A complete pressure conversion matrix for bar, psi, kPa, MPa, atm and kgf/cm² — read the row unit across to the column unit, with no intermediate step.
Data verified 2026-09-29 · based on NIST SP 811, 2008 edition
| Unit[2] | bar[1] | psi[1] | kPa[1] | MPa[1] | atm[1] | kgf/cm²[1] | Definition[2] |
|---|---|---|---|---|---|---|---|
| bar # | 1 | 14.5038 | 100 | 0.1 | 0.986923 | 1.01972 | Metric pressure; 1 bar = 100 kPa exactly |
| psi # | 0.0689476 | 1 | 6.89476 | 0.00689476 | 0.068046 | 0.070307 | Pound-force per square inch — the US customary unit |
| kPa # | 0.01 | 0.145038 | 1 | 0.001 | 0.00986923 | 0.0101972 | Kilopascal — the SI-adjacent metric engineering unit |
| MPa # | 10 | 145.038 | 1000 | 1 | 9.86923 | 10.1972 | Megapascal — the metric unit for material strength |
| atm # | 1.01325 | 14.6959 | 101.325 | 0.101325 | 1 | 1.03323 | Standard atmosphere — exactly 101 325 Pa by definition |
| kgf/cm² # | 0.980665 | 14.2233 | 98.0665 | 0.0980665 | 0.967841 | 1 | Kilogram-force per square centimetre — the older metric unit, still common on gauges |
| mmHg # | 0.00133322 | 0.0193368 | 0.133322 | 0.000133322 | 0.00131579 | 0.00135951 | Millimetre of mercury at 0 °C — the conventional value, not the true 0 °C value |
| inHg # | 0.0338639 | 0.491154 | 3.38639 | 0.00338639 | 0.0334211 | 0.0345316 | Inch of mercury at 32 °F — the conventional value used for barometers and altimeters |
Each cell is the value of one unit of the row expressed in the column's unit — so the row for bar, read across to psi, gives 14.5038. Every cell is computed from the defining factor of each unit rather than copied from a table, so no pair can disagree with any other pair. mmHg and inHg use the conventional values (0 °C and 32 °F respectively) that gauges and barometers are calibrated against, not the true values at those temperatures — the two differ in the seventh significant figure.
This matrix converts units, not pressure references. Before using it, be sure which reference the number you have is measured against, because the same unit can mean three different pressures.
Absolute pressure is measured from a perfect vacuum and is what the gas laws and thermodynamic tables use. Gauge pressure is measured from ambient atmospheric pressure, and is what almost every pressure gauge in a plant reads. Differential pressure is the difference between two pressures, measured from neither.
The relationship is pabs = pgauge + patm. At sea level that offset is 1.01325 bar or 14.696 psi — which is why a tyre inflated to 32 psi gauge is at 46.7 psi absolute, and why a vacuum gauge reads −14.7 psi at a perfect vacuum. Converting a gauge reading as though it were absolute introduces an error of about 1 bar, which is enormous at low pressures and negligible above 100 bar.
Gauges are marked accordingly: psig and barg for gauge, psia and bara for absolute. Where no suffix is given, process instrumentation almost always means gauge, and vacuum systems almost always mean absolute.
Two different numbers appear in pressure work — 14.5038 and 14.6959 — and confusing them is a common error.
1 bar = 14.5038 psi, because a bar is defined as exactly 100 000 Pa and a psi as exactly 6894.757293168 Pa. Both are exact definitions, so this conversion is exact.
1 atm = 14.6959 psi, because a standard atmosphere is defined as exactly 101 325 Pa. Standard atmosphere and bar are not the same thing: 1 atm is about 1.01325 bar. The familiar 14.7 psi figure is the standard atmosphere rounded, and it belongs with atm, not with bar.
The practical consequence: 100 psi is 6.895 bar, while 100 psi is 6.805 atm. If you convert a gauge reading thinking the two references are interchangeable, you introduce a 1.3% error before you have done anything else wrong.
Each data column on this page is tied to the source it came from. The numbers in square brackets correspond to the table headers above.
| # | Source | Type | Revision / method |
|---|---|---|---|
| [1] | Conversion matrix computed from the defining factor of each unit | derived | Each unit is defined by its value in pascals. The cell at row r, column c is factor(r) ÷ factor(c). Every cell is recomputed at build time, and eight well-known pairs are held as known-value checks — for example 1 bar = 14.5037738 psi and 1 psi = 6.8947573 kPa. |
| [2] | Pressure unit definitions per ISO 80000-4 and NIST Special Publication 811 | standard | NIST SP 811 (2008 edition); ISO 80000-4:2019 |
| Standard | Revision | What it covers on this page |
|---|---|---|
| NIST Special Publication 811 — Guide for the Use of the International System of Units | NIST SP 811, 2008 edition | the exact definition of every unit in the matrix |
| ISO 80000-4 — Quantities and units, Part 4: Mechanics | ISO 80000-4:2019 | the pressure unit names and symbols |
| ISO 2533 — Standard Atmosphere | ISO 2533:1975 | the standard atmosphere definition |
Cross-checked against:
Derived values — the following values on this page are calculated, not taken directly from the standard:
| Value | How it is derived |
|---|---|
| Every conversion value in the matrix | factor(row) ÷ factor(column), using each unit's exact value in pascals. Self-consistency is checked at build time — the diagonal must equal 1 and mirrored cells must be reciprocals. |
The matrix converts units only. It does not convert between gauge, absolute and differential pressure — add or subtract atmospheric pressure separately, and be sure which reference the number you have is measured against. mmHg and inHg use the conventional values (0 °C and 32 °F) that instruments are calibrated to.
Every value on this page is traceable to the sources listed above. If you use the data in a document, paper or report, cite it as:
Each row in the tables above also has a permanent link — hover a row and use the # link to cite a single value rather than the whole page.
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