Pressure Converter
High-precision calculator for fluid dynamics, atmospheric barometry, tire inflation, and materials yield stress. Seamlessly convert between SI Pascals, Bar, PSI, standard atmospheres (atm), Torr, and millimeters of mercury (mmHg).
Pressure Configuration
1 Pa = 1 N/m² = 1 kg/(m⋅s²) • SI StandardLoading pressure ratio...
1 Bar = 14.5038 PSI
Gauge Pressure vs. Absolute Pressure Analyzer
Accounting for 1.00 atm ambient sea-level barometric pressure Tire Gauges & Pressure Sensors: Mechanical dial and digital tire gauges read gauge pressure (psig), which measures the pressure differential above atmospheric ambient. A tire showing 32.0 psi actually holds an internal absolute pressure of 46.7 psia (3.22 bar absolute).
Ocean Depth Hydrostatic Submersion Equivalent
Hydrostatic pressure gradient: P = ρgh (≈ 1 atm per 10m / 33 ft seawater)Step-by-Step Conversion Arithmetic
Simultaneous Multi-Unit Pressure Grid
Real-time converted values across all 16 major SI metric, barometric, manometric, and imperial pressure standards
How to Convert Pressure Units
In physics and engineering, the SI unit of pressure and mechanical stress is the Pascal (Pa), defined as 1 Newton per square meter (1 N/m²). Standard atmospheric and industrial conversion identities include: 1 Bar = 100,000 Pascals (100 kPa) ≈ 14.5038 PSI; 1 Standard Atmosphere (atm) = exactly 101,325 Pascals = 1.01325 Bar = 14.69595 PSI; and 1 PSI (lbf/in²) = 6,894.757 Pascals.
1. The SI Pascal: Force Over Area & Base Dimensional Mechanics
Named in honor of French mathematician, physicist, and philosopher Blaise Pascal, who investigated fluid hydrostatics and atmospheric variations in 1648, the Pascal (symbol Pa) is the derived International System (SI) unit of pressure, compressive stress, tensile strength, and Young's modulus.
The fundamental dimensional equation of pressure is force divided by the area over which that force acts:
1 Pascal = 1 Newton / meter² (1 N/m²). In SI base units: 1 kg⋅m⁻¹⋅s⁻². It represents the perpendicular compressive force of 1 Newton over 1 square meter.
Pressure also represents energy stored per unit volume of fluid: 1 N/m² = 1 (N⋅m) / m³ = 1 Joule per cubic meter.
Tire pressure is rated in kPa (220–250 kPa); structural concrete and steel yield in MPa (1 N/mm²); planetary mantles in GPa.
2. Atmospheric & Meteorological Standards: atm, Bar & hPa
Atmospheric air exerts continuous downward pressure on Earth's surface due to the gravitational weight of the air column above. In 1954, the 10th General Conference on Weights and Measures legally defined the standard atmosphere:
The Bar was introduced by British meteorologist William Napier Shaw in 1909 as a convenient round metric multiple (1 bar = 100,000 Pa). Although not an official SI unit, the Bar is legally accepted throughout the European Union and international chemical processing.
3. Gauge Pressure vs. Absolute Pressure: PSIG vs. PSIA & Vacuum
A crucial source of engineering and mechanical failure is confusing gauge pressure with absolute pressure:
| Measurement Type | Imperial Symbol | Metric Symbol | Reference Zero Point | Formula Relationship |
|---|---|---|---|---|
| Absolute Pressure | psia | bar(a) or Pa | Perfect vacuum (0 absolute Pa) | Pabs = Pgauge + Patm |
| Gauge Pressure | psig | bar(g) | Local ambient atmosphere | Pgauge = Pabs − Patm |
| Vacuum Pressure | inHg vac | Torr / mbar | Atmospheric ambient down to 0 | Pvac = Patm − Pabs |
When an automotive tire dial gauge reads zero, the tire is not a vacuum—it simply contains air at the identical pressure as the outside atmosphere. At sea level, a tire inflated to 32.0 psig possesses an absolute internal pressure of 46.7 psia (3.22 bar absolute).
4. Manometric Liquid Columns: mmHg, Torr & Inches of Water
Before the advent of piezoelectric transducers and strain gauges, pressure was measured by observing the vertical displacement of liquid in a U-tube manometer. The height of the liquid column is given by the hydrostatic relation P = ρ × g × h:
- Millimeters of Mercury (mmHg): Uses liquid mercury (ρ ≈ 13,595.1 kg/m³). Standardized in medical cardiovascular monitoring for arterial blood pressure (e.g. 120/80 mmHg = 16.0 / 10.7 kPa).
