Why is 1 bar equal to 14.5037738 psi rather than rounded 14.5 psi?

By international SI definition, 1 bar = 100,000 Pa (exact) and 1 psi = 6,894.757293 Pa (exact). Dividing yields \(100,000 / 6,894.757293 = 14.5037738...\). Using the rounded shortcut 14.5 psi introduces a 0.026% error, which creates significant cumulative volume and custody transfer billing discrepancies in high-pressure gas headers (e.g. at 100 bar, 14.5 yields 1,450 psi instead of the true 1,450.38 psi).

How does fluid temperature affect the conversion between m³/h and kg/h?

Volumetric flow rate \(Q\) and mass flow rate \(\dot{m}\) are linked by fluid density (\(\dot{m} = Q \times \rho\)). Water density is 1,000 kg/m³ at 4 °C, but expands to 998.2 kg/m³ at 20 °C, 958.4 kg/m³ at 100 °C, and 887.0 kg/m³ at 180 °C. Converting \(100\text{ m}^3/\text{h}\) of hot boiler feedwater at 180 °C produces 88,700 kg/h, not 100,000 kg/h.

Why is the US gallon different from the UK Imperial gallon?

A US liquid gallon is historically defined as 231 cubic inches = 3.785411784 liters. A UK Imperial gallon is defined as the volume of 10 pounds of distilled water at 62 °F = 4.54609 liters. A UK gallon is 20.1% larger than a US gallon. Control valve and pump sizing datasheets from US manufacturers universally use US GPM.

Dimension Quick Engineering Unit Converter | ASME & API Calculations

Engineering Reference & ASME Code Basis

1. Core Formula & Variable Definitions

ISO 80000-1 (Quantities and Units - General) · NIST SP 811 (Guide for the Use of the International System of Units) · ASME B31.3 (2022 Edition) · / B16.5 (Engineering Units and Conversion Conventions) · ASTM E380 / IEEE SI 10 (American National Standard for Metric Practice)

P_psi = P_bar × 14.5037738 · T_°F = T_°C × 1.8 + 32 · L_mm = L_in × 25.4

1 ft·lb = 1.355817948 N·m · 1 m³/h = 4.402867655 GPM · ṁ = Q × ρ

ISO 80000-1 Quantities and Units & NIST Special Publication 811 Guide for SI

1 bar 14.5037738 psi (10⁵ Pa)1 inch 25.4 mm (Exact)1 ft·lb 1.355818 N·m1 m³/h 4.402868 US GPM

Precision engineering conversions follow ISO 80000-1 and NIST SP 811 authoritative standards. 1 bar is defined as exactly 100,000 Pa (100 kPa / 0.1 MPa). Exact standard inch-millimetre relationship is defined as 1 in = 25.4 mm (International Yard and Pound Agreement of 1959). Fluid volumetric and mass flow conversions use fluid density ρ at flowing reference temperature (default 1,000 kg/m³ for water).

P (Pressure Conversion) — 1 bar = 14.5037738 psi = 0.10 MPa = 100 kPa = 1.019716 kgf/cm².
T (Temperature Conversion) — T(°F) = 1.8·T(°C) + 32; T(K) = T(°C) + 273.15; T(°R) = T(°F) + 459.67.
L (Length / Dimension) — 1 inch = 25.4 mm (exact); 1 foot = 0.3048 m; 1 meter = 39.3700787 inches.
τ (Torque Conversion) — 1 ft·lb = 1.355817948 N·m; 1 N·m = 0.737562149 ft·lb; 1 kgf·m = 9.80665 N·m.
Q / ṁ (Volumetric & Mass Flow) — 1 m³/h = 4.402867655 US GPM; Mass flow ṁ (kg/h) = Q (m³/h) × ρ (kg/m³).
ρ (Fluid Reference Density) — Density used for mass-to-volumetric flow rate translation (kg/m³ or lb/ft³).

2. Allowances, Tolerances & Standards

Field engineering calculations require strict differentiation between gauge and absolute pressures, standard vs normal gas volumes, and preservation of significant digits.

