Pressure Conversion

Convert between various pressure units including Pascal, Bar, PSI, and atmosphere

Pressure Conversion Formulas

Pascal to Other Units

1 Pa = 1 N/m² = 1 kg/(m·s²)

Bar: P_bar = P_Pa / 100,000

PSI: P_psi = P_Pa / 6,894.75729

atm: P_atm = P_Pa / 101,325

Torr: P_torr = P_Pa / 133.322387415

Bar Conversions

1 bar = 100,000 Pa = 0.1 MPa

PSI: P_psi = P_bar × 14.503773773

atm: P_atm = P_bar / 1.01325

mbar: P_mbar = P_bar × 1,000

PSI Conversions

1 PSI = 6,894.75729 Pa = 0.0689475729 bar

kgf/cm²: P_kgf = P_psi × 0.0703069579639

atm: P_atm = P_psi / 14.6959487755

KSI: P_ksi = P_psi / 1,000

Hydraulic Pressure (mH2O)

1 mH2O = 9,806.65 Pa (at 4°C)

P_Pa = P_mH2O × ρ_water × g

Where: ρ_water = 1,000 kg/m³, g = 9.80665 m/s²

Reference Values Table

Pressure Source Pascal (Pa) Bar PSI atm
Standard Atmosphere 101,325 1.01325 14.6959 1.0000
Car Tire (Typical) 220,632 2.2063 32.0 2.177
Deep Sea (10km) 100,000,000 1,000 14,503.8 986.92
Perfect Vacuum 0 0 0 0
Blood Pressure (120/80) 16,000 / 10,667 0.16 / 0.107 2.32 / 1.55 0.158 / 0.105

Quick Conversion Reference: 1 Unit to All Others

From Unit Value Equals
1 Pascal 1 Pa = 0.00001 bar = 0.01 mbar = 0.001 kPa
= 0.0001450377 PSI = 0.020885434 PSF
= 0.00000986923 atm = 0.0075006168 Torr
= 0.0000101972 kgf/cm²
= 0.000101972 mH2O
1 Bar 1 bar = 100,000 Pa = 100 kPa = 0.1 MPa
= 14.503773773 PSI = 2088.5434 PSF
= 0.986923 atm = 750.0618 Torr = 1000 mbar
= 1.01972 kgf/cm² = 10.1972 mH2O
1 PSI 1 PSI = 6,894.75729 Pa = 6.89476 kPa
= 0.0689476 bar = 68.9476 mbar
= 0.06804596 atm = 51.7149 Torr
= 0.0703070 kgf/cm² = 0.703070 mH2O = 144 PSF
1 Atmosphere 1 atm = 101,325 Pa = 101.325 kPa = 0.101325 MPa
= 1.01325 bar = 1013.25 mbar
= 14.6959 PSI = 760 Torr = 1.03323 kgf/cm²
1 Torr (mmHg) 1 Torr = 133.322387 Pa = 0.133322 kPa
= 0.00133322 bar = 1.33322 mbar
= 0.0193368 PSI = 0.00131579 atm
1 kgf/cm² 1 kgf/cm² = 98,066.5 Pa = 98.0665 kPa
= 0.980665 bar = 980.665 mbar
= 14.2233 PSI = 0.96784 atm = 10 mH2O
1 mH2O 1 mH2O = 9,806.65 Pa = 9.80665 kPa
= 0.0980665 bar = 98.0665 mbar
= 1.42233 PSI = 0.096784 atm = 0.1 kgf/cm²
1 KSI 1 KSI = 6,894,757.29 Pa = 6.89476 MPa = 68.9476 bar
= 1,000 PSI = 68.0460 atm = 70.3070 kgf/cm²
1 PSF 1 PSF = 47.8802589 Pa = 0.000478803 bar
= 0.00694444 PSI = 0.000472541 atm
1 kPa 1 kPa = 1,000 Pa = 0.01 bar = 0.145038 PSI
1 MPa 1 MPa = 1,000,000 Pa = 10 bar = 145.038 PSI
1 mbar 1 mbar = 100 Pa = 0.001 bar = 0.0145038 PSI = 1 hPa

Pressure Unit Definitions

Pascal (Pa) - SI Base Unit

The SI unit of pressure, defined as one Newton per square meter (1 N/m²). Named after French mathematician Blaise Pascal.

