A pressure specification in psi from an American supplier, a torque value in kgf·m from a Japanese drawing, and a force calculation in Newtons from your FEA software — navigating these unit systems is a daily reality for engineers working in global supply chains.
Unit conversion errors have caused real engineering failures — including NASA’s Mars Climate Orbiter loss in 1999 due to a metric/imperial confusion in software. This reference guide provides accurate conversion factors for the unit combinations that mechanical engineers encounter most frequently, organized by physical quantity with worked examples. Keep it bookmarked.
Force
| From | To N | To kgf | To lbf | To kN |
|---|---|---|---|---|
| 1 N | 1 | 0.10197 | 0.22481 | 0.001 |
| 1 kgf | 9.8067 | 1 | 2.2046 | 0.0098067 |
| 1 lbf | 4.4482 | 0.45359 | 1 | 0.0044482 |
| 1 kN | 1000 | 101.97 | 224.81 | 1 |
| 1 tonf (short, US) | 8896.4 | 907.19 | 2000 | 8.8964 |
| 1 tonf (long, UK) | 9964.0 | 1016.0 | 2240 | 9.9640 |
Key relationships to memorize: 1 kgf ≈ 9.81 N; 1 lbf ≈ 4.45 N; 1 kN ≈ 102 kgf ≈ 225 lbf
Worked example: A hydraulic cylinder with 50 mm bore at 200 bar pressure. Force = P × A = 200 × 10⁵ Pa × π/4 × (0.05)² m² = 39,270 N = 3,999 kgf ≈ 4.0 tonnes-force. In imperial: 39,270 N ÷ 4.4482 = 8,828 lbf ≈ 8,830 lbf.
Pressure and Stress
| From | To MPa | To kgf/cm² | To psi | To bar | To kPa |
|---|---|---|---|---|---|
| 1 MPa (= 1 N/mm²) | 1 | 10.197 | 145.04 | 10.000 | 1000 |
| 1 kgf/cm² | 0.098067 | 1 | 14.223 | 0.98067 | 98.067 |
| 1 psi (lbf/in²) | 0.0068948 | 0.070307 | 1 | 0.068948 | 6.8948 |
| 1 bar | 0.10000 | 1.0197 | 14.504 | 1 | 100 |
| 1 atm (standard) | 0.10133 | 1.0332 | 14.696 | 1.0133 | 101.33 |
| 1 ksi (kip/in²) | 6.8948 | 70.307 | 1000 | 68.948 | 6894.8 |
Key relationships to memorize: 1 MPa = 1 N/mm² = 10 bar ≈ 145 psi ≈ 10.2 kgf/cm²; 1 bar ≈ 14.5 psi ≈ 1 kgf/cm²
Worked example: A bolt specified at 600 MPa proof stress. In psi: 600 × 145.04 = 87,024 psi ≈ 87 ksi. In kgf/mm²: 600 × 10.197 / 100 = 61.2 kgf/mm². (Note: kgf/mm² is an older Japanese unit: 1 kgf/mm² = 9.807 MPa; so 600 MPa = 61.2 kgf/mm²)
Torque and Moment
| From | To N·m | To kgf·m | To lbf·ft | To lbf·in | To kgf·cm |
|---|---|---|---|---|---|
| 1 N·m | 1 | 0.10197 | 0.73756 | 8.8508 | 10.197 |
| 1 kgf·m | 9.8067 | 1 | 7.2330 | 86.796 | 100 |
| 1 lbf·ft | 1.3558 | 0.13826 | 1 | 12 | 13.826 |
| 1 lbf·in | 0.11298 | 0.011521 | 0.083333 | 1 | 1.1521 |
| 1 kgf·cm | 0.098067 | 0.01 | 0.072330 | 0.86796 | 1 |
Key relationships: 1 N·m ≈ 0.102 kgf·m ≈ 0.738 lbf·ft ≈ 8.85 lbf·in; 1 kgf·m ≈ 9.81 N·m ≈ 7.23 lbf·ft
Worked example: A motor producing 50 N·m torque. In lbf·ft: 50 × 0.73756 = 36.9 lbf·ft. In kgf·m: 50 × 0.10197 = 5.10 kgf·m.
