Skip to main content
0 results ↑ ↓ navigate, ↵ select

Pascal to Bar (Pa to bar) Conversion Calculator & Formula

Rate this converter 0 of 0 ratings
Live Conversion • ISO 80000-4:2019 Certified
1 Pascal = 1 × 10⁻⁵ Bar
1 Pa = 1 × 10⁻⁵ bar • 1 bar = 100000 Pa
Pascal to Bar: One Pascal is equal to 1 × 10⁻⁵ Bars.
Certified Authority Value
0.00001000
bar
Exact: 1 bar ≡ 100000 Pa
Pa
Pa
Swap to Bar to Pascal
bar
bar 1 × 10⁻⁵
Quick Values:
1 Pa 5 Pa 10 Pa 25 Pa 50 Pa 100 Pa 250 Pa 500 Pa 1,000 Pa
Conversion Formula
To convert Pascal to Bar, multiply by 1 × 10⁻⁵
Pa × 1 × 10⁻⁵ = bar

Calculation: 1 Pa × 1 × 10⁻⁵ = 1 × 10⁻⁵ bar

Common Pascal to Bar Calculations

Quick-lookup reference table showing calculated equivalents for standard increments between Pascal (Pa) and Bar (bar).

Tap any row to calculate
Bar to Pascal: Reciprocal Summary
Bar to Pascal Conversion Reference Table
Reciprocal & Equivalent Value Scientific Notation
1 bar is equal to 100000 Pa (Pascal) 1 × 10⁵
5 bar is equal to 500000 Pa (Pascal) 5 × 10⁵
10 bar is equal to 1000000 Pa (Pascal) 1 × 10⁶
50 bar is equal to 5000000 Pa (Pascal) 5 × 10⁶
100 bar is equal to 1 × 10⁷ Pa (Pascal) 1 × 10⁷
View Complete 15-Row Bar to Pascal Table

Real-World Context & Everyday Benchmarks

Tap to load into converter

To help contextualize these units in everyday life, science, and engineering, here are verified real-world reference points for Pascal (Pa) and Bar (bar):

Pascal References:

  • Pressure exerted by a single dollar banknote resting flat on a table 1 Pa
  • Gentle falling winter snowflake landing pressure on surface 1 Pa
  • Quiet rural night ambient acoustic sound pressure wave in air 0.002 Pa

Bar References:

  • Standard atmospheric pressure at sea level (1.01325 bar) 1 bar
  • Commercial espresso machine coffee extraction group head pressure 9 bar
  • Standard scuba diving compressed breathing air cylinder pressure 200 bar
  • Deep ocean floor water pressure at bottom of the Mariana Trench 1086 bar

Tap any benchmark above to automatically calculate its exact equivalent in Bar.

ISQ Dimension: [M L⁻¹ T⁻²] Coherent SI Unit: pascal (Pa) Chemical Engineering, Solutions & Physical Chemistry

How to Convert Pascal to Bar

Converting Pascal (Pa) to Bar (bar) is a core calculation in Pressure and Stress, which measures the perpendicular force exerted by a fluid or contact load per unit surface area. This calculation navigates the boundary between the International Metric System (SI) and British Imperial / US Customary engineering standards. In contemporary metrology, Imperial units are defined in terms of exact SI standards via international agreements—notably NIST SP 811 and the 1959 International Yard and Pound Agreement. Exactly 1 Pascal equals 1 × 10⁻⁵ Bar, while 1 bar equals 100000 Pa.

Direct Factor1 Pa = 1 × 10⁻⁵ bar
Inverse Ratio1 bar = 100000 Pa
Conversion ScaleMetric SI to British Imperial / US Customary Bridge
First-Principles SI Derivation ProofNIST SP 811 / ISO 80000 Compliance

Mathematical Conversion Derivation via Coherent SI Base Unit

Under the International System of Quantities (ISQ), dimensional conversion between non-SI units is rigorously resolved by bridging through the coherent SI base unit (pascal (Pa)) without arbitrary rounding:

Vtarget=Vsource×(ksource→SIktarget→SI)V_{\text{target}} = V_{\text{source}} \times \left( \frac{k_{\text{source} \to \text{SI}}}{k_{\text{target} \to \text{SI}}} \right)
Universal Dimensional Conversion Law (ISO 80000 / NIST SP 811)
1. Source SI Bridge (ksource):1 Pa = 1 pascal (Pa)
2. Target SI Bridge (ktarget):1 bar = 100000 pascal (Pa)
Step-by-step substitution for Pascal → Bar:V(bar) = V(Pa) × ( 1 / 100000 ) = V(Pa) × 1 × 10⁻⁵
Mathematical FormulaValue in Bar = Value in Pascal × 1 × 10⁻⁵Direct computational formula applied for standard conversion.
Worked Example

For an engineering input of 75 Pa, applying the conversion factor yields exactly 0.00075 bar. At larger operational scale, 240 Pascal corresponds to 0.0024 bar.

