The core Ohms law table combines Voltage (V), Current (I), Resistance (R), and Power (P). For DC circuits, the base relationships are straightforward: P = V × I and V = I × R. However, the moment you step into AC or 3-phase territory, you must multiply by Power Factor (PF) for real power, and by the square root of 3 (1.732) for 3-phase systems. Below is the master reference chart used on the bench and jobsite, expanding the classic 12-formula wheel into practical AC applications.

The Master Ohms Law and Power Table

The following table provides the exact formulas needed to solve for any missing variable. The mathematical derivations and symbol conventions align with IEEE Std 141 (Red Book) for power distribution calculations and IEC 60027 for standard electrical symbols.

To Find DC Circuits Single-Phase AC 3-Phase AC
Current (I)
Amps		 I = P / V
I = V / R		 I = P / (V × PF)
I = V / Z		 I = P / (V × 1.732 × PF)
I = V / (Z × 1.732)
Voltage (V)
Volts		 V = P / I
V = I × R		 V = P / (I × PF)
V = I × Z		 V = P / (I × 1.732 × PF)
V = I × Z × 1.732
Resistance/Impedance (R/Z)
Ohms (Ω)		 R = V / I
R = P / I²		 Z = V / I
Z = V² / P		 Z = (V / I) / 1.732
Z = V² / (P × 1.732)
Real Power (P)
Watts (W)		 P = V × I
P = I² × R		 P = V × I × PF
P = I² × R		 P = V × I × 1.732 × PF
P = I² × R × 3
Bench Tip: In AC circuits, Resistance (R) is replaced by Impedance (Z), which accounts for both resistance and reactance (inductive/capacitive). If you are measuring a purely resistive AC load (like a baseboard heater), PF = 1, and Z = R, meaning the AC columns collapse into the exact same math as the DC column.

How to Read the Table and Apply Modifiers

To use this table accurately, you must first identify your circuit topology (DC, 1-Phase AC, or 3-Phase AC) and then apply the correct modifiers. The base values in the table assume ideal conditions. In the real world, two modifiers will change your calculated results:

  • Power Factor (PF): This is the ratio of Real Power (Watts) to Apparent Power (Volt-Amps). For purely resistive loads (incandescent bulbs, space heaters), PF is 1.0. For inductive loads (motors, transformers, fluorescent ballasts), PF typically ranges from 0.80 to 0.95. If you ignore PF on an inductive load, your calculated current will be dangerously low, leading to undersized breakers.
  • Efficiency (η): When calculating the electrical input power required for a mechanical output (like a motor rated in Horsepower), you must divide by the motor's efficiency. A 10 HP motor (7460 W) at 90% efficiency actually draws 8288 W from the electrical supply.

How Derating Rows Modify the Base Value: The formulas above calculate nominal steady-state values. If your installation environment exceeds standard ambient temperatures (usually 30°C / 86°F per NEC guidelines), the calculated current remains the same, but the wire ampacity required to carry that current must be derated. The table gives you the load current; the NEC derating tables tell you if your wire will melt carrying it.

Decision Tree: Which Column Applies to Your Installation?

Use this decision path to lock in the exact formula column and default values for your specific scenario.

Circuit Condition Diagnostic Question Action & Formula Column
Battery, Solar, or LED Strip Is the current unidirectional and constant? Use DC Column. No modifiers needed.
Standard US Wall Outlet / Heater Is it 120V/240V AC and purely resistive? Use 1-Phase AC Column. Set PF = 1.0.
HVAC Compressor / Industrial Motor Is it 208V/480V AC with 3 hot legs? Use 3-Phase AC Column. Multiply by 1.732.
Missing Motor Nameplate Data Do you lack the exact PF or Efficiency? Default Pick: Use the 3-Phase AC column and assume PF = 0.85 and η = 0.90 to calculate a safe baseline current for breaker sizing.

Quick-Jump Bookmark Rows for Common Queries

Here are the most frequently queried jobsite calculations, solved using the master table above.

Scenario 1: 12V DC LED Strip (Finding Resistance)

  • Knowns: V = 12V, I = 5A (measured with a multimeter).
  • Formula: R = V / I (DC Column).
  • Result: 12 / 5 = 2.4 Ω.
  • Application: If you need to replace a burnt-out current-limiting resistor on the driver board, you need a 2.4Ω resistor rated for at least 60W (P = I² × R = 25 × 2.4).

Scenario 2: 240V Single-Phase Baseboard Heater (Finding Current)

  • Knowns: V = 240V, P = 2000W (from nameplate).
  • Formula: I = P / (V × PF). Since it's a resistive heater, PF = 1.0.
  • Result: 2000 / 240 = 8.33A.
  • Application: Per NEC 210.20(A), continuous loads (on for 3+ hours) require the breaker to be sized at 125% of the load. 8.33A × 1.25 = 10.4A. Concrete Pick: Install a 15A double-pole breaker and use 14 AWG THHN wire.

Scenario 3: 480V 3-Phase 10HP Motor (Finding Current)

  • Knowns: V = 480V, P = 10 HP (7460W mechanical output).
  • Formula: I = P / (V × 1.732 × PF × η).
  • Assumptions: PF = 0.85, η = 0.90 (Standard industrial defaults).
  • Result: 7460 / (480 × 1.732 × 0.85 × 0.90) = 7460 / 636.5 = 11.72A.
  • Application: This is the Full Load Amps (FLA). Motor branch circuits require specific overcurrent protection per NEC 430.52 (typically 250% for inverse-time breakers). 11.72A × 2.5 = 29.3A. Concrete Pick: Install a 30A 3-pole breaker and size wire per NEC 430.22 (125% of FLA = 14.65A, requiring 12 AWG copper).

What the Table Cannot Tell You (And Where to Look Instead)

Ohm's law is a fundamental physics principle, but it is not a complete electrical design tool. Relying solely on this table will cause failures if you ignore the following physical realities:

  1. Wire Ampacity and Thermal Limits: The table will tell you that a 120V circuit drawing 15A requires 1800W of power. It will not tell you that running 15A through 14 AWG wire bundled in a hot attic will melt the insulation. For thermal limits, you must cross-reference your calculated current with NEC Table 310.16 (or your local equivalent), applying ambient temperature correction factors.
  2. Transient Inrush Current: A 12V DC motor might have a running current of 2A (calculated via R = V/I). However, at startup, before back-EMF builds up, the stalled-rotor current can spike to 10A or more. The table only calculates steady-state values. You must size fuses and MOSFETs to handle the inrush spike, not just the running current.
  3. Voltage Drop Over Distance: The formulas assume the voltage at the load is exactly the same as the voltage at the source. In reality, wire has resistance. If you are running a 240V heater 200 feet away, the wire itself will drop voltage. Use the formula V_drop = 2 × I × R_wire (for single-phase) to ensure your load receives adequate voltage. For comprehensive limits, refer to standard voltage drop guidelines which recommend keeping drop under 3% for branch circuits.
Final Directive: Use the Ohms law table to find your exact baseline current and power values. Once you have that number, immediately close the table and open the NEC (or local codebook) to size your conductors, breakers, and protective devices based on that calculated load.