Exact Definition: 1 Pa = 1 kg·m⁻¹·s⁻² = 1 N/m²

To Bar: P_bar = P_Pa / 100,000

To PSI: P_psi = P_Pa / 6,894.75729

To atm: P_atm = P_Pa / 101,325

To Torr: P_torr = P_Pa / 133.322387415

To kgf/cm²: P_kgf = P_Pa / 98,066.5

To mH2O: P_mH2O = P_Pa / 9,806.65

Bar - Metric Standard

A metric unit exactly equal to 100,000 Pascals. Approximately equal to atmospheric pressure at sea level.

Exact Value: 1 bar = 10⁵ Pa = 0.1 MPa

To Pascal: P_Pa = P_bar × 100,000

To PSI: P_psi = P_bar × 14.503773773

To atm: P_atm = P_bar / 1.01325

To Torr: P_torr = P_bar × 750.0618

To kgf/cm²: P_kgf = P_bar × 1.01972

To mH2O: P_mH2O = P_bar × 10.1972

Standard Atmosphere (atm)

Defined as exactly 101,325 Pascals. Represents average atmospheric pressure at sea level.

Exact Definition: 1 atm = 101,325 Pa = 1.01325 bar

To Pascal: P_Pa = P_atm × 101,325

To Bar: P_bar = P_atm × 1.01325

To PSI: P_psi = P_atm × 14.6959

To Torr: P_torr = P_atm × 760

To kgf/cm²: P_kgf = P_atm × 1.03323

To mH2O: P_mH2O = P_atm × 10.3323

PSI (Pounds per Square Inch)

Imperial unit commonly used in the United States for tire pressure, compressed air systems, and industrial applications.

Conversion: 1 PSI = 6,894.75729 Pa (exact)

To Pascal: P_Pa = P_psi × 6,894.75729

To Bar: P_bar = P_psi / 14.503773773

To atm: P_atm = P_psi / 14.6959487755

To Torr: P_torr = P_psi × 51.71492564

To kgf/cm²: P_kgf = P_psi × 0.0703069579639

To KSI: P_ksi = P_psi ÷ 1,000

To mH2O: P_mH2O = P_psi × 0.7030695796

Torr / mmHg

Units based on mercury column height. 1 Torr = 1 mmHg exactly. Named after Evangelista Torricelli.

Definition: 1 Torr = 1/760 atm = 133.322387415 Pa

To Pascal: P_Pa = P_torr × 133.322387415

To Bar: P_bar = P_torr / 750.0618

To atm: P_atm = P_torr / 760

To PSI: P_psi = P_torr / 51.71492564

To kgf/cm²: P_kgf = P_torr / 735.5591579

To mH2O: P_mH2O = P_torr / 73.55591579

kgf/cm² (Technical Atmosphere)

Engineering unit equal to one kilogram-force per square centimeter. Widely used in automotive and industrial applications.

Conversion: 1 kgf/cm² = 98,066.5 Pa = 0.980665 bar

To Pascal: P_Pa = P_kgf × 98,066.5

To Bar: P_bar = P_kgf × 0.980665

To atm: P_atm = P_kgf ÷ 1.03323

To PSI: P_psi = P_kgf × 14.2233

To Torr: P_torr = P_kgf × 735.559

To mH2O: P_mH2O = P_kgf × 10

mH2O (Meters Water Column)

Hydraulic pressure unit representing the pressure exerted by a column of water at 4°C under standard gravity.

Standard Value: 1 mH2O = 9,806.65 Pa = 0.0980665 bar

To Pascal: P_Pa = P_mH2O × 9,806.65

To Bar: P_bar = P_mH2O × 0.0980665

To atm: P_atm = P_mH2O ÷ 10.3323

To PSI: P_psi = P_mH2O × 1.42233

To Torr: P_torr = P_mH2O × 73.5559

To kgf/cm²: P_kgf = P_mH2O ÷ 10

Additional Units

Kilopascal (kPa):

• To Pascal: P_Pa = P_kPa × 1,000

• To Bar: P_bar = P_kPa ÷ 100

• To PSI: P_psi = P_kPa × 0.145038

Megapascal (MPa):

• To Pascal: P_Pa = P_MPa × 1,000,000

• To Bar: P_bar = P_MPa × 10

• To PSI: P_psi = P_MPa × 145.038

Millibar (mbar):

• To Pascal: P_Pa = P_mbar × 100

• To Bar: P_bar = P_mbar ÷ 1,000

• To PSI: P_psi = P_mbar × 0.0145038

KSI (Thousand PSI):