Length and Distance
| From | To mm | To cm | To m | To inch | To foot |
|---|---|---|---|---|---|
| 1 mm | 1 | 0.1 | 0.001 | 0.039370 | 0.0032808 |
| 1 cm | 10 | 1 | 0.01 | 0.39370 | 0.032808 |
| 1 m | 1000 | 100 | 1 | 39.370 | 3.2808 |
| 1 inch | 25.400 | 2.5400 | 0.025400 | 1 | 0.083333 |
| 1 foot | 304.80 | 30.480 | 0.30480 | 12 | 1 |
| 1 yard | 914.40 | 91.440 | 0.91440 | 36 | 3 |
Key relationship: 1 inch = 25.4 mm exactly (defined). All imperial-metric length conversions derive from this.
Mass and Weight
| From | To kg | To g | To lb | To oz | To tonne (metric) |
|---|---|---|---|---|---|
| 1 kg | 1 | 1000 | 2.2046 | 35.274 | 0.001 |
| 1 g | 0.001 | 1 | 0.0022046 | 0.035274 | 10⁻⁶ |
| 1 lb (avoirdupois) | 0.45359 | 453.59 | 1 | 16 | 0.00045359 |
| 1 oz (avoirdupois) | 0.028350 | 28.350 | 0.0625 | 1 | 2.835×10⁻⁵ |
| 1 tonne (metric, 1000 kg) | 1000 | 10⁶ | 2204.6 | 35274 | 1 |
| 1 ton (short, US, 2000 lb) | 907.18 | 907180 | 2000 | 32000 | 0.90718 |
Temperature
| Conversion | Formula | Example |
|---|---|---|
| °C to °F | °F = (°C × 9/5) + 32 | 100°C = 212°F |
| °F to °C | °C = (°F − 32) × 5/9 | 350°F = 176.7°C |
| °C to K | K = °C + 273.15 | 20°C = 293.15 K |
| °F to R (Rankine) | R = °F + 459.67 | 70°F = 529.67 R |
Quick estimates: 0°C = 32°F; 20°C ≈ 68°F; 100°C = 212°F; 200°C ≈ 392°F; 450°C ≈ 842°F (zinc bath temperature). A 10°C change = 18°F change.
Power
| From | To W (= J/s) | To kW | To HP (mechanical) | To kgf·m/s |
|---|---|---|---|---|
| 1 W | 1 | 0.001 | 0.0013410 | 0.10197 |
| 1 kW | 1000 | 1 | 1.3410 | 101.97 |
| 1 HP (mechanical, US) | 745.70 | 0.74570 | 1 | 76.040 |
| 1 PS (metric horsepower) | 735.50 | 0.73550 | 0.98632 | 75 |
| 1 kgf·m/s | 9.8067 | 0.0098067 | 0.013151 | 1 |
Key relationships: 1 HP ≈ 0.746 kW; 1 PS (metric hp) ≈ 0.736 kW; 1 kW ≈ 1.34 HP ≈ 1.36 PS. Note: “PS” (Pferdestärke) is still used for automotive engine ratings in Germany and Japan.
Energy and Impact
| From | To J | To kJ | To ft·lbf | To kW·h |
|---|---|---|---|---|
| 1 J (= 1 N·m) | 1 | 0.001 | 0.73756 | 2.778×10⁻⁷ |
| 1 kJ | 1000 | 1 | 737.56 | 2.778×10⁻⁴ |
| 1 ft·lbf | 1.3558 | 0.0013558 | 1 | 3.766×10⁻⁷ |
| 1 kW·h | 3,600,000 | 3600 | 2,655,200 | 1 |
Impact testing: Charpy V-notch impact energy is specified in joules (J) per ISO 148-1, or in ft·lbf per ASTM E23. 1 J = 0.738 ft·lbf. Minimum 27 J = 20 ft·lbf is a common low-temperature toughness requirement for structural steel.
