Ohm's Law in Practice — The Four Formulas That Run Every Circuit
You'll meet Ohm's Law in your first electrical class and forget it within a week. Then the day comes when you need to size a heating element, troubleshoot a motor that's pulling too much current, or check whether a circuit will trip — and the wheel chart shows up taped to a workbench because nobody can keep all four formulas in their head at once.
The four formulas are tied together by two laws of nature, expressed four ways:
- V = I × R (Ohm's Law proper)
- P = V × I (electrical power)
- P = I² × R (resistive form, current)
- P = V² / R (resistive form, voltage)
Combine any two of {voltage, current, resistance, power} and the other two fall out. That's the wheel chart in one paragraph.
What each variable means in the field
Voltage (V) is the pressure that pushes electrons through the circuit. House outlets in North America are 120 V single-phase, dryer/range circuits are 240 V single-phase, three-phase commercial is typically 208 V or 480 V depending on the building. Voltage drops along a wire — by a tiny amount on short runs, by enough to matter on long ones (see the voltage drop guide).
Current (I) is the flow of electrons in amps. The breaker is sized to limit current — when the load draws more than the breaker rating for too long, the breaker opens. Tools, motors, and heating elements have nameplate current ratings that let you size the circuit.
Resistance (R) is the opposition to current flow, in ohms (Ω). A short copper wire is fractions of an ohm. A 100 W incandescent bulb at room temperature is around 10 Ω, climbing to 144 Ω when hot. Heating elements are designed for specific resistance values to dissipate the right power at the right voltage.
Power (P) is the rate at which the circuit does work, in watts. Multiply watts by hours to get watt-hours (energy), which is what utilities bill you for. A 1500 W space heater at 120 V draws 12.5 A. A 5500 W water heater at 240 V draws about 23 A.
When each formula earns its keep
V = IR is the troubleshooting friend. You measure voltage at one point, current through one branch, and the formula tells you whether the resistance you're seeing matches what you expected. Loose connection making contact intermittently? You'll see voltage drop across the connection that doesn't belong there.
P = VI is the planning friend. You're sizing a circuit. The fan motor nameplate says 600 W at 120 V. That's 5 A nominal, and you'll size the wire and breaker around that.
P = I² R is the dissipation friend. You're sizing a heating element or worried about wire heating. Resistance heaters are rated this way — a 12 Ω element at 20 A dissipates 4800 W as heat. The same form tells you how much heat your wire is making (and why upsizing it cools things down).
P = V² / R is the load-distribution friend. Resistive loads on a constant-voltage source — heating elements, baseboard heaters, incandescent lights — all draw power proportional to V². Source voltage drops 10% under load? The element makes 19% less heat. That's why low source voltage feels so much worse than the percentage suggests.
The AC gotcha
These four formulas are exact for DC and for purely resistive AC loads. For AC with reactive loads — motors, transformers, anything with a coil or capacitor — there's a phase angle between voltage and current. Real power is then P = V × I × cos(φ), where cos(φ) is the power factor.
Resistive loads have a power factor of 1.0 — the formulas above are exact.
Typical motor power factor is around 0.85. A motor that draws 10 A at 240 V isn't pulling 2400 W of real power — it's pulling 2400 × 0.85 = 2040 W of real work plus 1264 var of reactive power that bounces back and forth without doing anything useful. The breaker still has to handle the full 10 A; the utility still has to deliver it. But your kWh meter only counts the 2040 W.
This is why power factor correction matters in industrial settings — adding capacitors to cancel out motor inductance brings the power factor closer to 1.0 and lets the same wires deliver more useful power.
Skip the wheel chart
The Ohm's Law Calculator does any of the six pairwise combinations in one click. Pick which two values you have (V+I, V+R, V+P, I+R, I+P, R+P) and it returns the other two with auto-scaling units — 0.005 A becomes 5 mA, 1200 W becomes 1.2 kW, no manual conversion required.
The short version
V = IR is the universe. P = VI is the wallet. The square forms (P = I²R, P = V²/R) are the heat. AC adds a power factor on top. All four are bolted to the same physics — pick the one whose inputs you already have.