Pressure Conversion Explained

Why pressure conversion has more traps than length or weight

Converting a pressure between psi and bar is one multiplication. The trap is that pressure has more close-but-not-quite duplicate units than any other family of measurement, and more silent context errors: gauge versus absolute pressure, mmHg versus torr, atm versus bar, hPa versus mbar. The number is right; the meaning is wrong. The pressure converter on Calc Dragon handles every common unit using exact SI and NIST factors, but the answers only mean what you think they mean if you know which of those traps applies. This article walks through the maths, the exact constants, the gauge-versus-absolute distinction every tyre gauge quietly assumes, the close pairs that are interchangeable in practice but not in metrology, and the reference pressures that make a wrong figure obvious in seconds.

The piece covers the pascal-bridge formula every conversion uses, where the SI factors come from (the 9th and 10th General Conferences on Weights and Measures, BIPM, NIST SP 811), where the imperial factors come from (the 1959 International Yard and Pound Agreement), the gauge/absolute distinction that catches everyone who builds an actual instrument, the small differences between torr and mmHg and between atm and bar, the units used in weather, in tyres, in vacuum and in engineering stress, and the cases where a unit converter is the wrong tool — altitude-corrected weather pressure, blood pressure at altitude, and high-precision metrology.

The math behind every pressure conversion

Every conversion in the pressure converter uses a single intermediate unit: the pascal (Pa = N/m²). Each unit has a "pascals per unit" factor, and the conversion is two multiplications:

result = value × (Pa per source unit) ÷ (Pa per target unit)

So 32 psi expressed in bar is 32 × 6 894.757 293 168 ÷ 100 000 ≈ 2.2063 bar. The same pascal bridge handles every pair without needing one factor per source-target combination — only one number per unit is stored, and every other conversion follows from it. This is the standard pattern in scientific software, units libraries, and the SI brochure itself.

The factors are exact wherever possible. The SI metric units (Pa, hPa, kPa, MPa) are exact by definition. The bar is fixed by the BIPM at exactly 100 000 Pa, and the millibar at exactly 100 Pa, so 1 hPa and 1 mbar are identical. The standard atmosphere was fixed at exactly 101 325 Pa by the 10th General Conference on Weights and Measures in 1954. The torr is defined as exactly 1/760 of a standard atmosphere, which is 133.322 368 421… Pa — irrational, but exact in form. The conventional millimetre of mercury (mmHg) uses a fixed mercury density (13 595.1 kg/m³) and standard gravity (9.806 65 m/s²), giving 133.322 387 415 Pa exactly under NIST SP 811. The pound-force per square inch (psi) is exact under the 1959 International Yard and Pound Agreement: 1 lbf = 4.448 221 615 260 5 N exactly, 1 in² = 0.000 645 16 m² exactly, so 1 psi = 6 894.757 293 168 Pa exactly. The kilopound per square inch (ksi) is exactly 1000 psi.

Worked example: a tyre at 32 psi in seven different units

Take a typical car tyre inflated to 32 psi — the pressure on a standard sedan placard. The pressure converter gives:

• In pascals: 32 × 6 894.757 293 168 ÷ 1 ≈ 220 632 Pa.
• In kilopascals: 32 × 6 894.757 293 168 ÷ 1000 ≈ 220.63 kPa. This is what most modern TPMS displays show.
• In bar: 32 × 6 894.757 293 168 ÷ 100 000 ≈ 2.2063 bar. European tyre placards usually round this to "2.2 bar".
• In atmospheres: 32 × 6 894.757 293 168 ÷ 101 325 ≈ 2.1773 atm. The number is close to the bar value, but 1.3% smaller — the same trap that catches people on weather data.
• In mmHg: 32 × 6 894.757 293 168 ÷ 133.322 387 ≈ 1654.9 mmHg. Rarely used for tyres but useful as a sanity check against weather and medical pressures.
• In hPa (mbar): 32 × 6 894.757 293 168 ÷ 100 ≈ 2206.3 hPa. About 2.2× standard sea-level atmospheric pressure (1013.25 hPa), which is what a 32-psi tyre actually is — about twice atmospheric, gauge.
• In MPa: 32 × 6 894.757 293 168 ÷ 10⁶ ≈ 0.221 MPa. Megapascals are the SI unit for engineering stress and high industrial pressures; for tyre work they make the number small and clumsy.

Going the other way is symmetric: 1013.25 hPa (standard atmosphere) in psi is 1013.25 × 100 ÷ 6 894.757 293 168 ≈ 14.696 psi. This is the number that "absolute" tyre gauges and altimeters quietly add to gauge pressure to convert it. The converter handles all twelve units in a single dropdown, so the source and target can be chosen independently and any pair works.

Gauge versus absolute pressure: the silent killer

The most expensive mistake in pressure work is not getting the unit wrong — it is getting the reference wrong. Most pressure instruments measure relative to atmospheric pressure (gauge pressure), not absolute zero (absolute pressure). A tyre gauge reading "32 psi" is reporting 32 psi above the local atmospheric pressure of about 14.7 psi. The absolute pressure inside the tyre is 32 + 14.7 = 46.7 psi.

