Table of Contents
The Complete Engineering Unit Converter Guide
100 GPM at 50 psi = 22.7 m³/h at 3.45 bar
Introduction
Unit conversion is the foundation of engineering communication. Whether you're designing an HVAC system with American equipment specifications, analyzing a European pump curve, or reviewing historical calculations from decades past—the ability to convert between unit systems accurately separates professional engineers from amateurs.
This comprehensive guide serves as your definitive reference. We cover not just conversion tables, but the deep understanding of measurement systems, their origins, and critical nuances that prevent costly errors.
Try our Unit Converter Calculator for instant, accurate conversions. Export your results as a professional PDF report for documentation or client deliverables—a feature you won't find on other engineering tools.
Why Does Unit Conversion Mastery Matter?
Per NIST SP 811 guidelines, consistent unit handling prevents measurement errors that can cascade through engineering calculations. IEEE Standard 260.1 and ISO 80000-1:2022 establish international conventions for quantity symbols and unit notation that ensure unambiguous technical communication.
Field Tip: The most common unit conversion error I encounter in 20+ years of engineering is confusing bar(g) with bar(a). Atmospheric pressure (1.01325 bar) makes a significant difference in vacuum applications and pressure vessel design per ASME BPVC. A tank rated for 10 bar(g) actually experiences 11 bar(a) internally—critical for material stress calculations.
Also watch for US vs UK gallons (3.785 L vs 4.546 L)—a 20% error that's caused expensive equipment mismatches on international projects. I once saw a 50,000 USD fuel system undersized because someone assumed "gallons" meant the same thing in Texas and London.
Reference: ISO 80000-1:2022 Section 3, NIST SP 811 Appendix B, IEEE 260.1
Safety-Critical Applications
A 125 million USD Mars Climate Orbiter was lost in 1999 because one team used metric units while another used imperial. In pressure vessel design, gauge/absolute pressure confusion can lead to catastrophic failure.
These aren't theoretical concerns—they're documented disasters that our engineering team sees reflected in real project specifications every day.
International Collaboration
Modern engineering is global. A project might use German pumps (rated in bar and m³/hr), American chillers (rated in tons and GPM), and Japanese controls (rated in kW and L/min). Seamless conversion isn't optional—it's essential.
Equipment Specification
Manufacturers worldwide use different unit systems. Understanding conversions means you can:
- Compare equipment from different regions accurately
- Verify that installed equipment meets specifications
- Troubleshoot performance issues by checking actual vs rated conditions
Code Compliance
Building codes, safety standards, and specifications often require specific units. ASHRAE uses IP (inch-pound) units, European standards use SI, and many local codes use practical metric variants.
What Are the Three Major Unit Systems?
SI (Système International d'Unités)
The International System of Units is the modern standard, adopted by almost every country except the United States, Myanmar, and Liberia for everyday use.
Seven Base Units:
| Quantity | Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
Key Characteristics:
- Coherent: Derived units follow directly without conversion factors (1 N = 1 kg·m/s²)
- Decimal: Prefixes scale by powers of 10 (kilo = 10³, milli = 10⁻³)
- Universal: Same units worldwide, reducing confusion
Metric (Practical Engineering Units)
While SI is the standard, engineers often use "practical metric" units that are more convenient for everyday calculations:
| SI Unit | Practical Metric | Conversion |
|---|---|---|
| Pascal (Pa) | bar | 1 bar = 100,000 Pa |
| m³/s | m³/hr, L/min | 1 m³/s = 3600 m³/hr |
| Joule (J) | kWh | 1 kWh = 3.6 MJ |
| Kelvin (K) | Celsius (°C) | °C = K - 273.15 |
Imperial/US Customary
Used primarily in the United States and for historical British Commonwealth equipment:
Common Engineering Units:
- Length: inch (in), foot (ft), mile
- Mass: pound (lb), ounce (oz), ton
- Pressure: psi (lb/in²), inches of water (in. wc)
- Power: horsepower (hp), BTU/hr
- Flow: GPM (gallons per minute), CFM (cubic feet per minute)
Important Note: US and UK systems differ for volume:
- US gallon = 3.785 liters
- UK (Imperial) gallon = 4.546 liters
Length Conversions
Complete Conversion Table
| From → To | mm | cm | m | km | in | ft | yd | mile |
|---|---|---|---|---|---|---|---|---|
| 1 mm | 1 | 0.1 | 0.001 | 1×10⁻⁶ | 0.03937 | 0.003281 | 0.001094 | 6.21×10⁻⁷ |
| 1 cm | 10 | 1 | 0.01 | 1×10⁻⁵ | 0.3937 | 0.03281 | 0.01094 | 6.21×10⁻⁶ |
| 1 m | 1000 | 100 | 1 | 0.001 | 39.37 | 3.281 | 1.094 | 6.214×10⁻⁴ |
| 1 km | 1×10⁶ | 1×10⁵ | 1000 | 1 | 39,370 | 3281 | 1094 | 0.6214 |
| 1 in | 25.4 | 2.54 | 0.0254 | 2.54×10⁻⁵ | 1 | 0.08333 | 0.02778 | 1.578×10⁻⁵ |
| 1 ft | 304.8 | 30.48 | 0.3048 | 3.048×10⁻⁴ | 12 | 1 | 0.3333 | 1.894×10⁻⁴ |
| 1 yd | 914.4 | 91.44 | 0.9144 | 9.144×10⁻⁴ | 36 | 3 | 1 | 5.682×10⁻⁴ |
| 1 mile | 1.609×10⁶ | 1.609×10⁵ | 1609 | 1.609 | 63,360 | 5280 | 1760 | 1 |
Key Conversion Formulas
Metric to Imperial:
Imperial to Metric:
Pipe Sizing Reference (DN ↔ NPS)
| DN (mm) | NPS (in) | OD (mm) | OD (in) |
|---|---|---|---|
| 15 | ½" | 21.3 | 0.840 |
| 20 | ¾" | 26.7 | 1.050 |
| 25 | 1" | 33.4 | 1.315 |
| 32 | 1¼" | 42.2 | 1.660 |
| 40 | 1½" | 48.3 | 1.900 |
| 50 | 2" | 60.3 | 2.375 |
| 65 | 2½" | 73.0 | 2.875 |
| 80 | 3" | 88.9 | 3.500 |
| 100 | 4" | 114.3 | 4.500 |
| 150 | 6" | 168.3 | 6.625 |
| 200 | 8" | 219.1 | 8.625 |
| 250 | 10" | 273.1 | 10.75 |
| 300 | 12" | 323.9 | 12.75 |
Critical Note on Pipe Sizes
DN and NPS are nominal designations, not actual dimensions. The outside diameter (OD) is standardized, but inside diameter (ID) varies with wall thickness (schedule). Always use pipe tables for flow calculations.
Area Conversions
Complete Conversion Table
| From → To | mm² | cm² | m² | ha | km² | in² | ft² | yd² | acre |
|---|---|---|---|---|---|---|---|---|---|
| 1 m² | 10⁶ | 10⁴ | 1 | 10⁻⁴ | 10⁻⁶ | 1550 | 10.76 | 1.196 | 2.47×10⁻⁴ |
| 1 ft² | 92,903 | 929.0 | 0.0929 | 9.29×10⁻⁶ | 9.29×10⁻⁸ | 144 | 1 | 0.111 | 2.30×10⁻⁵ |
| 1 ha | 10¹⁰ | 10⁸ | 10,000 | 1 | 0.01 | 1.55×10⁷ | 107,639 | 11,960 | 2.471 |
| 1 acre | 4.05×10⁹ | 4.05×10⁷ | 4,047 | 0.405 | 4.05×10⁻³ | 6.27×10⁶ | 43,560 | 4,840 | 1 |
Key Formulas
Important: When converting area, you must square the linear conversion factor:
Volume Conversions
Complete Conversion Table
| From → To | mL | L | m³ | gal (US) | gal (UK) | ft³ | in³ |
|---|---|---|---|---|---|---|---|
| 1 L | 1000 | 1 | 0.001 | 0.2642 | 0.2200 | 0.03531 | 61.02 |
| 1 m³ | 10⁶ | 1000 | 1 | 264.2 | 220.0 | 35.31 | 61,024 |
| 1 gal (US) | 3785 | 3.785 | 0.00379 | 1 | 0.8327 | 0.1337 | 231 |
| 1 gal (UK) | 4546 | 4.546 | 0.00455 | 1.201 | 1 | 0.1605 | 277.4 |
| 1 ft³ | 28,317 | 28.32 | 0.02832 | 7.481 | 6.229 | 1 | 1728 |
Key Engineering Volumes
| Container | Typical Volume |
|---|---|
| Water tank (residential) | 200-500 L |
| Expansion vessel | 8-50 L |
| Cooling tower sump | 1-10 m³ |
| Swimming pool (Olympic) | 2,500 m³ |
| Oil barrel | 159 L (42 US gal) |
US vs UK Gallons
The US gallon (3.785 L) is approximately 20% smaller than the UK Imperial gallon (4.546 L). Always verify which gallon is referenced in specifications, especially for fuel consumption and pump flow rates.