• To Pascal: P_Pa = P_ksi × 6,894,757.29

• To PSI: P_psi = P_ksi × 1,000

• To Bar: P_bar = P_ksi × 68.9475729

PSF (Pounds per Square Foot):

• To Pascal: P_Pa = P_psf × 47.8802589

• To PSI: P_psi = P_psf / 144

• To Bar: P_bar = P_psf × 0.000478802589

Complete List of Supported Pressure Units

1. Pascal (Pa) - SI Base Unit

Definition: One newton per square meter (1 N/m² = 1 kg·m⁻¹·s⁻²)

Conversion Factor: 1 Pa = 1 Pa (base unit)

Common Usage: Scientific calculations, meteorology, material science

Typical Range: Small pressures, sound pressure levels (20 µPa to 100 Pa)

Named After: Blaise Pascal (1623-1662), French mathematician and physicist

2. Kilopascal (kPa)

Definition: 1,000 Pascals

Conversion Factor: 1 kPa = 1,000 Pa

Common Usage: Weather forecasting, automotive specifications, building codes

Typical Range: Atmospheric pressure (80-110 kPa), tire pressure (150-250 kPa)

Advantage: More practical size than Pa for everyday engineering applications

3. Megapascal (MPa)

Definition: 1,000,000 Pascals (1 million Pa)

Conversion Factor: 1 MPa = 1,000,000 Pa = 10 bar

Common Usage: Material strength testing, hydraulic systems, gas cylinders

Typical Range: Concrete strength (20-50 MPa), hydraulic pressure (10-70 MPa)

Note: Commonly used in structural and mechanical engineering

4. Bar

Definition: Exactly 100,000 Pascals

Conversion Factor: 1 bar = 100,000 Pa = 0.1 MPa

Common Usage: European industry standard, scuba diving, meteorology

Typical Range: Atmospheric pressure (~1 bar), industrial systems (1-300 bar)

Practical Note: Nearly equal to atmospheric pressure at sea level (1.01325 bar)

5. Millibar (mbar)

Definition: One-thousandth of a bar

Conversion Factor: 1 mbar = 100 Pa = 0.001 bar

Common Usage: Meteorology, weather maps, barometric pressure readings

Typical Range: Weather systems (950-1050 mbar), vacuum systems (0.01-1000 mbar)

Note: 1 mbar = 1 hPa (hectopascal), commonly used in aviation

6. Standard Atmosphere (atm)

Definition: Exactly 101,325 Pa by international agreement

Conversion Factor: 1 atm = 101,325 Pa = 1.01325 bar

Common Usage: Chemistry, physics, gas law calculations

Typical Range: Sea level (1 atm), diving depths (1-10 atm)

Historical Note: Based on average atmospheric pressure at sea level and 15°C

7. Torr

Definition: 1/760 of standard atmosphere

Conversion Factor: 1 Torr = 133.322387415 Pa = 1/760 atm

Common Usage: Vacuum technology, vapor pressure measurements

Typical Range: High vacuum (10⁻⁹ to 10⁻³ Torr), rough vacuum (1-760 Torr)

Named After: Evangelista Torricelli (1608-1647), inventor of the barometer

8. Millimeters of Mercury (mmHg)

Definition: Pressure exerted by 1 mm column of mercury at 0°C and standard gravity

Conversion Factor: 1 mmHg = 133.322387415 Pa (exactly equal to 1 Torr)

Common Usage: Medical blood pressure, vacuum gauges, manometers

Typical Range: Blood pressure (80-120 mmHg), atmospheric (760 mmHg at sea level)

Medical Standard: Universal unit for blood pressure measurements worldwide

9. Pounds per Square Inch (PSI)

Definition: Force of one pound-force applied to one square inch

Conversion Factor: 1 PSI = 6,894.75729 Pa = 0.0689476 bar

Common Usage: US automotive industry, tire pressure, compressed air systems

Typical Range: Car tires (30-35 PSI), hydraulic systems (1000-5000 PSI)

Regional Note: Primary pressure unit in the United States

10. Kilopounds per Square Inch (KSI)

Definition: 1,000 pounds-force per square inch

Conversion Factor: 1 KSI = 6,894,757.29 Pa = 6.89476 MPa

Common Usage: Material strength specifications, structural engineering

Typical Range: Steel strength (30-200 KSI), concrete (3-10 KSI)

