Mechanical Engineering Formulas

Force Calculation

F = ma

Where F is force (N), m is mass (kg), and a is acceleration (m/s²).

Work Formula

W = Fd

Where W is work (J), F is force (N), and d is distance (m).

Kinetic Energy

KE = ½ mv²

Where KE is kinetic energy (J), m is mass (kg), and v is velocity (m/s).

Power Formula

P = W/t

Where P is power (W), W is work (J), and t is time (s).

Stress Formula

σ = F/A

Where σ is stress (Pa), F is force (N), and A is area (m²).

Strain Formula

ε = ΔL/L

Where ε is strain (dimensionless), ΔL is the change in length (m), and L is the original length (m).

Hooke's Law

F = -kx

Where F is the force (N), k is the spring constant (N/m), and x is the displacement (m).

Bernoulli's Equation

P + ½ ρv² + ρgh = constant

Where P is pressure (Pa), ρ is density (kg/m³), v is velocity (m/s), g is acceleration due to gravity (m/s²), and h is height (m).

Reynolds Number

Re = ρvd/μ

Where Re is Reynolds number (dimensionless), ρ is fluid density (kg/m³), v is velocity (m/s), d is characteristic length (m), and μ is dynamic viscosity (Pa·s).

Efficiency Formula

η = (Useful work output / Total energy input) × 100%

Where η is efficiency (%), useful work output is in joules, and total energy input is in joules.

Specific Heat Capacity

Q = mcΔT

Where Q is heat energy (J), m is mass (kg), c is specific heat capacity (J/kg·°C), and ΔT is the temperature change (°C).

Thermodynamics First Law

ΔU = Q - W

Where ΔU is the change in internal energy (J), Q is heat added to the system (J), and W is work done by the system (J).

Physics Formulas

Formula

Density

Average velocity

Acceleration

Force

Weight

Centripetal acceleration

Centripetal force

Work done

Efficiency

Power

Potential energy

Kinetic energy

Moment

Angular velocity

Linear velocity

Relationships (initial velocity, displacement, acceleration)

Relationships (angular velocity, angular acceleration)

Frictional force

Force ratio

Symbols

ρ = m / V

v = s / t

a = (v − u) / t

F = ma

W = mg

a = v² / r

F = mv² / r

W = F × s

Efficiency = useful output energy / input energy

P = E / t = Fv

Ep = mgh

Ek = ½ mv²

M = Fd

ω = θ / t = 2πn

v = ωr

s = ut + ½ at², v² = u² + 2as

θ = ω₁t + ½ αt², ω₂² = ω₁² + 2αθ

F = μN

Force ratio = load / effort

Units

kg/m³

m/s

m/s²

N

N

m/s²

N

J

-

W

J

J

N·m

rad/s

m/s

m (m/s)²

rad (rad/s)²

N

-

Unit Conversions

Mass

  • 1 kg = 2.205 lbm
  • 1 slug = 32.2 lbm
  • 1 ton = 2000 lbm

Force

  • 1 N = 0.225 lbf
  • 1 kip = 1,000 lbf

Length

  • 1 m = 3.28 ft
  • 1 km = 0.621 mi
  • 1 in = 2.54 cm
  • 1 mi = 5280 ft
  • 1 yd = 3 ft

Area

  • 1 acre = 4047 m2
  • = 43,560 ft2
  • = 0.00156 mi2

Volume

  • 1 L = 0.264 gal
  • = 0.0353 ft3
  • = 33.8 fl oz
  • 1 mL = 1 cm3 = 1 cc

Pressure

  • 1 atm = 1.01325 bar
  • = 33.9 ft H2O
  • = 29.92 in Hg
  • = 760 mm Hg
  • = 101,325 Pa
  • = 14.7 psi
  • 1 psi = 2.31 ft of H2O

Power

  • 1 W = 3.412 Btu/h
  • = 0.00134 hp
  • = 14.34 cal/min
  • = 0.7376 ft·lbf/s

Energy

  • 1 J = 0.239 cal
  • = 9.48 x 10-4 Btu
  • = 0.7376 ft·lbf
  • 1 kWh = 3,600,000 J

Temperature Unit Equivalents

  • 1 K = 1 ºC
  • = 1.8 ºF
  • = 1.8 ºR

Time

  • 1 d = 24 h
  • 1 h = 60 min
  • 1 min = 60 s
  • 1 yr = 365 d