Inverse check: 1 bar = 100000 Pa.

Understanding Pascal and Bar

Pascal

Pa
Coherent SI Unit

The pascal (Pa) is the coherent SI-derived unit of pressure and mechanical stress, named after Blaise Pascal.

Applications & Practical Context

In practical pressure terms, a pressure exerted by a single dollar banknote resting flat on a table equals 1 Pa, a gentle falling winter snowflake landing pressure on surface equals 1 Pa, a quiet rural night ambient acoustic sound pressure wave in air equals 0.002 Pa.

Physical Setup

A pressure of 1 pascal corresponds to a normal force of 1 newton applied perpendicularly over an area of 1 square meter (roughly the downward pressure of a single sheet of paper lying flat on a desk).

Conversion to SI Unit: pascal (Pa)
1 Pa = 1 N/m² (SI Standard)

Bar

bar
Metric Unit

The bar (bar) is a non-SI metric unit of pressure widely used in meteorology, engineering, and diving.

Applications & Practical Context

In practical pressure terms, a standard atmospheric pressure at sea level (1.01325 bar) equals 1 bar, a commercial espresso machine coffee extraction group head pressure equals 9 bar, a standard scuba diving compressed breathing air cylinder pressure equals 200 bar.

Physical Setup

A pressure of 1 bar is defined as exactly 100,000 pascals (100 kPa), approximating standard Earth atmospheric air pressure at sea level (1.01325 bar).

Conversion to SI Unit: pascal (Pa)
1 bar = 100,000 Pa

Domain Metrology & Engineering Applications

Governing Law & Equation

Pascal's Principle of Fluid Pressure (P = F / A)

Measurement Instrumentation

Rigorously quantified in laboratory and field settings using primary deadweight piston gauges, piezoresistive silicon pressure transmitters, and Bourdon tube test gauges.

Primary Industry Sectors

Applied across aerospace hydraulic flight actuators, oil & gas pipeline monitoring, chemical autoclave pressure safety, and industrial compressed air under international metrology standard ISO 80000-4:2019, NIST SP 811.

Physical Orders of Magnitude & Laboratory Reference Benchmarks

Physical Phenomenon / Engineering ReferenceReference ValueConverted to Bar
Pressure exerted by a single dollar banknote resting flat on a table1 Pa1 × 10⁻⁵ bar
Gentle falling winter snowflake landing pressure on surface1 Pa1 × 10⁻⁵ bar
Quiet rural night ambient acoustic sound pressure wave in air0.002 Pa2 × 10⁻⁸ bar
Institutional Metrology & Standard Authority:

Formulas, conversion coefficients, and base definitions on this page strictly adhere to the ISO 80000-4:2019, NIST SP 811 and the BIPM SI Brochure (9th Edition). Governed by Pascal's Principle of Fluid Pressure (P = F / A) under ISO 80000 dimensional vector [M L⁻¹ T⁻²].

Multi-Variable Engineering Bridge Fluid Power & Contact Mechanics

Hydraulic Cylinder & Contact Force Bridge (kN • lbf • Metric Tons • Bar • PSI • Pascals)

Calculate total thrust, clamp load, or bolt pretension from hydrostatic pressure [M L⁻¹ T⁻²] acting over cross-sectional geometry [L²] via Pascal's hydraulic principle F = P × A.