The convention is sometimes made explicit by appending a suffix: "psig" for gauge pressure, "psia" for absolute pressure. In engineering specifications, "psia" almost always means absolute and "psig" almost always means gauge. In everyday speech, "psi" is almost always gauge. In scientific work, the same number written as "kPa" with no suffix is almost always absolute. The convention flips depending on context, and the converter does not know which you mean — it converts the number, not the reference. A "32 psig" and a "32 psia" become "220.63 kPa" with no distinction; you have to track the reference yourself.

Practical rules: tyre placards, blood pressure, and most domestic gas-line readings are gauge. Weather forecasts, altimeter settings, and chemistry textbook pressures are absolute. Vacuum gauges are usually absolute, expressed below atmospheric (a "10 mmHg vacuum" is 10 mmHg of absolute pressure remaining, not 10 mmHg below atmospheric). Industrial process gauges almost always default to gauge unless the spec says otherwise. When using the pressure converter on a value from an instrument, write down whether the reading was gauge or absolute before doing anything else with the converted number.

The close pairs: torr/mmHg, hPa/mbar, atm/bar

Three pairs of pressure units look almost identical on the page, and only one pair is actually identical:

hPa and mbar are exactly the same

1 hectopascal = 100 Pa = 1 millibar, exactly. The two are interchangeable in every respect — different names for the same number. Weather services worldwide migrated from "millibar" to "hectopascal" in the 1970s and 1980s as part of SI alignment, but the figures on a weather map are unchanged. A reading of "1013 hPa" is the same as "1013 mbar". If the unit on a chart is hPa or mbar, treat them as identical.

torr and mmHg are interchangeable to 7 significant figures

1 torr = 133.322 368 421… Pa exactly (defined as 1/760 of a standard atmosphere). 1 conventional mmHg = 133.322 387 415 Pa exactly (defined from a fixed mercury density and standard gravity). The two agree to better than 0.000 015%. For medical, vacuum and weather purposes, and for any instrument with less than 7-digit accuracy, the distinction is invisible. For high-precision barometric metrology and for primary mercury manometers, the distinction matters. The pressure converter exposes both as separate units so the user can pick the one their reference document specifies, but the displayed result is identical to four or five significant figures in every realistic case.

atm and bar are 1.3% apart

1 atm = 101 325 Pa exactly. 1 bar = 100 000 Pa exactly. The atmosphere is 1.325% larger than the bar. This is the close pair most often confused, because both are casually labelled "about one atmosphere of pressure" in conversation. The difference is not small enough to ignore: a chemistry experiment specified at "1.0 atm" is at 101.325 kPa, not 100 kPa, and the 1.3% gap matters in any quantitative work. For tyre and weather use, the atm has almost completely been displaced by bar (or hPa). For older chemistry textbooks, oceanography (where pressure is often expressed in atm relative to sea level), and aviation altimetry (where the standard atmosphere ISA is 1 atm = 1013.25 hPa), it survives.

Reference pressures to anchor a figure

Pure numbers are hard to picture. A few reference pressures make it easier to spot when a converted figure is obviously wrong:

• Standard sea-level atmospheric pressure: 1013.25 hPa = 1013.25 mbar = 1 atm = 760 mmHg = 14.696 psi = 29.9213 inHg. The ISA reference; every barometric reading is relative to this.
• Typical car tyre (cold): 28–35 psi gauge ≈ 1.9–2.4 bar gauge ≈ 190–240 kPa gauge.
• Bicycle road tyre: 80–130 psi ≈ 5.5–9 bar. Mountain bike: 25–50 psi ≈ 1.7–3.4 bar.
• Espresso brewing: 9 bar ≈ 130 psi. The industry-standard extraction pressure.
• Domestic mains water: 2–5 bar ≈ 30–75 psi depending on location and elevation.
• Domestic gas supply (UK natural gas, into the meter): 21 mbar ≈ 0.3 psi above atmospheric. Low and stable by design.
• Adult resting blood pressure: 120/80 mmHg systolic/diastolic ≈ 16/10.7 kPa. Always quoted as gauge above atmospheric.
• "Bar" of vacuum used in industry: a "good industrial vacuum" is around 0.001 mbar = 0.1 Pa. A "very high vacuum" used for thin-film deposition is 10⁻⁷ mbar = 10⁻⁵ Pa.
• Mariana Trench bottom: ≈ 1 086 bar ≈ 15 750 psi ≈ 108.6 MPa. About 1 071 atm.
• Mount Everest summit air pressure: ≈ 337 hPa ≈ 0.333 atm ≈ 4.89 psi — about a third of sea level.
• Steel yield stress (typical structural): ≈ 250 MPa ≈ 36 250 psi ≈ 36.25 ksi. Engineering stress is where MPa and ksi feel natural.
• Hydraulic system (industrial): 200–400 bar ≈ 2900–5800 psi. High-pressure hydraulic rams: up to 700 bar.

If a converted "tyre pressure" comes out at 100 bar or 0.02 psi, the conversion has gone wrong by orders of magnitude — or the reference (gauge versus absolute) has been confused. The pressure converter is exact, so a wildly off result almost always means the unit was misread or the gauge/absolute distinction was missed.

