Pressure Converter

One physical quantity, four labels that never agree. The sticker inside your car door says 35 psi. The European owner's manual quotes the same tyre as 2.4 bar. Tonight's weather forecast reads 1013 hPa. The cuff at the doctor's office shows 120 mmHg. All four describe pressure — force pushing on an area — and not one of them shares a unit with the others. That mismatch is the whole reason this converter exists: it takes any one of those readings and gives you the equivalent in any of the others.

The trick is that every conversion routes through a single base unit, the pascal (Pa), using each unit's defined factor to pascals. Pressure is force per area — formally 1 Pa = 1 N/m² — and the standard atmosphere is fixed at exactly 101 325 Pa, so 14.7 psi at sea level and 1013 hPa on the forecast are the same air pushing down on you, expressed two ways. Anchoring on the pascal lets the same engine cross-convert SI engineering units (Pa, kPa, MPa), atmospheric units (bar, millibar, standard atmosphere), an imperial industrial unit (psi), a gravitational technical unit (kgf/cm²), and the liquid-column units used in medicine and HVAC (torr, mmHg, cmH₂O, inH₂O).

The single most-important fact about a serious pressure converter is honesty about which factors are exact and which are not. Eight of the twelve units in this set have exact rational factors to the pascal: pascal (1, SI base), kilopascal (1 000), megapascal (1 000 000), bar (100 000, BIPM-accepted), millibar (100, identical to the hectopascal), standard atmosphere (101 325 Pa exact, fixed by the 10th CGPM in 1954 and embedded in ISO 2533:1975), pound-force per square inch (6 894.757293168361 Pa, the IEEE-754 product of NIST-exact upstream rationals 4.4482216152605 lbf/N and 0.0254 m/in), and kilogram-force per square centimetre (98 066.5 Pa, the so-called technical atmosphere, fixed by CGPM 1901 standard gravity × 1 kg/cm² with no rounding). The four remaining units — torr, mmHg, cmH₂O and inH₂O — are conventional values and the converter tags them as inexact. Most online converters call every unit exact; we do not, and the difference matters in metrology and clinical contexts where the gap between two near-identical units is the entire point.

The distinctions inside the inexact group are subtle but real. Torr is defined as exactly 1/760 of a standard atmosphere — a clean rational definition (101 325 ÷ 760) — but the resulting quotient 133.32236842105263… Pa is irrational in IEEE-754 double-precision binary, so it cannot be stored without truncation. Millimetre of mercury (mmHg) is a separate empirical convention from ISO 31-3 / NIST SP 811 fixed at exactly 133.322387415 Pa, derived from a mercury density of 13.5951 g/cm³ at 0 °C under standard gravity. Torr and mmHg therefore differ by about 5 × 10⁻⁵ Pa — less than 0.000015 % — close enough to be interchangeable in clinical blood-pressure work but distinct in vacuum metrology. Centimetre of water (cmH₂O = 98.0665 Pa) and inch of water (inH₂O = 249.0889 Pa) both assume a water density of exactly 1 000 kg/m³ at 4 °C; real water density at room temperature is 999.972 kg/m³, so the underlying physical assumption drifts by ~28 ppm versus the conventional value.

This converter supports the entire industrial and medical pressure landscape. Mechanical and pneumatic engineers move between MPa, bar and psi; weather services publish in hPa (numerically identical to millibar — the WMO migrated officially in 1986 but kept the same scale, so 1013 hPa and 1013 mbar are the same atmospheric reading); automotive technicians read tyres in psi, kPa or bar (a typical passenger-car spec of 32 psi = 220.6 kPa = 2.21 bar); medical clinicians read systolic blood pressure in mmHg (a healthy adult value of 120 mmHg = 16.0 kPa per the 2017 ACC/AHA guideline); CPAP and ventilator technicians read airway pressure in cmH₂O (a typical CPAP spec of 5–20 cmH₂O = 0.49–1.96 kPa); HVAC designers read duct static pressure in inches of water column (a residential system runs at 0.3–0.6 inH₂O = 75–150 Pa); divers read absolute depth pressure in bar (~1 bar per 10 m of seawater; the Mariana Trench bottom is roughly 1 086 bar ≈ 15 750 psi); ASME boiler engineers split low-pressure (≤ 15 psi = 103.4 kPa, Section IV) from high-pressure (> 15 psi, Section I); and physics students do the routine Pa↔atm↔bar conversions that show up in every gas-law problem.