- Torr: Defined as exactly 1/760 of an atmosphere (≈ 133.322 Pa). Universally utilized in semiconductor manufacturing, vacuum chamber sputtering, and cryogenics.
- Inches of Water Column (inWC / inH₂O): Because mercury is toxic and water is light, small air pressure differentials in HVAC ventilation ducts and residential natural gas burners (typically 3.5 to 7.0 inWC = 870 to 1,740 Pa) are measured using inches of water column (1 inH₂O ≈ 249.09 Pa ≈ 0.0361 psi).
5. Comprehensive Multi-Unit Pressure Conversion Reference Matrix
The reference table below lists exact algebraic conversion factors to translate any standard pressure unit directly into SI Pascals (Pa):
| Unit Name | Symbol | Category | Pascal Equivalent (Pa) | PSI Equivalent |
|---|---|---|---|---|
| Pascal | Pa | SI Base | 1 | 1.45038 × 10⁻⁴ |
| Hectopascal | hPa | Aviation/Weather | 100 | 0.014504 |
| Kilopascal | kPa | SI Metric | 1,000 | 0.145038 |
| Megapascal | MPa | Engineering Stress | 1,000,000 | 145.0377 |
| Gigapascal | GPa | Materials Modulus | 10⁹ | 145,038 |
| Bar | bar | Atmospheric | 100,000 | 14.50377 |
| Millibar | mbar | Meteorology | 100 | 0.014504 |
| Standard Atmosphere | atm | Atmospheric | 101,325 | 14.69595 |
| Pounds per sq inch | PSI | Imperial | 6,894.757 | 1.000000 |
| Kilopounds/sq inch | ksi | Metallurgy | 6,894,757 | 1,000 |
| Pounds per sq foot | psf | Civil Foundation | 47.8803 | 0.006944 |
| Millimeters of Mercury | mmHg | Medical | 133.3224 | 0.019337 |
| Torr | Torr | Vacuum Physics | 133.3224 | 0.019337 |
| Inches of Mercury | inHg | Aviation QNH | 3,386.389 | 0.491154 |
| Inches of Water Column | inH₂O | HVAC / Gas | 249.0889 | 0.036127 |
6. Ocean Hydrostatics & Geophysics: Mariana Trench to Earth's Core
Fluid pressure scales continuously from marine oceanography to geodynamic planetary cores:
At 40 meters depth, hydrostatic pressure reaches 5.0 bar absolute (72.5 psia). Nitrogen partial pressure causes inert gas narcosis, necessitating special gas mixes.
In the Challenger Deep, hydrostatic pressure exceeds 1,086 bar (108.6 MPa or 15,750 psi)—over 1,000 times atmospheric surface pressure, exerting 8 tons per square inch on submarine hulls.
At Earth's core-mantle boundary and solid iron inner core, overburden pressure reaches 330 to 360 Gigapascals (3.3 to 3.6 million atmospheres), keeping iron solid despite temperatures exceeding 5,000°C.
7. Step-by-Step Worked Conversion Problems
A vehicle owner's manual recommends inflating front tires to 35.0 PSI. Convert this specification into Bar and Kilopascals (kPa).
Step 1: Convert PSI to Base SI Pascals (6,894.757 Pa per PSI)
Total Pascals = 35.0 × 6,894.75729 Pa ≈ 241,316.5 Pascals
Step 2: Convert Pascals to Bar (100,000 Pa per Bar)
Pressure in Bar = 241,316.5 ÷ 100,000 = 2.413 Bar (commonly rounded to 2.4 bar)
Step 3: Convert Pascals to Kilopascals (1,000 Pa per kPa)
Pressure in kPa = 241,316.5 ÷ 1,000 = 241.32 kPa
An air traffic controller issues an altimeter barometric setting of 30.12 inHg. Convert this QNH into Hectopascals (hPa / millibars).
Step 1: Identify the inHg to Pascal Constant (3,386.389 Pa per inHg)
Pressure in Pascals = 30.12 × 3,386.389 Pa ≈ 101,998.04 Pascals
Step 2: Divide by 100 to Obtain Hectopascals (hPa)
QNH Barometer = 101,998.04 ÷ 100 = 1,019.98 hPa ≈ 1020 hPa
This reading is slightly above standard 1013.25 hPa, indicating a local high-pressure meteorological system.
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