Flow Rate and Velocity
| Volume Flow | Conversion |
|---|---|
| 1 L/min | = 0.01667 L/s = 0.2642 US gal/min (GPM) = 0.000016667 m³/s |
| 1 m³/h | = 16.67 L/min = 4.403 US GPM |
| 1 US GPM | = 3.785 L/min = 0.2271 m³/h |
| 1 UK GPM (Imperial) | = 4.546 L/min = 1.201 US GPM |
| Velocity | Conversion |
|---|---|
| 1 m/s | = 3.281 ft/s = 196.85 ft/min = 3.600 km/h = 2.237 mph |
| 1 km/h | = 0.6214 mph = 0.2778 m/s = 0.9113 ft/s |
| 1 mph | = 1.6093 km/h = 0.4470 m/s = 1.467 ft/s |
Stress Intensity and Fracture Mechanics
| From | To MPa·√m | To ksi·√in |
|---|---|---|
| 1 MPa·√m | 1 | 0.9099 |
| 1 ksi·√in | 1.0989 | 1 |
Fracture toughness values in ASTM test reports are often in ksi·√in (US); ISO test reports use MPa·√m. Multiply ksi·√in by 1.099 to get MPa·√m.
Viscosity
| Dynamic Viscosity | Equivalence |
|---|---|
| 1 Pa·s (= 1 N·s/m²) | = 1000 mPa·s = 1000 cP (centipoise) |
| 1 cP (centipoise) | = 1 mPa·s = 0.001 Pa·s = 0.000672 lbm/(ft·s) |
| Kinematic Viscosity | Equivalence |
|---|---|
| 1 m²/s | = 10⁶ mm²/s = 10⁶ cSt (centistokes) |
| 1 cSt (centistoke) | = 1 mm²/s = 10⁻⁶ m²/s |
ISO VG viscosity grades (ISO 3448) specify kinematic viscosity in cSt at 40°C. VG 46: 41.4–50.6 cSt at 40°C. VG 68: 61.2–74.8 cSt. VG 100: 90–110 cSt.
Common Engineering Constants
| Constant | Value | Notes |
|---|---|---|
| Standard gravity (g) | 9.80665 m/s² | Defines kgf: 1 kgf = 9.80665 N exactly |
| π (pi) | 3.14159265 | Used constantly in circular area, torque, angular calculations |
| Steel density | 7850 kg/m³ | = 7.85 g/cm³ = 0.284 lb/in³ |
| Aluminum density | 2700 kg/m³ | = 2.70 g/cm³ = 0.0975 lb/in³ |
| Steel E modulus | 200 GPa | = 29,000 ksi = 20,400 kgf/mm² |
| Aluminum E modulus | 69 GPa | = 10,000 ksi |
Worked Example: Multi-Step Conversion
Problem: A Japanese drawing specifies a shaft surface hardness of 60 kgf/mm² minimum bending fatigue strength. Convert to MPa for use in FEA material properties.
Solution: 1 kgf/mm² = 9.80665 N/mm² = 9.80665 MPa. Therefore: 60 kgf/mm² × 9.80665 MPa/(kgf/mm²) = 588.4 MPa ≈ 590 MPa.
Problem 2: A hydraulic pump delivers 80 L/min at 250 bar. Calculate power in kW.
Solution: P = Q × p. Q = 80 L/min = 80/60 L/s = 1.333 × 10⁻³ m³/s. p = 250 bar = 25 × 10⁶ Pa. P = 1.333 × 10⁻³ × 25 × 10⁶ = 33,333 W = 33.3 kW. (Actual power will be higher by pump efficiency factor, typically ÷ 0.85–0.90.)
Conclusion
Accurate unit conversion is a fundamental engineering competency. The most important habits: always write units explicitly in calculations (cancellation of unit labels prevents errors), use the 1 inch = 25.4 mm relationship as the anchor for all imperial-metric length conversions, and remember that 1 MPa = 1 N/mm² — the single most useful equivalence in daily mechanical stress calculations. Keep this reference alongside your other calculation tools and check it any time you are working across unit systems.
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