Gauge vs Absolute Pressure (barg vs bara)P_abs = P_gauge + P_atm (1.01325 bar / 14.696 psi)

Pressure gauges read zero at atmospheric ambient. Thermodynamic gas calculations (ideal gas law, compressor sizing) require absolute pressure (bara / psia); hydraulic piping calculations use gauge pressure (barg / psig).

Gas Flow Standard Reference ConditionsNormal (Nm³/h @ 0 °C) vs Standard (Sm³/h / SCFM @ 15 °C or 60 °F)

Normal m³/h (Nm³/h) is referenced to 0 °C (273.15 K) and 1.01325 bar abs per DIN/ISO. Standard m³/h (Sm³/h) is referenced to 15 °C (288.15 K) per ISO 13443. Standard Cubic Feet per Minute (SCFM) uses 60 °F and 14.696 psia.

US Gallon vs UK Imperial Gallon1 US Gallon = 3.7854 L vs 1 UK Gal = 4.5461 L (+20.1%)

American plant nameplates (GPM) refer to US gallons (231 in³ / 3.7854 L). UK / Commonwealth legacy documentation often cites Imperial gallons (4.5461 L); confusing the two leads to a 20.1% flow sizing error.

Rounding & Significant Digit PracticeMaintain 6 Digits in Engines, 2–3 in Reports

All internal conversion arithmetic must use double-precision IEEE-754 factors. Final engineering deliverable reports round pressure to 1 decimal place (bar) or whole number (psi), and thickness to 2 decimal places (mm).

Quick Reference Lookup Table

Pressure quick reference — bar to psi, MPa, and kgf/cm²
Input	psi	MPa	kgf/cm²
1 bar	14.504	0.10	1.0197
5 bar	72.519	0.50	5.0986
10 bar	145.038	1.00	10.1972
20 bar	290.075	2.00	20.3943
50 bar	725.189	5.00	50.9858
100 bar	1450.377	10.00	101.9716

1 bar = 14.5037738 psi = 0.1 MPa = 1.019716 kgf/cm². Screening values; use the live converter for other magnitudes.

3. Material & Code Limitations

Unit conversions involving material properties (thermal expansion, elasticity, density) depend on physical temperature baselines and reference states.

Material Group	Temperature Range	Allowable Stress / Limit	Engineering Notes
Stress & Elastic Modulus Units	1 MPa = 1 N/mm² = 10 bar = 145.0377 psi = 0.145038 ksi	Standard ASME Section II-D Conversion	SI structural stress is expressed in MPa (N/mm²); US customary is ksi (1,000 psi).
Thermal Expansion Coefficient (α)	1 × 10⁻⁶ /°C = 0.555556 × 10⁻⁶ /°F (Factor 5/9)	Linear Thermal Strain Rate	Converting thermal expansion coefficients between °C and °F requires multiplying by 5/9 (1.8 inverse).
Liquid Density vs Specific Gravity	SG = ρ_fluid / ρ_water @ 4 °C (1,000 kg/m³ / 62.428 lb/ft³)	Dimensionless Density Ratio	In pump hydraulic calculations, water density shifts from 1,000 kg/m³ at 4 °C to 998 kg/m³ at 20 °C and 958 kg/m³ at 100 °C.
Energy, Power & Heat Rate	1 kW = 1.341022 HP = 3,412.142 BTU/hr = 859.845 kcal/hr	Equipment Mechanical Power	Pump brake horsepower (BHP) and heat exchanger duty conversions across international project consortiums.

Code Applicability & Safety Boundaries

Prohibition of Dual-Unit Mixing in Governing Formulas: Never mix metric and imperial units within a single empirical code formula (e.g. ASME B31.3 wall thickness or API RP 14E erosion); convert all inputs to the formula's native unit system before evaluation.
Absolute Zero Temperature Conversion: When performing thermodynamic gas volume or expansion calculations, always convert to absolute Rankine (°R = °F + 459.67) or Kelvin (K = °C + 273.15).
Torque Wrench Scaling Verification: When calibrating pneumatic or hydraulic torque tools, verify whether torque charts cite N·m, ft·lb, or kgf·m to prevent over-torquing flange studs by 35% (1 ft·lb ≈ 1.356 N·m).