Mass Conversions
Complete Conversion Table
| From → To | mg | g | kg | t (metric) | oz | lb | ton (US) | ton (UK) |
|---|---|---|---|---|---|---|---|---|
| 1 kg | 10⁶ | 1000 | 1 | 0.001 | 35.27 | 2.205 | 0.001102 | 0.000984 |
| 1 lb | 453,592 | 453.6 | 0.4536 | 4.54×10⁻⁴ | 16 | 1 | 0.0005 | 0.000446 |
| 1 t (metric) | 10⁹ | 10⁶ | 1000 | 1 | 35,274 | 2205 | 1.102 | 0.984 |
| 1 ton (US) | 9.07×10⁸ | 9.07×10⁵ | 907.2 | 0.9072 | 32,000 | 2000 | 1 | 0.893 |
| 1 ton (UK) | 1.02×10⁹ | 1.02×10⁶ | 1016 | 1.016 | 35,840 | 2240 | 1.12 | 1 |
Ton Variations
| Type | Definition | kg Equivalent |
|---|---|---|
| Metric ton (tonne) | 1000 kg | 1000 |
| US (short) ton | 2000 lb | 907.2 |
| UK (long) ton | 2240 lb | 1016 |
| Ton of refrigeration | Cooling capacity | N/A (3.517 kW) |
Pressure Conversions
Pressure conversion is perhaps the most critical for engineering applications. Understanding the relationships between units—and especially gauge vs absolute pressure—prevents dangerous errors.
Complete Conversion Table
| From → To | Pa | kPa | bar | psi | atm | mmHg | mH₂O | inH₂O |
|---|---|---|---|---|---|---|---|---|
| 1 bar | 10⁵ | 100 | 1 | 14.504 | 0.9869 | 750.1 | 10.20 | 401.5 |
| 1 psi | 6895 | 6.895 | 0.06895 | 1 | 0.06805 | 51.71 | 0.7031 | 27.68 |
| 1 atm | 101,325 | 101.3 | 1.013 | 14.70 | 1 | 760 | 10.33 | 406.8 |
| 1 kPa | 1000 | 1 | 0.01 | 0.1450 | 0.00987 | 7.501 | 0.102 | 4.015 |
| 1 mH₂O | 9807 | 9.807 | 0.09807 | 1.422 | 0.09678 | 73.56 | 1 | 39.37 |
Gauge vs Absolute Pressure
Critical Safety Concept
Gauge pressure measures relative to atmospheric pressure. Absolute pressure measures relative to perfect vacuum.
At sea level: ≈ 14.7 psi ≈ 1.013 bar ≈ 101.325 kPa
Example:
- 50 psig = 50 + 14.7 = 64.7 psia
- 5 barg = 5 + 1.013 = 6.013 bara
Always use absolute pressure for:
- Gas law calculations (PV = nRT)
- Refrigeration cycle analysis
- Compressor ratios
- Cavitation calculations
Pressure Head Conversions
In pump and piping systems, pressure is often expressed as "head" (height of fluid column):
For Water at 4°C (maximum density):
| Head | Pressure |
|---|---|
| 1 m H₂O | 9.807 kPa = 0.0981 bar = 1.422 psi |
| 1 ft H₂O | 2.989 kPa = 0.0299 bar = 0.433 psi |
| 10 m H₂O | 0.981 bar ≈ 1 bar |
Temperature Conversions
Temperature requires special attention because conversions involve both multiplication and addition (offset).
