Engineering Formula Library
Find an engineering equation by discipline, review every variable and unit, and calculate a result with a worked substitution and evaluation.
Mathematics formulas
- Pythagorean Theorem — c = √(a² + b²)
- Distance Between Two Points — d = √((x₂ - x₁)² + (y₂ - y₁)²)
- Slope Between Two Points — m = (y₂ - y₁)/(x₂ - x₁)
- Area of a Circle — A = π × r²
- Circumference of a Circle — C = 2 × π × r
- Area of a Triangle — A = 0.5 × b × h
- Volume of a Sphere — V = (4/3) × π × r³
- Quadratic Discriminant — Δ = b² - 4 × a × c
- Arithmetic Series Sum — S = n/2 × (2a + (n - 1)d)
- Geometric Series Sum — S = a × (1 - r^n)/(1 - r)
- Percentage Change — Δ = ((V₁ - V₀)/V₀) × 100
- Linear Interpolation — y = y₁ + (x - x₁) × (y₂ - y₁)/(x₂ - x₁)
Mechanics formulas
- Newton's Second Law — F = ma
- Work Done — W = F·d·cos(θ)
- Kinetic Energy — KE = ½mv²
- Potential Energy — PE = mgh
- Momentum — p = mv
- Centripetal Force — Fc = mv²/r
- Impulse — J = FΔt
- Mechanical Power — P = W/t
Fluid Mechanics formulas
- Bernoulli's Equation — P₂ = P₁ + 0.5ρv₁² + ρgh₁ - 0.5ρv₂² - ρgh₂
- Reynolds Number — Re = ρvL/μ
- Darcy-Weisbach Equation — Δp = f × (L/D) × (ρv²/2)
- Flow Rate — Q = vA
- Hydrostatic Pressure — P = ρgh
- Dynamic Pressure — q = 0.5ρv²
Electrical formulas
- Ohm's Law — V = IR
- Power — P = VI
- Capacitive Reactance — Xc = 1/(2πfC)
- Inductive Reactance — XL = 2πfL
- RC Time Constant — τ = RC
- Voltage Divider — Vout = (Vin × R2) / (R1 + R2)
- Capacitor Energy — E = 0.5CV²
Statics & Structural formulas
- Beam Deflection — δ = PL³/3EI
- Bending Moment — M = WL/4
- Flexure Formula — σ = My/I
- Euler's Column Formula — Pcr = π²EI/L²
- Axial Stress — σ = P/A
- Engineering Strain — ε = ΔL/L
Thermodynamics formulas
- Ideal Gas Law — P = nRT/V
- Heat Transfer — Q = mcΔT
- Conduction — q = kAΔT/L
- Thermal Efficiency — η = W/Qh
- Entropy Change — ΔS = Q/T
- Carnot Efficiency — η = 1 - Tc/Th
- Convection Heat Transfer — q = hAΔT
Chemical Engineering formulas
- Mass Balance — Σmin = Σmout
- Energy Balance — ΔU = Q - W
- Reaction Rate — rA = k·CA^n
- Arrhenius Equation — k = A·e^(-Ea/RT)
- Residence Time — τ = V/Q
Materials Engineering formulas
- Hooke's Law — σ = Eε
- Thermal Expansion — ΔL = αL₀ΔT
- Stress Concentration — σmax = Ktσnom
- Fatigue Life (S-N) — S = aN^b
- Factor of Safety — N = Sy/σ
Hydraulics formulas
- Manning's Equation — V = (1/n) × R^(2/3) × S^(1/2)
- Darcy-Weisbach Equation — hf = f × (L/D) × (V²/2g)
- Continuity Equation — Q = A × V
Geotechnical Engineering formulas
- Bearing Capacity — qu = c×Nc + γ×D×Nq + 0.5×γ×B×Nγ
- Rankine Active Pressure — Ka = tan(pi/4 - φ/2)^2
Environmental Engineering formulas
- BOD Removal — S = S₀ × e^(-kt)
- Air Quality Index — AQI = ((IHi - ILo)/(CHi - CLo)) × (C - CLo) + ILo
- Dilution Concentration — C2 = C1V1/V2
Aerospace Engineering formulas
- Lift Equation — L = 0.5 × ρ × V² × S × CL
- Rocket Equation — Δv = ve × ln(m₀/mf)
- Drag Equation — D = 0.5ρV²SCD
- Lift Force — L = CL · 0.5 · ρ · v² · A
- Drag Force — D = CD · 0.5 · ρ · v² · A
- Tsiolkovsky Rocket Equation — Δv = ve · ln(m0/mf)
- Mach Number — M = v/c
- Aspect Ratio — AR = b²/S
- Orbital Velocity — v = √(GM/r)
Civil Engineering formulas
- Stress in Concrete — σc = P/A
- Reinforced Concrete Beam Capacity — Mn = As · fy · (d - a/2)
- Manning's Equation — v = (1/n) · R^(2/3) · S^(1/2)
- Soil Bearing Capacity — qult = c·Nc + q·Nq + 0.5·γ·B·Nγ
- Hazen-Williams Equation — v = 0.85 · C · R^0.63 · S^0.54
Electronics Engineering formulas
- Resistors in Series — Req = R₁ + R₂ + R₃ + ... + Rₙ
- Resistors in Parallel — 1/Req = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ
- RC Time Constant — τ = RC
- Resonant Frequency — f = 1/(2π√(LC))
- Transistor Current Gain — β = Ic/Ib
- Impedance of Capacitor — Zc = 1/(2πfC)
- Impedance of Inductor — ZL = 2πfL
Computer Science formulas
- Time Complexity — T(n) = O(f(n))
- Shannon's Information Content — I(x) = -log₂(p(x))
- Shannon Entropy — H(X) = -Σ p(x) · log₂(p(x))
- Amdahl's Law — S = 1/((1-p) + p/s)
Quantum Physics formulas
- de Broglie Wavelength — λ = h/p
- Heisenberg Uncertainty Principle — ΔxΔp ≥ ℏ/2
- Schrödinger Equation (Time-Independent) — Hψ = Eψ
- Photon Energy — E = hf