Unit Conversion • Calculator

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).

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Last Updated: September 2026
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BIPM SI • ISO 80000-4 • NIST SP 811 Legal Standards Verified
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Pressure Configuration

1 Pa = 1 N/m² = 1 kg/(m⋅s²) • SI Standard
Dimensional Force/Area Constant

Loading pressure ratio...

Physical Pressure Benchmarks Order of Magnitude
Dollar bill resting flat on table: ~1 Pascal (1 N/m²)
Standard Sea-Level Atmosphere: 101,325 Pa (14.70 PSI / 1.013 bar)
Normal Human Blood Pressure: 120 / 80 mmHg (16.0 / 10.7 kPa)
Passenger Car Tire Inflation: 32–36 PSI (2.2–2.5 bar gauge)
Scuba Diving Tank (Full): 3,000 PSI (207 bar / 20.7 MPa)
Bottom of Mariana Trench (11 km): ~1,086 bar (15,750 PSI / 108.6 MPa)
Earth Inner Core Boundary: ~330–360 GPa (~3.3M atm)
Evaluated Pressure Measurement
-- PSI

1 Bar = 14.5038 PSI

SI Pressure: -- Pascals (N/m²) Atmospheric: -- atm

Gauge Pressure vs. Absolute Pressure Analyzer

Accounting for 1.00 atm ambient sea-level barometric pressure
PSIG vs PSIA
Gauge Reading (Relative) -- psig Pressure relative to atmosphere
Ambient Atmosphere 14.70 psia (1.013 bar) Standard sea-level 1 atm
True Absolute Pressure -- psia P_abs = P_gauge + P_atm

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)
-- Meters
Water Column Depth -- meters Seawater density 1025 kg/m³
Imperial Depth -- feet 1 atm ≈ 33 feet seawater
Submersion Zone Surface Tier Oceanographic biome

Step-by-Step Conversion Arithmetic

1. Normalize Source to SI Base Pascals: ...
2. Divide by Target Unit Constant: ...
3. Final Evaluated Pressure: ...

Simultaneous Multi-Unit Pressure Grid

Real-time converted values across all 16 major SI metric, barometric, manometric, and imperial pressure standards

Live Synchronized
Direct Answer & Overview
Verified Educational Guide

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.

Primary Mathematical Formula Standard Mathematical Model
Standard Equation
ƒ(x)
Q.E.D.
1 bar=105 Pa,1 atm=101,325 Pa=14.696 PSI,1 PSI≈6,894.76 Pa1\text{ bar} = 10^{5}\text{ Pa}, \quad 1\text{ atm} = 101{,}325\text{ Pa} = 14.696\text{ PSI}, \quad 1\text{ PSI} \approx 6{,}894.76\text{ Pa}
Evaluated with exact mathematical formulation • Rigorously verified
Exact Formula
Input Parameters
Required
1
Known pressure magnitude and originating unit (Pa, Bar, PSI, atm, Torr, mmHg)
2
Measurement mode: Absolute Pressure (psia) vs Gauge Pressure (psig, adding 1 atm ambient)
3
Hydrostatic fluid parameters (fluid density ρ and fluid column depth h)
Expected Outputs
Calculated
Instant multi-unit converted values across 10+ standard international engineering units
Hydrostatic ocean & fluid depth equivalent in meters and feet
Vacuum and altitude barometric reference (Torr, inHg, standard atmospheres)
Worked Numerical Example
Instant Verification
Convert 35.0 PSI (typical automotive tire pressure) to Bar and kPa
→ 35.0 PSI × 6,894.757 Pa/PSI = 241,316.5 Pa. In Bar: 241,316.5 ÷ 100,000 = 2.413 Bar. In kPa: 241.32 kPa.
35.0 PSI = 2.413 Bar = 241.32 kPa

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. Dimensional Definition
P = F / A

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.

2. Volumetric Energy Density
1 Pa = 1 J / m³

Pressure also represents energy stored per unit volume of fluid: 1 N/m² = 1 (N⋅m) / m³ = 1 Joule per cubic meter.

3. Engineering Prefixes
kPa, MPa & GPa

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:

Standard Atmosphere (1 atm) Physical Equivalence:
1 atm = 101,325 Pascals (Exact) = 101.325 kPa
1 atm = 1.01325 Bar = 1,013.25 Millibars (mbar / hPa)
1 atm = 14.6959488 Pounds per square inch (PSI)
1 atm = 760.000 Millimeters of Mercury (0°C) = 760 Torr
1 atm = 29.9213 Inches of Mercury (inHg at 32°F)

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:

Recreational Scuba (40m)

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.

Mariana Trench (11,000m)

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.

