Electrical Formulas: Complete Reference with Examples
Use this formula sheet to choose the right equation, keep units consistent, expose assumptions, and continue into an interactive calculator or editable circuit.
Core electrical formulas
| Quantity | Formula | Use |
|---|---|---|
| Ohm’s law | V = I × R | Relates voltage, current and resistance in a resistive element. |
| DC/resistive power | P = V × I = I²R = V²/R | Calculates electrical power and resistor dissipation. |
| Energy | E = P × t | Converts power over time to Wh, kWh or joules with consistent units. |
| Series resistance | Req = R1 + R2 + … | Combines resistors carrying the same current. |
| Parallel resistance | 1/Req = 1/R1 + 1/R2 + … | Combines branches sharing the same voltage. |
| Voltage divider | Vout = Vin × R2/(R1 + R2) | Estimates an unloaded two-resistor divider. |
| RC time constant | τ = R × C | Sets the first-order charge/discharge time scale. |
| RL time constant | τ = L/R | Sets the first-order current-change time scale. |
| LC resonance | f₀ = 1/(2π√LC) | Estimates ideal resonant frequency. |
Single-phase and three-phase AC power
| System | Real power | Apparent power | Current solved from real power |
|---|---|---|---|
| Single phase | P = V × I × PF | S = V × I | I = P/(V × PF) |
| Balanced three phase | P = √3 × VLL × IL × PF | S = √3 × VLL × IL | I = P/(√3 × VLL × PF) |
For a motor’s mechanical output, divide by efficiency before solving input current. Real motor current should be verified from the nameplate and the applicable code tables; starting current and protection use additional rules.
Transformer formulas
- Turns/voltage ratio: Vp/Vs = Np/Ns for an ideal transformer.
- Single-phase winding current: I = VA/V.
- Three-phase transformer line current: I = kVA × 1000/(√3 × VLL).
- Simplified terminal fault estimate: If transformer percent impedance is Z%, Isc ≈ Irated × 100/Z%. This omits upstream and downstream detail and is not a complete short-circuit study.
Voltage drop
For a simple copper/aluminum K-method calculation using circular mils and feet:
- Single phase: VD = 2 × K × I × L/CM.
- Balanced three phase: VD = √3 × K × I × L/CM.
- Percentage: VD% = 100 × VD/Vsystem.
L is one-way length. The simple K method is an approximation; larger AC conductors, power factor and reactance can require an impedance-based method.
LED series resistor
For n LEDs in series, R = (Vs − nVf)/I. Resistor dissipation is P = I²R. Check highest supply, lowest credible forward voltage, resistor tolerance, LED temperature, standard resistor value and power derating. Give separate parallel LED branches their own current control.
Conduit fill
Fill percentage = 100 × total conductor area/conduit internal area. Under NEC Chapter 9 Table 1, the nominal limits are 53% for one conductor, 31% for two and 40% for three or more. Use the exact conductor insulation and raceway tables rather than bare-conductor diameter.
Units and prefixes
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| milli | m | 10⁻³ | 20 mA = 0.020 A |
| micro | µ | 10⁻⁶ | 100 µF = 0.000100 F |
| kilo | k | 10³ | 10 kΩ = 10,000 Ω |
| mega | M | 10⁶ | 1 MΩ = 1,000,000 Ω |
Prefixes are case-sensitive: m means milli while M means mega. Convert to base units before substituting into an equation, calculate, then convert the result to a readable engineering unit.
A five-step formula workflow
- Draw the circuit or system boundary and mark known values.
- Choose an equation whose assumptions match that boundary.
- Convert every input to consistent units.
- Calculate the nominal value and sanity-check its order of magnitude.
- Repeat with tolerance, temperature, supply and load limits; then verify against component data, simulation or measurement.
Important limitations
Compact formulas are models. They do not automatically include component tolerance, temperature, parasitics, harmonics, transient energy, inrush, magnetic saturation, cable installation, fault contribution, protection clearing time, thermal environment or the applicable legal standard. Use them to make assumptions visible—not to hide engineering review.
Primary standards context
- IEC 60034-30-1:2025 defines efficiency classes for covered line-operated AC motors; actual motor performance remains nameplate and design specific.
- IEC 60287-1-1:2023 covers cable current-rating equations and the thermal parameters that simple amp charts cannot express.
- Schneider Electric’s transformer fault-current example demonstrates the rated-current divided by per-unit impedance screening method.
Frequently asked questions
What are the three forms of Ohm’s law?
V = I × R, I = V/R, and R = V/I. Pair them with P = V × I to solve electrical power.
What is the three-phase power formula?
For a balanced system using line-to-line voltage and line current, real power is P = √3 × VLL × IL × power factor. Include efficiency when solving motor input from mechanical output.
Why must units be converted first?
Equations assume compatible units. For example, 20 mA is 0.020 A and 100 µF is 0.000100 F; substituting the prefix value directly produces errors of thousands or millions.
Can a formula replace simulation?
No. Hand equations, simulation and measurement answer different questions. Use a formula for transparent first-order reasoning, simulation for supported interactions and waveforms, and measurement for the physical implementation.
Can these equations be used for final electrical installation design?
They are educational references. Final installation work must use the complete locally adopted standard, verified equipment data and competent professional review.
Related tools & references
- Ohm’s law calculator
- Voltage divider calculator
- Transformer calculator
- Motor current calculator
- Fault current calculator
- Circuit simulation examples
Last verified: 2026-07-30