How to convert pressures in your head

For mental estimation, a small set of shortcuts covers most common conversions:

• bar → psi: multiply by 14.5. So 2.5 bar → 36.25 psi (exact 36.26).
• psi → bar: divide by 14.5. So 100 psi → 6.9 bar (exact 6.895).
• bar → kPa: multiply by 100. Exact.
• psi → kPa: multiply by 7 and subtract 2%. So 32 psi → 224 − 4.5 = 219.5 kPa (exact 220.63).
• hPa → mmHg: multiply by 0.75. So 1013 hPa → 760 mmHg (exact 759.97).
• mmHg → hPa: multiply by 1.333. So 760 mmHg → 1013.3 hPa (exact 1013.25).
• atm → bar: add 1.3%. So 5 atm → 5 × 1.013 ≈ 5.065 bar (exact 5.066).
• MPa → psi: multiply by 145. So 1 MPa → 145 psi (exact 145.04). Useful for engineering stress.
• ksi → MPa: multiply by 6.9. So 50 ksi → 345 MPa (exact 344.7).

These approximations are not meant to replace the converter — the exact answer is one input away — but they make it possible to spot when a quoted figure is wrong by an order of magnitude. If a weather forecast in hPa is off by 100 from the equivalent in mmHg, the conversion is wrong.

Common mistakes

Adding atmospheric pressure where it should not be added

A "32 psi" tyre placard is gauge pressure. Converting it to bar gives 2.2 bar gauge, not 2.2 bar absolute. Some online calculators and some industrial gauges silently switch between gauge and absolute when changing units, which is the opposite of what should happen — the unit changes; the reference does not. The Calc Dragon converter does the right thing: it converts the number, leaves the reference alone, and lets you decide whether to add or subtract atmospheric pressure yourself if the use case requires it.

Treating atm and bar as identical

"About one atmosphere of pressure" gets used loosely for both units in conversation, but the 1.325% gap is real. A diving table that specifies "decompression at 6 atm" means 6 × 101.325 = 607.95 kPa, not 600 kPa. For most casual work the gap can be ignored; for anything quantitative, it cannot. When a number is quoted to three or more significant figures, atm and bar are different units.

Confusing weather pressure with elevation-corrected pressure

A weather report quotes "sea-level pressure" — the local barometric reading corrected for elevation back to what it would read at sea level. The actual ambient pressure at altitude is lower. Denver, Colorado, at 1609 m elevation, has an ambient pressure around 830 hPa, but the weather report says "1013 hPa" because that is the sea-level-equivalent. Converting the reported figure to psi and then trying to use it as the actual local pressure is a common engineering mistake. Aviation altimeters explicitly correct for this; everyday weather forecasts do not flag it.

Using mmHg or torr at non-standard temperature

The conventional mmHg and torr factors assume mercury at 0 °C and standard gravity. Real mercury manometers at 25 °C read about 0.4% lower. For everyday medical, weather and vacuum work the temperature correction is irrelevant; for primary metrology it matters. The pressure converter uses the conventional factors throughout, which is the universal engineering and medical convention.

When the converter is not enough

For altitude-corrected weather work, the converter handles the unit but not the elevation correction. Convert the local barometric reading first; then apply the standard atmosphere altitude correction (about 1 hPa per 8 m of elevation up to a few hundred metres) to get sea-level pressure, or work backwards to get the altitude. Aviation uses ISA (the International Standard Atmosphere, ICAO Doc 7488) for the reference temperature/pressure profile.

For blood pressure at altitude, the gauge reading does not change appreciably — blood pressure is the difference between arterial and ambient pressure, and a sphygmomanometer measures that difference directly. Where altitude does affect the figure is in oxygen partial pressure, which is the actual reason high altitude feels "thinner". A unit converter is the wrong tool there; an atmospheric model (ICAO ISA, US Standard Atmosphere 1976) is needed.

For very-high-vacuum work below about 10⁻³ Pa, a pressure converter is technically still correct but practically misleading: at those pressures the gas behaviour stops being continuum-fluid and starts being molecular, the gauges measure ionisation rate or thermal conductivity rather than direct force per area, and the gauge-specific calibration matters more than the unit conversion. The pressure converter can express a 10⁻⁵ mbar reading in pascals or torr, but reading the underlying gauge correctly is its own problem.

For the day-to-day questions — "how many psi in 2.2 bar", "what is 100 kPa in atm", "how many mmHg in a kilopascal", "what is the SI equivalent of 50 ksi steel" — the Calc Dragon pressure converter gives the exact answer using NIST and SI factors. The maths is simple, the constants are exact, and the result is the same number every accurate converter on the internet should return.

Frequently asked questions

See the FAQ on the pressure converter page for direct answers on how many psi in 1 bar, how atm and bar differ, why torr and mmHg are not quite identical, why a tyre gauge reads differently from absolute, and what hPa means on a weather map. For related conversions, the area converter handles m², ft², acres and hectares; the volume converter handles litres, gallons and cups; and the weight converter handles kilograms, pounds and stones — the four most common unit families on a builder's, plumber's or engineer's desk.