Conversion Formulas
Celsius ↔ Fahrenheit:
Celsius ↔ Kelvin:
Fahrenheit ↔ Rankine:
Reference Temperatures
| Description | °C | °F | K |
|---|---|---|---|
| Absolute zero | -273.15 | -459.67 | 0 |
| Water freezing | 0 | 32 | 273.15 |
| Room temperature | 20-25 | 68-77 | 293-298 |
| Human body | 37 | 98.6 | 310.15 |
| Water boiling | 100 | 212 | 373.15 |
Temperature Difference (ΔT) Conversions
Critical Distinction
For temperature differences, do NOT add the offset:
Example:
- A 10°C temperature rise = 10 × 1.8 = 18°F rise
- NOT: 10 × 1.8 + 32 = 50°F (this is wrong!)
Memory Aid:
- 1°C change = 1.8°F change
- 1 K change = 1.8°R change
Power Conversions
Complete Conversion Table
| From → To | W | kW | MW | hp (mech) | BTU/hr | TR | kcal/hr |
|---|---|---|---|---|---|---|---|
| 1 kW | 1000 | 1 | 0.001 | 1.341 | 3412 | 0.2843 | 860.4 |
| 1 hp | 745.7 | 0.7457 | 7.46×10⁻⁴ | 1 | 2545 | 0.212 | 641.2 |
| 1 BTU/hr | 0.2931 | 2.93×10⁻⁴ | 2.93×10⁻⁷ | 3.93×10⁻⁴ | 1 | 8.33×10⁻⁵ | 0.252 |
| 1 TR | 3517 | 3.517 | 0.00352 | 4.716 | 12,000 | 1 | 3024 |
Ton of Refrigeration
The ton of refrigeration (TR) is fundamental in HVAC:
Definition: Heat removal rate to freeze 1 short ton (2000 lb) of water at 0°C in 24 hours.
Key Conversions:
- 1 TR = 3.517 kW (thermal)
- 1 TR = 12,000 BTU/hr
- 1 TR = 3,024 kcal/hr
Horsepower Variations
| Type | Definition | Watts |
|---|---|---|
| Mechanical hp | 550 ft·lbf/s | 745.7 W |
| Electrical hp | Common in US motors | 746 W |
| Metric hp (PS) | 75 kgf·m/s | 735.5 W |
| Boiler hp | Steam generation rate | 9,810 W |
Energy Conversions
Complete Conversion Table
| From → To | J | kJ | MJ | kWh | BTU | kcal | therm |
|---|---|---|---|---|---|---|---|
| 1 kWh | 3.6×10⁶ | 3600 | 3.6 | 1 | 3412 | 860.4 | 0.0341 |
| 1 BTU | 1055 | 1.055 | 0.00106 | 2.93×10⁻⁴ | 1 | 0.252 | 10⁻⁵ |
| 1 therm | 1.055×10⁸ | 1.055×10⁵ | 105.5 | 29.3 | 100,000 | 25,200 | 1 |
| 1 kcal | 4184 | 4.184 | 0.00418 | 0.00116 | 3.968 | 1 | 3.97×10⁻⁵ |
Power vs Energy
Fundamental Distinction
- Power = Rate of energy transfer (kW, hp, BTU/hr)
- Energy = Total quantity (kWh, BTU, MJ)
Example: A 10 kW heater running for 3 hours uses:
Fuel Heating Values
| Fuel | Higher Heating Value (HHV) |
|---|---|
| Natural gas | 10.5 kWh/m³ ≈ 1000 BTU/ft³ |
| LPG (propane) | 25.3 kWh/m³ ≈ 91,500 BTU/gal |
| Diesel | 10.7 kWh/L ≈ 138,700 BTU/gal |
| Heating oil | 10.3 kWh/L ≈ 138,500 BTU/gal |
Flow Rate Conversions
Volumetric Flow Rates
| From → To | m³/s | m³/hr | L/s | L/min | GPM | CFM |
|---|---|---|---|---|---|---|
| 1 m³/hr | 2.78×10⁻⁴ | 1 | 0.278 | 16.67 | 4.403 | 0.589 |
| 1 L/s | 0.001 | 3.6 | 1 | 60 | 15.85 | 2.119 |
| 1 GPM | 6.31×10⁻⁵ | 0.227 | 0.0631 | 3.785 | 1 | 0.134 |
| 1 CFM | 4.72×10⁻⁴ | 1.699 | 0.472 | 28.32 | 7.481 | 1 |
Key HVAC Flow Conversions
Water Systems:
Air Systems:
Mass Flow Rate Conversion
For water at 20°C (ρ ≈ 998 kg/m³):
| Volumetric | Mass |
|---|---|
| 1 m³/hr | 998 kg/hr ≈ 1000 kg/hr |
| 1 L/s | 0.998 kg/s ≈ 1 kg/s |
| 1 GPM | 3.78 kg/min = 227 kg/hr |
Velocity Conversions
Complete Conversion Table
| From → To | m/s | km/h | ft/s | ft/min | mph | knot |
|---|---|---|---|---|---|---|
| 1 m/s | 1 | 3.6 | 3.281 | 196.9 | 2.237 | 1.944 |
| 1 km/h | 0.278 | 1 | 0.911 | 54.68 | 0.621 | 0.540 |
| 1 ft/s | 0.305 | 1.097 | 1 | 60 | 0.682 | 0.592 |
| 1 ft/min | 0.00508 | 0.0183 | 0.0167 | 1 | 0.0114 | 0.00987 |
| 1 mph | 0.447 | 1.609 | 1.467 | 88 | 1 | 0.869 |
Engineering Velocity Guidelines
| Application | Typical Velocity |
|---|---|
| Duct air (main) | 5-10 m/s (1000-2000 ft/min) |
| Duct air (branch) | 3-5 m/s (600-1000 ft/min) |
| Chilled water pipe | 1.5-3 m/s (5-10 ft/s) |
| Condenser water | 2-3.5 m/s (6.5-11.5 ft/s) |
| Steam (low pressure) | 25-40 m/s (80-130 ft/s) |
Special Engineering Conversions
Specific Heat Capacity
| From → To | kJ/(kg·K) | BTU/(lb·°F) | cal/(g·°C) |
|---|---|---|---|
| 1 kJ/(kg·K) | 1 | 0.2388 | 0.2388 |
| 1 BTU/(lb·°F) | 4.187 | 1 | 1 |
Water: cp = 4.186 kJ/(kg·K) = 1.0 BTU/(lb·°F)
Thermal Conductivity
| From → To | W/(m·K) | BTU/(hr·ft·°F) |
|---|---|---|
| 1 W/(m·K) | 1 | 0.5778 |
| 1 BTU/(hr·ft·°F) | 1.731 | 1 |
Heat Transfer Coefficient
| From → To | W/(m²·K) | BTU/(hr·ft²·°F) |
|---|---|---|
| 1 W/(m²·K) | 1 | 0.1761 |
| 1 BTU/(hr·ft²·°F) | 5.678 | 1 |
How Can You Avoid Common Conversion Errors?