4. Step-by-Step Worked Example

Field Verification

Convert an overseas piping data sheet for a high-pressure pump system: internal design pressure P = 35.0 bar gauge, design temperature T = 180.0 °C, volumetric flow rate Q = 150.0 m³/h (water at 180 °C, density ρ = 887.0 kg/m³), and stud bolt tightening torque τ = 450 N·m into US Customary engineering units (psig, °F, US GPM, lb/hr mass flow, and ft·lb torque).

Gauge Pressure (P):35.0 bar gauge (barg)Design Temperature (T):180.0 °CVolumetric Flow (Q):150.0 m³/hFluid Density (ρ @ 180 °C):887.0 kg/m³ (Hot Boiler Feedwater)Bolt Assembly Torque (τ):450.0 N·m

Convert Pressure from bar to psig

Formula: P_{\text{psig}} = P_{\text{bar}} · 14.5037738

P_psig = 35.0 × 14.5037738 = 507.632 psi gauge.

Result:P = 507.6\text{ psig} (3.50\text{ MPa / 35.7 kgf/cm}^2)

Standard Class 300 pressure range.

Convert Temperature from °C to °F

Formula: T_{^{\circ}\text{F}} = T_{^{\circ}\text{C}} · 1.8 + 32

T_°F = (180.0 × 1.8) + 32 = 324.0 + 32 = 356.0 °F (Absolute T = 453.15 K / 815.67 °R).

Result:T = 356.0\text{ }^{\circ}\text{F}

Exact conversion without rounding errors.

Convert Volumetric Flow Rate from m³/h to US GPM

Formula: Q_{\text{GPM}} = Q_{\text{m}^3/\text{h}} · 4.402867655

Q_GPM = 150.0 × 4.402867655 = 660.430 US gpm.

Result:Q = 660.4\text{ US GPM} (41.67\text{ L/s})

Based on 1 US gallon = 3.785411784 L.

Calculate Mass Flow Rate in kg/h and Convert to lb/hr

Formula: \dot{m}_{\text{kg/h}} = Q · \rho,\quad \dot{m}_{\text{lb/hr}} = \dot{m}_{\text{kg/h}} · 2.20462262

Mass flow = 150.0 m³/h × 887.0 kg/m³ = 133,050 kg/h. In US pounds: 133,050 × 2.20462262 = 293,325.04 lb/hr.

Result:\dot{m} = 133,050\text{ kg/h} = 293,325\text{ lb/hr}

Density at 180 °C (887 kg/m³) accounts for thermal liquid expansion.

Convert Bolt Assembly Torque from N·m to ft·lb

Formula: \tau_{\text{ft}\cdot\text{lb}} = \tau_{\text{N}\cdot\text{m}} · 0.737562149

τ_ft·lb = 450.0 × 0.737562149 = 331.903 ft·lb (or 450 / 1.355817948 = 331.903 ft·lb).

Result:\tau = 331.9\text{ ft}\cdot\text{lb} (45.89\text{ kgf}\cdot\text{m})

Directly dial into torque wrench calibration certificate.

Conclusion: The converted process operating conditions are 507.6 psig design pressure, 356.0 °F design temperature, 660.4 US GPM volumetric flow (293,325 lb/hr mass flow), and 331.9 ft·lb stud bolt makeup torque, fully verified against ISO 80000-1 and NIST standards.

5. Code Limitations & FAQ

barg (bar gauge) is the pressure relative to local atmospheric pressure (gauges read 0.0 at sea level). bara (bar absolute) is the total pressure relative to a perfect absolute vacuum (\(P_{\text{abs}} = P_{\text{gauge}} + 1.01325\text{ bar}\) at sea level). Process piping design pressures on P&IDs and datasheets are almost universally gauge pressures (barg / psig), while thermodynamic thermodynamic gas expansion formulas require absolute pressures (bara / psia).