And a third: a residential natural gas line delivering 7 inches of water column. 7 × 249.08891 = 1,743.6 Pa, about 1.74 kPa or 0.25 psi. Inches of water survive precisely because they make such small pressures legible — quoting the same figure as 0.0174 bar would be unreadable on a manometer.

What this converter assumes

• Your reading and the answer are the same kind of pressure. The conversion is a change of units only; no atmospheric offset is added or removed. The absolute equivalent shown alongside assumes a standard atmosphere of exactly 101,325 Pa, which is the defined reference, not your local weather or altitude.
• The mercury and water columns use their conventional densities at standard gravity — 13,595.1 kg/m³ and 1,000 kg/m³, 9.80665 m/s². No temperature correction is applied, because doing it properly needs the fluid temperature and the local gravity, and a unit converter knows neither.
• Negative values are accepted and treated as signed magnitudes, for vacuum gauge readings. Nothing here checks whether a negative absolute pressure is physically possible; it is not, and that is your call to make.
• Results carry twelve significant figures internally and are displayed to ten. Neither is a claim about your instrument — a tyre gauge accurate to ±1 psi stays accurate to ±1 psi after conversion.
• Pressure is not stress, though both are measured in pascals. Converting a material stress figure works arithmetically, but MPa in a materials datasheet and MPa in a hydraulic circuit are describing different physics.

Pressure conversion FAQ

Sources and review notes

1. NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), including the conversion factors for psi, bar, atmosphere, torr, mmHg, inHg and inH₂O
2. BIPM — The International System of Units (SI) Brochure, for the pascal and for the status of the bar and the atmosphere as non-SI units accepted for use with the SI
3. Resolution 4 of the 10th General Conference on Weights and Measures (1954), which defined the standard atmosphere as exactly 101,325 pascals.

These are defined and conventional values rather than measured ones, so they do not drift: the bar has been exactly 100,000 Pa and the atmosphere exactly 101,325 Pa for decades. What does vary is the atmospheric pressure where you are standing, which is why the gauge-to-absolute figure on this page uses the defined standard atmosphere and says so rather than pretending to know your altitude.