Dimensional Analysis
Always verify conversions using dimensional analysis—tracking units through calculations:
Significant Figures
- Don't add false precision through conversion
- Round final results appropriately
- Maintain 2-4 significant figures for engineering calculations
Example:
- Input: 5.0 m (2 sig figs)
- Exact conversion: 5.0 × 3.28084 = 16.4042 ft
- Reported: 16 ft (2 sig figs)
Common Error Prevention
- Always write units in calculations
- Verify with inverse conversion (convert back and check)
- Use dimensional analysis to confirm factor application
- Clearly label gauge vs absolute pressure
- Distinguish temperature vs temperature difference
- Note US vs UK gallons in documentation
- Specify nominal vs actual pipe dimensions
Quick Reference Tables
Most Common Engineering Conversions
| Conversion | Factor | Inverse |
|---|---|---|
| m → ft | 3.281 | 0.3048 |
| m² → ft² | 10.76 | 0.0929 |
| m³ → ft³ | 35.31 | 0.0283 |
| L → gal (US) | 0.264 | 3.785 |
| bar → psi | 14.50 | 0.0689 |
| kPa → psi | 0.145 | 6.895 |
| kW → hp | 1.341 | 0.746 |
| kW → BTU/hr | 3412 | 2.93×10⁻⁴ |
| kW → TR | 0.284 | 3.517 |
| m³/hr → GPM | 4.403 | 0.227 |
| L/s → GPM | 15.85 | 0.0631 |
| m/s → ft/min | 196.9 | 0.00508 |
Pressure Quick Reference
| Common Value | bar | psi | kPa | atm |
|---|---|---|---|---|
| Atmospheric | 1.013 | 14.7 | 101.3 | 1 |
| 2 bar | 2 | 29.0 | 200 | 1.97 |
| 50 psi | 3.45 | 50 | 345 | 3.40 |
| 10 bar | 10 | 145 | 1000 | 9.87 |
Conclusion
Unit conversion mastery is a fundamental engineering skill that directly impacts safety, accuracy, and professional credibility. This guide has covered:
- Three major unit systems (SI, practical metric, imperial) and when to use each
- Comprehensive conversion tables for all major engineering quantities
- Critical distinctions (gauge vs absolute, temperature vs ΔT, US vs UK gallons)
- Special engineering conversions (specific heat, conductivity, heat transfer)
- Best practices for accuracy and error prevention
Our engineering team has developed the interactive converter at the top of this page to provide instant, accurate conversions verified against NIST SP 811. Our calculations follow ISO 80000-1:2022 standards for maximum accuracy. Bookmark this guide as your definitive engineering unit reference.
Key Takeaways
- Always specify units explicitly—ambiguity causes errors
- Use dimensional analysis to verify every conversion
- Distinguish temperature from temperature difference in conversions
- Specify gauge vs absolute for all pressure values
- Remember area/volume require squared/cubed factors for linear unit conversions
- Know your gallon—US and UK differ by 20%
- Use the interactive converter for quick verification
Further Learning
- Water Properties Guide - Thermophysical property data at various temperatures
- City Distance Calculator - Geographic distance calculations
- Boiler Sizing Guide - Heating system calculations
- Voltage Drop Calculator - Electrical system calculations
References & Standards
Primary Standards
ISO 80000-1:2022 Quantities and units — Part 1: General. Defines the International System of Units (SI), conversion principles, and unit symbol conventions. Section 3 defines fundamental terms; Section 6 specifies rules for unit symbols and names; Annex A provides guidance on expressing uncertainty in measurements.
NIST Special Publication 811 (2008) Guide for the Use of the International System of Units (SI). Appendix B contains comprehensive conversion factors with 10+ significant figures for all engineering units. Section 4.2 covers rules for unit symbols; Section 7 addresses expressing measurement uncertainty. All conversions in this calculator use NIST SP 811 Appendix B factors.
BIPM SI Brochure, 9th Edition (2019) The international authority on SI unit definitions. Chapter 2 defines the seven base units with explicit constants; Table 4 lists derived units with special names; Table 8 provides non-SI units accepted for use with SI (bar, liter, etc.).
Engineering Standards
ASHRAE Handbook Fundamentals Comprehensive reference including unit conversion tables and psychrometric data for HVAC applications.
ASME Standards Pipe dimensions, pressure vessel standards, and mechanical engineering specifications.
API Standards Petroleum industry standards including barrel definitions and flow measurement.
Further Reading
- NIST Physical Measurement Laboratory - Measurement science resources
- ISO Technical Committee 12 - Quantities and units standardization
- Engineering Toolbox - Practical engineering reference
Disclaimer: This guide provides general technical information for reference purposes. Always verify results with applicable standards and engineering references. For critical applications or professional projects, consult with licensed engineers and verify all calculations independently.