Application: Common in US civil and mechanical engineering specifications

11. Pounds per Square Foot (PSF)

Definition: Force of one pound-force applied to one square foot

Conversion Factor: 1 PSF = 47.8802589 Pa (1 PSF = 1/144 PSI)

Common Usage: Building loads, wind pressure, floor loading specifications

Typical Range: Wind loads (10-50 PSF), floor loads (40-150 PSF)

Advantage: More appropriate scale for distributed loads in construction

12. Kilogram-force per Square Centimeter (kgf/cm²)

Definition: Pressure from one kilogram-force over one square centimeter

Conversion Factor: 1 kgf/cm² = 98,066.5 Pa = 0.980665 bar

Common Usage: Automotive industry, hydraulics in Europe and Asia

Typical Range: Engine oil pressure (3-7 kgf/cm²), hydraulics (100-700 kgf/cm²)

Also Known As: Technical atmosphere (at), metric atmosphere

13. Meters of Water Column (mH2O)

Definition: Pressure from a 1-meter column of water at 4°C under standard gravity

Conversion Factor: 1 mH2O = 9,806.65 Pa = 0.0980665 bar

Common Usage: Water distribution systems, HVAC, hydrostatic testing

Typical Range: Water towers (10-50 mH2O), pump heads (5-100 mH2O)

Calculation: P = ρ × g × h, where ρ = 1000 kg/m³, g = 9.80665 m/s²

Unit Selection Guide

When to Use SI Units (Pa, kPa, MPa, bar)

Pascal (Pa): Small pressures, acoustics, scientific research

Kilopascal (kPa): General engineering, automotive, weather reports (outside US)

Megapascal (MPa): Material properties, high-pressure systems, structural analysis

Bar/Millibar: Industrial processes, meteorology, scuba diving, European standards

When to Use Imperial Units (PSI, KSI, PSF)

PSI: US automotive, tire pressure, air compressors, industrial gauges

KSI: Material specifications in US construction and manufacturing

PSF: Building codes, structural loads, wind and snow loads in US

When to Use Specialized Units

Atmosphere (atm): Chemistry, thermodynamics, gas law problems

Torr/mmHg: Vacuum systems, medical applications, vapor pressure

kgf/cm²: Older European/Asian automotive and hydraulic specifications

mH2O: Water systems, pump specifications, low-pressure hydraulics

Scientific Applications

Fluid Mechanics

Bernoulli's Equation: P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

Used in pipe flow analysis, pump design, and hydraulic systems.

Thermodynamics

Vapor Pressure: Critical for distillation, HVAC design, and phase change calculations.

Compressor Design: Pressure ratios determine compression work and efficiency.

Structural Engineering

Wind Load: P_wind = ½ρv²C_p (dynamic pressure calculation)

Soil Pressure: Foundation design and bearing capacity analysis.

Process Engineering

Reactor Design: Pressure drop calculations across catalyst beds.

Safety Systems: Relief valve sizing and pressure vessel design.

Geotechnical Engineering

Pore Water Pressure: P_pore = γ_w × h_w

Effective Stress: σ' = σ_total - u (where u = pore pressure)

Environmental Engineering

Atmospheric Modeling: Pressure gradient calculations for weather prediction.

Water Treatment: Membrane filtration and reverse osmosis pressure requirements.

Measurement Considerations

Gauge vs Absolute Pressure

Gauge Pressure: Measured relative to atmospheric pressure (P_gauge = P_absolute - P_atmospheric)

Absolute Pressure: Measured relative to perfect vacuum

Critical for: Gas law calculations, vapor pressure determinations, vacuum systems

Temperature Dependency

Vapor Pressure: Increases exponentially with temperature (Antoine equation)

Gas Pressure: Directly proportional to absolute temperature (Gay-Lussac's Law)

Liquid Pressure: Density changes with temperature affect hydrostatic calculations

Accuracy and Precision

Measurement Uncertainty: Consider instrument calibration and environmental effects

Significant Figures: Match precision to measurement capability and application requirements

Standard Conditions: Always specify temperature and reference conditions

Fundamental Pressure Equations

Basic Pressure Definition

P = F/A

Where: P = pressure, F = force, A = area

Hydrostatic Pressure

P = ρgh

Where: ρ = fluid density, g = gravitational acceleration, h = height

Ideal Gas Law (Pressure)

P = nRT/V

Where: n = moles, R = gas constant, T = temperature, V = volume

Gauge vs Absolute Pressure

P_absolute = P_gauge + P_atmospheric

P_atmospheric ≈ 101.325 kPa at sea level