Mechanical Engineering Calculators and Formulas
Formulas for strength of materials, thermal growth, fluid flow and compressed air, each with a calculator that accepts SI or US units and shows the working.
7 calculators · 11 converters · common conversions
Mechanical Engineering Formulas and Calculators
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Tensile Stress Calculator
σ = F ÷ A
σ normal stress, F axial force, A cross-sectional area
Example: 10 kN on a 10 mm bar = 127.3 MPa.
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Young's Modulus Calculator
E = σ ÷ ε
E Young's modulus, σ stress, ε strain = ΔL ÷ L₀
Example: 250 MPa at 0.125 % strain gives E = 200 GPa.
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Thermal Expansion Calculator
ΔL = α L₀ ΔT
α coefficient of linear expansion, L₀ original length, ΔT temperature change
Example: 10 m of steel heated by 50 °C grows 6 mm.
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Pipe Pressure Drop Calculator
ΔP = f (L ÷ D) (ρ v² ÷ 2)
f Darcy friction factor (64/Re laminar, Colebrook–White turbulent), L pipe length, D inside diameter, ρ density, v mean velocity
Example: Darcy–Weisbach with the Colebrook friction factor.
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Reynolds Number Calculator
Re = ρ v D ÷ μ = v D ÷ ν
ρ density, v velocity, D pipe diameter, μ dynamic viscosity, ν kinematic viscosity
Example: Pipe flow is laminar below Re ≈ 2300 and turbulent above about 4000.
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SCFM to ACFM Calculator
Q_act = Q_std × (T_act ÷ T_std) × (P_std ÷ P_act)
Q gas flow, T absolute temperature, P absolute pressure
Example: 100 SCFM at 100 psig and 68 °F = 12.82 ACFM.
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Face Velocity Calculator
v = Q ÷ A
v face velocity, Q airflow, A face area
Example: 2000 CFM ÷ 4 ft² = 500 ft/min.
Unit Converters for Mechanical Engineering
- Pressure Converter – Pa, kPa, psi, bar, inH₂O, mmHg, torr, atm
- Force Converter – N, kN, lbf, kgf, kip, dyn, ozf, gf
- Torque Converter – N·m, lbf·ft, lbf·in, kgf·cm, kgf·m, ozf·in
- Power Converter – W, kW, MW, hp, PS, BTU/h, TR, kcal/h
- Energy Converter – J, kJ, kWh, kcal, cal, BTU, therm, eV
- Temperature Converter – °C, °F, K, °R
- Heat Transfer Coefficient Converter – W/(m²·K), BTU/(h·ft²·°F), kcal/(h·m²·°C), U-value
- Thermal Conductivity Converter – W/(m·K), mW/(m·K), BTU/(h·ft·°F), k-value, kcal/(h·m·°C)
- Flow Rate Converter – CFM, m³/h, L/min, L/s, GPM, sccm, SLPM
- Length Converter – m, km, cm, mm, µm, ft, in, mi, yd, nmi
- Fuel Economy Converter – mpg (US, UK), L/100 km, km/L
Common Mechanical Engineering Conversions
Using these mechanical engineering calculators
Most mechanical design checks come down to three questions: will the part carry the load, will it deform too much, and will the fluid or air system deliver what it should. The stress and Young’s modulus calculators answer the first two for simple members, the thermal expansion calculator covers growth with temperature, and the Reynolds number, pipe pressure drop and SCFM to ACFM tools cover piping and compressed air.
The commonest source of error is units rather than formulas. A stress in N/mm² is the same number in MPa, but psi and ksi differ by a factor of 1000, and gauge and absolute pressure differ by the local atmospheric pressure. Every calculator here converts each input separately, so you can enter millimetres, inches, kilonewtons or pounds-force without converting first.
Treat the results as first-pass engineering estimates. Stress concentrations at holes and fillets, fatigue under cyclic loads and buckling of slender members need their own checks, and design codes add safety factors on top of the calculated values.