ENGINEERING REFERENCE
Formula Library
Find formulas by tool and open the details for units, substitutions and applicable conditions.
Electrical and automation calculations
Ohm's LawFind voltage, current or resistance from the other two values.
U = I × RDC PowerCalculate DC power, or solve for voltage or current.P = U × ISingle-Phase CurrentCalculate single-phase operating current from power, voltage, power factor and efficiency.I = P / (U × cosφ × η)Three-Phase CurrentEstimate balanced three-phase operating current from line voltage and power.I = P / (√3 × U × cosφ × η)Motor Rated CurrentEstimate three-phase motor rated current from shaft power, line voltage, power factor and efficiency.I = P / (√3 × U × cosφ × η)Motor TorqueCalculate steady-state shaft torque from output power and speed.T = P / ω ≈ 9550 × P(kW) / n(rpm)Cable Voltage DropEstimate steady-state single-phase or three-phase cable voltage drop and percentage.ΔU ≈ k × I × L × (R′ × cosφ + X′ × sinφ)Power FactorConvert active power, apparent power and power factor, and calculate reactive-power magnitude.cosφ = P / S · |Q| = √(S² − P²)AC / RLC ImpedanceCalculate series RLC impedance, phase angle, power factor and resonant frequency.Z = R + j(2πfL − 1/(2πfC))Power Factor CorrectionEstimate compensation for an inductive load and single-phase, star or delta capacitor values.Qc = P × (tanφ₁ − tanφ₂)TransformerConvert ideal winding voltage and turns, and single-phase or balanced three-phase apparent power and current.V₁/V₂ = N₁/N₂ · S = k × V × IRC Time ConstantConvert resistance and capacitance units and review capacitor charging and discharging times.τ = R × CRL Time ConstantCalculate the current-response time constant from inductance and equivalent circuit resistance.τ = L / RCapacitor EnergyCalculate energy stored in an ideal capacitor from capacitance and terminal voltage.E = ½ × C × U²4–20 mA / PLC ScalingScale engineering values bidirectionally with 4–20 mA, 0–10 V or PLC raw counts.y = yₘᵢₙ + (x − xₘᵢₙ) / (xₘₐₓ − xₘᵢₙ) × (yₘₐₓ − yₘᵢₙ)Selection basis
Circuit Breaker SelectionScreen reference ratings by load type, starting method and operating current.
Iᴮ ≤ Iₙ ≤ Iᴢ · I_screen = Iᴮ × kContactor SelectionCheck motor operating current, utilization category and control coil.Iₑ (at the utilization category and Uₑ) ≥ IᴮThermal Overload Relay SelectionFind adjustment ranges that cover motor nameplate current.Iₘᵢₙ ≤ I_nameplate ≤ IₘₐₓCable SelectionScreen conductor cross-sections using current, length, installation method and ambient temperature.Iᴢ = I_table × k_temperature · ΔU% = ΔU / U × 100%24 VDC Power Supply SelectionTotal DC loads such as PLCs, instruments and relays to estimate supply capacity.P_total = Σ(n × P_unit) · P_target = P_total × (1 + reserve)PLC I/O SelectionPlan CPU and expansion modules from I/O counts, high-speed counters and network protocols.Planned points = ⌈required points × 1.20⌉