Category
Mechanical Engineering
Mechanical engineering formulas and calculators for statics, dynamics, and thermodynamics used to analyze forces, motion, and energy in mechanical systems. Includes stress, strain, work, and heat transfer equations.
41Formulas
3Subcategories
Updated Jul 2026
General
Feed Rate (Machining)
f_r = f * N
General
Thermal Efficiency of a Heat Engine
eta = W_net / Q_in
General
Machine Efficiency
eta = (Output / Input) * 100
General
Material Removal Rate (Turning)
MRR = V * f * d
General
Cutting Speed (Machining)
V = pi * D * N / 1000
General
Bearing L10 Life
L10 = (C / P)^p * 1,000,000
General
Bolt Preload Stress
sigma = F / A_stress
General
Gear Ratio
GR = N_driven / N_driver
General
Belt and Pulley Speed Ratio
N1 * D1 = N2 * D2
General
Power-Torque-Speed Relationship
P = T * omega
General
Spring Force (Hooke's Law)
F = k * x
General
Angular Momentum
L = I * omega
General
Centripetal Force
F_c = m * v^2 / r
General
Natural Frequency of a Spring-Mass System
omega_n = sqrt(k / m)
General
Gravitational Potential Energy
PE = m * g * h
General
Pump Hydraulic Power
P = rho * g * Q * H / eta
General
Torricelli's Law (Efflux Velocity)
v = sqrt(2 * g * h)
General
Buoyancy Force (Archimedes' Principle)
F_b = rho * g * V_displaced
General
Hydrostatic Pressure
P = rho * g * h
General
Volumetric Flow Rate
Q = A * v
General
Isothermal Work (Ideal Gas)
W = n * R * T * ln(V2 / V1)
General
Coefficient of Performance (Refrigeration)
COP = Qc / W
General
Otto Cycle Thermal Efficiency
eta = 1 - (1 / r^(gamma - 1))
General
Carnot Efficiency
eta = 1 - (Tc / Th)
General
First Law of Thermodynamics (Energy Balance)
delta_U = Q - W
General
Axial Strain Energy
U = F^2 * L / (2 * A * E)
General
Factor of Safety
FOS = sigma_yield / sigma_allowable
General
Beam Deflection (Simply Supported, Center Load)
delta = F * L^3 / (48 * E * I)
General
Torsional Shear Stress
tau = T * r / J
General
Bending Stress (Flexure Formula)
sigma = M * c / I
General
Axial Stress
sigma = F / A
Statics
Simply Supported Beam Reaction (Point Load)
R1 = (F * b) / L
Statics
Static Friction Force
F_f = mu_s * N
Statics
Center of Gravity (Two Point Masses)
x_cg = (m1*x1 + m2*x2) / (m1 + m2)
Statics
Resultant of Two Forces
R = sqrt(F1^2 + F2^2 + 2*F1*F2*cos(theta))
Statics
Moment of a Force (Torque)
M = F * d
Thermodynamics
Ideal Gas Law
PV = nRT
Dynamics
Work-Energy Theorem
W = ΔKE
Dynamics
Kinetic Energy
KE = ½mv²
Dynamics
Newton's Second Law
F = m · a
Statics
Stress
σ = F / A