1. Electrical Engineering Formulas
1.1 DC Circuit Fundamentals
| Formula | Equation | Variables | Calculator |
|---|---|---|---|
| Ohm's Law | V = I × R | V = voltage (V), I = current (A), R = resistance (Ω) | Calculate → |
| Power (DC) | P = V × I = I²R = V²/R | P = power (W) | Calculate → |
| Resistors in Series | RT = R₁ + R₂ + ... + Rn | RT = total resistance | — |
| Resistors in Parallel | 1/RT = 1/R₁ + 1/R₂ + ... + 1/Rn | RT = total resistance | — |
| Voltage Divider | Vout = Vin × R₂/(R₁+R₂) | R₁, R₂ = divider resistors | Calculate → |
| Energy | E = P × t | E = energy (J or Wh), t = time (s or h) | — |
1.2 AC Circuit Formulas
| Formula | Equation | Variables | Calculator |
|---|---|---|---|
| Three-Phase Power | P = √3 × VL × IL × PF | VL = line voltage, PF = power factor | Calculate → |
| Power Factor | PF = cos φ = P / S | P = real power (W), S = apparent power (VA) | Calculate → |
| Impedance | Z = √(R² + X²) | X = reactance (Ω), Z = impedance (Ω) | — |
| Capacitive Reactance | XC = 1/(2πfC) | f = frequency (Hz), C = capacitance (F) | — |
| Inductive Reactance | XL = 2πfL | L = inductance (H) | — |
| Resonant Frequency | f₀ = 1/(2π√(LC)) | L = inductance, C = capacitance | — |
| Transformer Ratio | V₁/V₂ = N₁/N₂ = I₂/I₁ | N = turns, V = voltage, I = current | Calculate → |
| Voltage Drop | Vd = (mV/A/m × Ib × L) / 1000 | L = length (m), Ib = current | Calculate → |
1.3 Electronics
| Formula | Equation | Calculator |
|---|---|---|
| LED Resistor | R = (Vs - Vf) / If | Calculate → |
| BJT Current Gain | β = IC / IB | Calculate → |
| RC Time Constant | τ = R × C | — |
| RL Time Constant | τ = L / R | — |
2. Mechanical Engineering Formulas
| Formula | Equation | Variables | Calculator |
|---|---|---|---|
| Torque | T = F × r | F = force (N), r = radius (m) | — |
| Power (Rotational) | P = T × ω = 2πnT / 60 | ω = rad/s, n = RPM, T = Nm | — |
| Stress | σ = F / A | σ = stress (Pa), A = area (m²) | — |
| Strain | ε = ΔL / L₀ | ΔL = deformation, L₀ = original length | — |
| Hooke's Law | σ = E × ε | E = Young's modulus (Pa) | — |
| Bernoulli's Equation | P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ | ρ = density, v = velocity, h = height | Calculate → |
| Reynolds Number | Re = ρvD / μ | D = diameter, μ = dynamic viscosity | Calculate → |
| Heat Transfer (LMTD) | Q = U × A × LMTD | U = overall coefficient, A = area | Calculate → |
| HVAC Duct Area | A = Q / V | Q = airflow (CFM), V = velocity (FPM) | Calculate → |
| Gear Ratio | GR = N₂/N₁ = ω₁/ω₂ | N = teeth, ω = angular velocity | — |
3. Civil & Structural Engineering Formulas
| Formula | Equation | Variables | Calculator |
|---|---|---|---|
| Beam Deflection (UDL) | δ = 5wL⁴ / (384EI) | w = load/length, L = span, E = modulus, I = moment of inertia | Calculate → |
| Beam Deflection (Point) | δ = PL³ / (48EI) | P = point load | Calculate → |
| Bending Stress | σ = M × y / I | M = bending moment, y = distance from N.A. | — |
| Concrete Volume | V = L × W × D | L = length, W = width, D = depth | Calculate → |
| Rebar Spacing | As = n × Abar | n = number of bars | Calculate → |
| Retaining Wall Overturning | FS = Mresist / Moverturning | FS ≥ 2.0 (typically) | Calculate → |
| Soil Bearing Capacity | qu = cNc + qNq + 0.5γBNγ | Terzaghi's equation | — |
| Euler's Buckling Load | Pcr = π²EI / (KL)² | K = effective length factor | — |
4. Chemical Engineering Formulas
| Formula | Equation | Calculator |
|---|---|---|
| Ideal Gas Law | PV = nRT | — |
| Chemical Dosing | D = (C × Q) / S | Calculate → |
| Dilution | C₁V₁ = C₂V₂ | — |
| pH | pH = -log₁₀[H⁺] | — |
| Molarity | M = mol / L | — |
| Heat of Reaction | ΔH = ΣH(products) - ΣH(reactants) | — |
| Mass Balance | Input = Output + Accumulation | — |
5. Physics Formulas
| Formula | Equation | Calculator |
|---|---|---|
| Projectile Range | R = v₀² sin(2θ) / g | Calculate → |
| Projectile Max Height | H = v₀² sin²θ / (2g) | Calculate → |
| Kinetic Energy | KE = ½mv² | — |
| Potential Energy | PE = mgh | — |
| Newton's Second Law | F = ma | — |
| Gravitational Force | F = Gm₁m₂/r² | — |
| Coulomb's Law | F = kq₁q₂/r² | — |
| Pendulum Period | T = 2π√(L/g) | — |
| Wave Speed | v = fλ | — |
| Einstein's Energy | E = mc² | — |
6. Engineering Constants
| Constant | Symbol | Value |
|---|---|---|
| Speed of Light | c | 2.998 × 10⁸ m/s |
| Gravitational Acceleration | g | 9.807 m/s² |
| Boltzmann Constant | kB | 1.381 × 10⁻²³ J/K |
| Planck's Constant | h | 6.626 × 10⁻³⁴ J·s |
| Gas Constant | R | 8.314 J/(mol·K) |
| Avogadro's Number | NA | 6.022 × 10²³ /mol |
| Electron Charge | e | 1.602 × 10⁻¹⁹ C |
| Permittivity (Free Space) | ε₀ | 8.854 × 10⁻¹² F/m |
| Permeability (Free Space) | μ₀ | 4π × 10⁻⁷ H/m |
| Stefan-Boltzmann | σ | 5.670 × 10⁻⁸ W/(m²·K⁴) |
| Steel Modulus (E) | Esteel | 200 GPa |
| Concrete Modulus (E) | Econcrete | 25–30 GPa |
| Copper Resistivity | ρCu | 1.72 × 10⁻⁸ Ω·m |