These electrical engineering calculators cover the fundamental quantities of low-voltage installations (LV ≤ 1000 V AC): Ohm's Law for linear resistors, active power in balanced single-phase and three-phase systems, phase current from rated power, percentage voltage drop along a conductor, power factor correction with capacitors, conductor resistance as a function of resistivity, cross-section and length, and electrical energy consumption over time. Formulas follow IEC sign conventions and steady-state assumptions.
V = R × I. Linear relationship between voltage V [V], resistance R [Ω], and current I [A] for ohmic conductors in DC or quasi-steady-state. Allows deriving any of the three quantities when the other two are known.
Single-phase active power
P = V × I × cos φ [W]. Where cos φ is the power factor (= 1 for purely resistive loads, < 1 for inductive/capacitive loads). Apparent power: S = V × I [VA].
Three-phase active power
P = √3 × V_L × I_L × cos φ [W]. V_L is line voltage (e.g., 480 V in US systems, 400 V in European systems), I_L is line current. Valid for balanced three-phase systems.
Voltage drop
ΔV = (2 × L × ρ × I) / S for single-phase circuits. L = conductor length [m], ρ = resistivity [Ω·m], I = current [A], S = cross-section [mm²]. NEC recommends ΔV% ≤ 3% for branch circuits, ≤ 5% total.
Power factor correction
Improving cos φ reduces reactive current. Q_C = P × (tan φ₁ − tan φ₂) [kVAr]. Capacitor: C = Q_C / (ω × V²). Reduces resistive losses and voltage drop.
Conductor resistance
R = ρ × L / S [Ω]. ρ is specific resistivity: copper ≈ 1.72×10⁻⁸ Ω·m, aluminum ≈ 2.82×10⁻⁸ Ω·m at 20°C. Resistivity increases with temperature: ρ(T) = ρ₀ × [1 + α×(T − T₀)].
Core formulas
V = R × I (Ohm's Law)
P = V × I × cos φ (single-phase)
P = √3 × V_L × I_L × cos φ (three-phase)
ΔV = 2 × L × ρ × I / S (voltage drop, single-phase)
Q_C = P × (tan φ₁ − tan φ₂) (reactive power to compensate)