F = P × A
Live Calculated Bridge Equivalent:
1 Pa at 100mm (4-inch) Standard Industrial Hydraulic Bore = 7.854 × 10⁻⁶ kN
Equals 0.001766 lbf • 8.0088 × 10⁻⁷ t-force • 0.007854 N
Civil & Press Metric
7.854 × 10⁻⁶
kN
Kilonewtons
US Hydraulic Standard
0.001766
lbf
Pounds-Force
Press Capacity
8.0088 × 10⁻⁷
t-force
Metric Tons Force
SI Standard
0.007854
N
Newtons
US Press Rating
8.8282 × 10⁻⁷
ton-force (US)
Short Tons Force
Workshop Standard
0.0008009
kgf
Kilograms-Force
  1. 1. Normalize Input to SI Base Unit (Pa):
    P = 1 Pa × 1 = 1 Pa
  2. 2. Apply Engineering Parameter (A):
    Selected condition: 100mm (4-inch) Standard Industrial Hydraulic Bore at A = 0.007854 m²
  3. 3. Execute Governing Physical Law in SI Units:
    F = P × A = (1) × (0.007854) = 0.007854 N
  4. 4. Convert to Standard Engineering Units:
    • kN: 0.007854 × 0.001 = 7.854 × 10⁻⁶ kN (Kilonewtons) • lbf: 0.007854 × 0.2248 = 0.001766 lbf (Pounds-Force) • t-force: 0.007854 × 0.000102 = 8.0088 × 10⁻⁷ t-force (Metric Tons Force) • N: 0.007854 × 1 = 0.007854 N (Newtons) • ton-force (US): 0.007854 × 0.0001124 = 8.8282 × 10⁻⁷ ton-force (US) (Short Tons Force) • kgf: 0.007854 × 0.102 = 0.0008009 kgf (Kilograms-Force)
Explore Full Area Converter →
Engineering Substance / Operating Standard Parameter Value (m²) Reference State / Condition Typical Industrial & Engineering Application
25mm (1-inch) Micro Pneumatic Bore 0.0004909 Area = π × (0.0125m)² Automation grippers & electronic assembly tooling
50mm (2-inch) Medium Pneumatic Ram 0.001964 Area = π × (0.025m)² Industrial packaging presses & clamping fixtures
100mm (4-inch) Standard Industrial Hydraulic Bore 0.007854 Area = π × (0.05m)² Excavator booms, log splitters & machine shop presses
150mm (6-inch) Heavy Mobile Hydraulic Ram 0.01767 Area = π × (0.075m)² Mining shovels, dump truck lifts & forge actuators
200mm (8-inch) Massive Press Cylinder 0.03142 Area = π × (0.10m)² Automotive body stamping presses & scrap balers
Vehicle Road Contact Patch (4 Car Tires) 0.06 4 × 150 cm² tire patches Total passenger tire road contact footprint
Standard M12 High-Strength Bolt Tensile Area 8.43 × 10⁻⁵ ISO 898-1 stress area 84.3 mm² Flange fastener clamping stress analysis
Standard M20 Structural Bolt Tensile Area 0.000245 Stress area 245 mm² Heavy structural steel framing & anchor rods
1.0 Square Meter Reference Plate Area 1 1.0 m × 1.0 m area Architectural wind load & hydrostatic flood gate
Embed
Need this Pascal to Bar calculator on your website, lab portal, or research blog?
Free HTML Widget 100% Responsive Zero Cookie Tracking
Notice a calculation discrepancy, rounding error, or glitch?
Help us maintain 100% scientific precision and report any issues directly to engineering.

Frequently Asked Questions

There are exactly 1 × 10⁻⁵ bars (bar) in 1 pascal (Pa). To calculate larger amounts manually, simply multiply your total number of pascals by the conversion multiplier of 1 × 10⁻⁵.

The mathematical formula to convert pascals to bars is: [value] * 1 × 10⁻⁵ = bars. Rather than doing the math manually, you can use our high-precision online calculator to process this exact equation instantly without rounding errors.

To perform the reverse calculation from bars back to pascals, you must divide your starting value by 1 × 10⁻⁵. Our bidirectional tool automatically computes this inverse equation the moment you type into the bar input field.

1 Bar is larger than 1 Pascal. Specifically, 1 Pascal equals 1 × 10⁻⁵ bars, meaning 1 Bar is 100000 times larger than 1 Pascal (a difference of 5.00 orders of magnitude). Expressing measurements in pascals requires a larger numerical value to represent the equivalent physical magnitude.

A typical pressure exerted by a single dollar banknote resting flat on a table measures 1 Pa, which corresponds to 1 × 10⁻⁵ bar (Bar).

One Pascal is equal to 1.00000 × 10⁻⁵ bar. Expressed mathematically: 1 Pa = 1.00000 × 10⁻⁵ bar.

To convert a pressure reading from Pascal to Bar, multiply the value in Pa by 1.00000 × 10⁻⁵ (or divide by 100,000). Equation: V(bar) = V(Pa) × 1.00000 × 10⁻⁵.

To calculate Pascals from a Bar measurement, multiply the Bar value by 100,000. The exact inverse calculation is: V(Pa) = V(bar) × 100000.

While the Pascal is the SI base unit of pressure, it is too small for many industrial applications. The Bar (100,000 Pa) is widely used in pneumatics, hydraulics, and atmospheric pressure reporting because it closely approximates atmospheric pressure at sea level.

Similar Categories