Ohm's Law Made Simple: V, I, R and P

The one equation everything rests on

Ohm’s law is the single most useful relationship in electrical work. It states that the current through a conductor is proportional to the voltage across it and inversely proportional to its resistance:

V = I × R

where V is voltage in volts, I is current in amps and R is resistance in ohms. Rearranged, the same equation gives I = V / R and R = V / I. Think of voltage as the electrical pressure pushing charge, current as the rate of flow, and resistance as the opposition to that flow. Raise the pressure and more current flows; add resistance and less flows.

Adding power

Power — the rate of doing electrical work, in watts — completes the picture. The core power equation is:

P = V × I

By substituting Ohm’s law you get two more forms that are often more convenient:

P = I² × R  and  P = V² / R

Together, the four quantities V, I, R and P form what electricians call the power wheel: knowing any two of them lets you compute the other two. The Ohm’s Law calculator implements every combination — enter the two you know and it returns the rest.

Worked example: current and resistance known

Suppose 10 amps flows through a 2-ohm element. Then:

V = I × R = 10 × 2 = 20 V, and P = V × I = 20 × 10 = 200 W.

You can confirm the power two ways: P = I² × R = 100 × 2 = 200 W, and P = V² / R = 400 / 2 = 200 W. All three forms agree, which is a good habit for catching arithmetic slips.

Worked example: voltage and resistance known

Now take 120 volts across a 60-ohm heater element:

I = V / R = 120 / 60 = 2 A, and P = V × I = 120 × 2 = 240 W.

This is exactly how you reason about resistive loads such as heaters and incandescent lamps: the resistance is fixed, the supply voltage is fixed, and Ohm’s law gives the current draw and wattage.

Where each form earns its keep

• V = I × R explains voltage drop: current through the resistance of a wire produces a voltage loss. That is the entire basis of the voltage-drop calculation.
• I = V / R tells you the inrush of a low-resistance load and why a near short circuit draws enormous current.
• P = I² × R is the heating law: power lost in a conductor rises with the square of the current, which is why high current on a thin wire is so punishing.
• P = V² / R is handy for fixed-voltage resistive loads where you know the element resistance.

AC, power factor and the limits of Ohm’s law

Ohm’s law in the simple form applies cleanly to DC and to purely resistive AC loads. With motors, transformers and electronics the current and voltage fall out of step, and real power becomes P = V × I × power factor. For those cases use the Power Converter, which handles single-phase and three-phase with power factor, or the 3-Phase Power calculator. The resistance relationships still hold for the conductors themselves, which is why wire heating and voltage drop are always governed by Ohm’s law even on an AC circuit.

A mental model you can carry

If you remember nothing else, remember the water analogy: voltage is pressure, current is flow, resistance is a narrow pipe, and power is the work the flow can do. Open the valve (more voltage) and flow rises; pinch the pipe (more resistance) and flow falls. Every formula above is just that picture written in symbols. To pair Ohm’s law with real conductors, the Wire Resistance calculator turns a gauge and length into the ohms you plug in.

The power wheel as a memory aid

The reason the four quantities are so easy to work with is that any one of them can be written in terms of any two others. Voltage can be found from current and resistance, from power and current, or from power and resistance. Power can be found from voltage and current, from current and resistance, or from voltage and resistance. This web of twelve relationships is what people draw as the power wheel, a circle split into four quadrants with three formulas each. You do not need to memorize all twelve; if you remember the two anchors, voltage equals current times resistance and power equals voltage times current, every other form follows by simple substitution. That is exactly what the calculator does internally when you give it any two values.

The squared term that punishes thin wire

Of all the forms, the one worth internalizing is that power lost as heat equals current squared times resistance. The squaring is the key insight. Double the current through a given wire and you do not double the heat, you quadruple it. This single fact explains why high current on a thin conductor is so dangerous, why upsizing a wire reduces its heating dramatically, and why utilities transmit power at high voltage and low current over long distances. It also explains voltage drop from a different angle: the same resistance that wastes voltage as a drop is dissipating that lost voltage as heat, and both effects grow with current. Once the squared relationship is intuitive, a great deal of electrical behavior stops being surprising.

Series and parallel resistance

Real circuits combine resistances, and two simple rules cover most cases. Resistances in series add directly, so two ten ohm elements in series present twenty ohms and draw half the current a single element would. Resistances in parallel combine by adding their reciprocals, so two ten ohm elements in parallel present five ohms and draw twice the current. The intuition matches the water analogy: series is a longer, narrower path that restricts flow, while parallel opens additional paths that ease it. Ohm law then gives the current and power for the combined resistance exactly as it does for a single one, which is why understanding these two rules lets you analyze far more than a lone resistor.

Everyday uses on the job

These relationships are not academic. An electrician uses them to predict the current a heater will draw before energizing it, to estimate the wattage of a load from a clamp-meter reading, to reason about why a circuit trips, and to understand why a long run dims a light. A solar or RV builder uses them to convert between the watts an appliance is rated for and the amps it pulls from a twelve volt bank, which sets the wire and fuse size. Whenever you find yourself unsure about a circuit, returning to voltage equals current times resistance and power equals voltage times current will usually untangle it, because every other electrical quantity is built from those two.

These relationships are exact physics, not estimates. The estimates on this site arise only where real-world constants (resistivity at temperature, derating, typical loads) enter the picture; Ohm’s law itself is always true.