Earth's Inner Core

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

Problem 1 • Tire Gauge Pressure to Bar & kPa PSI to Bar and kPa

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

Problem 2 • Aviation Altimeter Setting inHg to hPa (QNH)

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.

Fact-Checked & Verified • Computational Accuracy Standards
Updated September 2026 • Editorial Policy
Authored By
Sanjay Samanta

Lead Developer & Founder of Basic Math Tools. Specializes in browser-native computational algorithms and applied mathematics.

Reviewed & Verified By
Academic Review Board

Mathematics & curriculum specialists. Audited against standard algebraic and arithmetic principles.

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Frequently Asked Questions

What is the official SI definition of the Pascal (Pa)?
In the International System of Units (SI), the Pascal (symbol Pa) is the coherent derived unit of pressure, mechanical stress, and Young's modulus. It is defined as a perpendicular force of one Newton distributed uniformly across a planar area of one square meter (1 Pa = 1 N/m²). In SI base units, 1 Pa = 1 kg·m⁻¹·s⁻². Because one Pascal represents a very gentle force (approximately the pressure exerted by a single US dollar bill lying flat on a table), industrial engineering and materials science typically use Kilopascals (1 kPa = 1,000 Pa) or Megapascals (1 MPa = 1,000,000 Pa = 1 N/mm²).
What is the difference between Gauge Pressure (psig) and Absolute Pressure (psia)?
Absolute Pressure (psia) is measured relative to a perfect, complete vacuum (zero absolute pressure). Gauge Pressure (psig) is measured relative to local ambient atmospheric pressure (approximately 14.70 psi or 1.013 bar at sea level). The relationship is: Absolute Pressure = Gauge Pressure + Atmospheric Pressure. For example, when an automotive tire gauge reads 32.0 psig, the actual absolute gas pressure pressing against the inner tire wall is approximately 46.7 psia (3.22 bar absolute).
How is one Standard Atmosphere (atm) defined, and how does it relate to Bar?
At the 10th General Conference on Weights and Measures (CGPM) in 1954, standard atmospheric pressure was legally fixed at exactly 101,325 Pascals (101.325 kPa), equivalent to 1.01325 bar or 14.69595 PSI. One Bar is defined independently by metric conventions as exactly 100,000 Pascals (100 kPa). Consequently, 1 atm is approximately 1.325% greater than 1 bar (1 atm = 1.01325 bar).
Why is human blood pressure measured in millimeters of mercury (mmHg)?
Historical sphygmomanometers invented in the late 19th century used a vertical glass column containing liquid mercury (Hg). When the arm cuff inflated, arterial pressure pushed the heavy mercury column upward against gravity. Because mercury is 13.6 times denser than water, it requires only a compact 300 mm column rather than a 4-meter water tube. A standard clinical reading of '120 over 80 mmHg' corresponds to 16.0 kPa systolic and 10.7 kPa diastolic pressure above atmospheric ambient.
What is the difference between Torr and mmHg?
While often used interchangeably in clinical medicine, Torr and mmHg have subtle technical distinctions. The millimeter of mercury (mmHg) is a hydrostatic unit defined by mercury's density at 0°C under standard gravity (1 mmHg = 133.322387415 Pa). In 1954, the Torr (named after Evangelista Torricelli, inventor of the barometer) was redefined strictly as exactly 1/760 of a standard atmosphere: 1 Torr = 101,325 / 760 Pa ≈ 133.322368421 Pa. The fractional divergence is less than 0.000014%, making them practically identical for all but high-vacuum metrology.
How much pressure increases as you dive deeper underwater in the ocean?
Under the hydrostatic equation (P = ρgh), pressure in an incompressible fluid increases linearly with depth. Dense seawater has an average density (ρ) of approximately 1,025 kg/m³. Under Earth gravity (9.80665 m/s²), water weight exerts an additional 10,052 Pascals per meter of depth. Therefore, pressure increases by approximately 1 atmosphere (1.013 bar or 14.7 psi) for every 10.06 meters (33.0 feet) of ocean depth. At 30 meters (recreational scuba limit), divers experience roughly 4.0 atm total absolute pressure.
Why do meteorologists and pilots use hectopascals (hPa) and inches of mercury (inHg)?
In global meteorology and aviation, atmospheric pressure governs barometric altimetry. The hectopascal (1 hPa = 100 Pa) is numerically identical to the traditional millibar (1 mbar = 1 hPa = 0.001 bar), allowing seamless transition to SI units. Standard sea-level pressure is 1013.25 hPa. In US aviation weather reports (METAR), barometric pressure is reported in inches of mercury (inHg), where 1013.25 hPa translates to 29.92 inHg (the standard aircraft altimeter QNH setting).