Category
Materials Science
Materials science formulas and calculators for the mechanical and thermal properties of metals, polymers, and composites. Includes stress-strain behavior, thermal expansion, and material failure equations.
35Formulas
2Subcategories
Updated Jul 2026
General
Curie-Weiss Law
chi = C / (T - Tc)
General
Interplanar Spacing for Cubic Crystals
d_hkl = a / sqrt(h^2 + k^2 + l^2)
General
Norton's Power Law (Creep Rate)
epsilon_dot = A * sigma^n
General
Larson-Miller Parameter (Creep)
LMP = T * (C + log10(t_r))
General
Electrical Resistivity
R = rho * L / A
General
Vegard's Law
a_alloy = x*a_A + (1-x)*a_B
General
Atomic Packing Factor
APF = (N * V_atom) / V_cell
General
Inverse Rule of Mixtures (Reuss Model)
1/E_c = V_f/E_f + V_m/E_m
General
Rule of Mixtures (Composite Modulus, Voigt)
E_c = V_f * E_f + V_m * E_m
General
Modulus of Resilience
U_r = sigma_y^2 / (2*E)
General
Density
rho = m / V
General
Specific Heat Capacity
Q = m * c * delta_T
General
Fourier's Law of Heat Conduction
q = -k * (dT/dx)
General
Brinell Hardness Number
HB = 2F / (pi*D*(D - sqrt(D^2 - d^2)))
General
Vickers Hardness Number
HV = 1.854 * F / d^2
General
Bragg's Law (X-ray Diffraction)
n * lambda = 2 * d * sin(theta)
General
Hall-Petch Relationship
sigma_y = sigma_0 + k_y / sqrt(d)
General
Fick's Second Law of Diffusion
dC/dt = D * (d2C/dx2)
General
Fick's First Law of Diffusion (Materials)
J = -D * (dC/dx)
General
Arrhenius Diffusion Coefficient
D = D0 * exp(-Q / (R*T))
General
Basquin's Equation (S-N Fatigue Life)
sigma_a = sigma_f' * (2*N_f)^b
General
Paris' Law (Fatigue Crack Growth)
da/dN = C * (delta_K)^m
General
Griffith's Fracture Criterion
sigma_f = sqrt(2*E*gamma_s / (pi*a))
General
True Strain
epsilon_true = ln(1 + epsilon_eng)
General
True Stress
sigma_true = sigma_eng * (1 + epsilon_eng)
General
Bulk Modulus
K = -V * (dP/dV)
General
Poisson's Ratio
nu = -epsilon_lateral / epsilon_axial
General
Shear Modulus
G = tau / gamma
General
Engineering Strain
epsilon = (L - L0) / L0
General
Engineering Stress
sigma = F / A0
General
Young's Modulus
E = sigma / epsilon
General
Hooke's Law (Stress-Strain)
sigma = E * epsilon
Thermal Properties
Fourier's Law of Conduction
q = −k(dT/dx)
Thermal Properties
Linear Thermal Expansion
ΔL = αL₀ΔT
Mechanical Properties
Fracture Toughness
K_IC = Yσ√(πa)