What distinguishes a serious pressure converter from a marketing widget is calling out the conflations every other tool ignores. Torr is not mmHg. hPa is mbar (numerically) but the official meteorological unit is the hPa. Standard atmosphere (101 325 Pa) is not technical atmosphere (98 066.5 Pa = 1 kgf/cm²) — they differ by 3.21 % and the technical atmosphere survived in older European industrial drawings long after BIPM deprecated it. The pound per square inch is exact only because it inherits from two exact upstream definitions (the IYP-1959 inch at 0.0254 m and the CGPM-1901 pound-force at 4.4482216152605 N); strip either upstream definition and psi loses its exact-rational status. Every result in this calculator displays an "exact" badge when both endpoints are exact, and is silent when either endpoint depends on a conventional liquid-column value — full transparency, not marketing.

Every pressure conversion is one multiplication and one division through the pascal. The general formula is:

where x is your input value, a_from is the source unit's factor to pascals, and a_to is the target unit's factor to pascals. To do it by hand:

1. Look up the source-to-pascal factor. For psi, a_from = 6894.757293168361.

2. Multiply the input by that factor to get pascals. 32 psi × 6894.757293168361 = 220 632.2333813876 Pa.

3. Look up the target-to-pascal factor. For bar, a_to = 100000.

4. Divide the pascal value by the target factor. 220 632.2333813876 ÷ 100 000 = 2.20632 bar.

The same procedure works for every supported unit. Going from atmospheres to pascals: 1 atm × 101 325 Pa/atm = 101 325 Pa exact (the canonical ISO 2533 standard-atmosphere definition). Going from bars to psi: 1 bar × 100 000 ÷ 6 894.757293168361 = 14.5037738… psi (the irrational SI-to-imperial pressure quotient). Going from torr to mmHg: 1 Torr × 133.32236842105263 ÷ 133.322387415 = 0.99999985… mmHg — a useful sanity check that confirms the two units are not bit-identical despite being interchangeable in clinical work.

To use this calculator, pick the source unit from the "From" dropdown, type a value, then pick the target unit from the "To" dropdown. The result updates on every keystroke. Click the result card to copy it to the clipboard. Use the precision selector to switch between auto (6 significant figures), or a fixed 0, 2, 4, 6, 10 or 15 decimals. Auto-precision switches to scientific notation when the result is larger than 10¹² (one trillion) or smaller than 10⁻³, so converting a Mariana Trench-bottom pressure (~1 086 bar ≈ 108 600 000 Pa) all the way down to inches of water (≈ 436 000 inH₂O) still renders readably at every step. The "exact" badge appears when both endpoints have exact rational factors and is absent when either endpoint is a conventional liquid-column value (torr, mmHg, cmH₂O, inH₂O).

The formula is a two-step pivot through the pascal base unit. The factor table this calculator uses is sourced from NIST SP 811 Appendix B.8 (pressure section), the BIPM SI Brochure (accepted non-SI units), ISO 2533:1975 (standard atmosphere) and ISO 31-3 (mmHg conventional value), and is anchored to four exact upstream definitions — the SI pascal, the 1959 International Yard and Pound Agreement (1 in = 0.0254 m, 1 lb = 0.45359237 kg, both exact), the 3rd CGPM (1901) declaration that g_n = 9.80665 m/s² exact, and the 10th CGPM (1954) declaration that 1 atm = 101 325 Pa exact:

For the pascal → psi direction the calculator displays the irrational quotient 1 / 6 894.757293168361 = 1.45037737730209… × 10⁻⁴ psi/Pa. For the bar → atm direction: 100 000 / 101 325 = 0.98692326671601… atm/bar (the slightly-less-than-one ratio because the standard atmosphere is a touch above 1 bar). Both endpoints (Pa, psi) are exact rationals, so the exact badge fires; the printed inverse is mathematically irrational but the underlying definition is exact.