Ohm's Law Explained

Three quantities, one relationship

Almost everything you need to reason about a simple electrical circuit comes down to three numbers: the voltage pushing the electricity along, the current that flows as a result, and the resistance that opposes it. Ohm's law is the single equation that ties them together, and once you can move between them freely, most beginner electronics stops feeling like guesswork. The Ohm's law calculator does the arithmetic — enter any two of voltage, current, resistance or power and it returns the other two — but this guide is about the reasoning behind it, so the numbers mean something rather than just appearing.

We'll cover what each quantity actually is, the formula and the memory aids that let you rearrange it in your head, a worked example built around the single most common real task (picking a resistor for an LED), the reasons the law quietly breaks for some components, and the mistakes that trip up nearly everyone at first.

What Ohm's law actually says

Ohm's law states that the current through a conductor is directly proportional to the voltage across it, provided the temperature and physical conditions stay constant. The constant of proportionality is the resistance, which gives the familiar form:

V = I × R

Here V is voltage in volts, I is current in amperes (amps), and R is resistance in ohms (the Greek letter Ω). The plumbing analogy is worn but genuinely useful: voltage is the water pressure, current is the flow rate through the pipe, and resistance is how narrow the pipe is. Raise the pressure and more water flows; narrow the pipe and less flows. That is the whole intuition. A key point people miss is that voltage exists across two points while current flows through a component — they are not the same kind of measurement, and swapping them in your head is the root of most early confusion.

Rearranging the one equation gives the two other forms you'll reach for constantly: I = V ÷ R to find current, and R = V ÷ I to find resistance. The Ohm's law calculator picks the right rearrangement automatically from whichever pair you type in.

The triangle, power, and the wheel

The classic memory aid is the Ohm's law triangle: draw V in the top half, with I and R side by side in the bottom half. Cover the quantity you want and the triangle shows the formula. Cover V and you see I next to R (multiply: V = I × R). Cover I and you see V over R (divide: I = V ÷ R). Cover R and you see V over I (R = V ÷ I). It's a crutch, but a good one while the algebra becomes second nature.

Power extends the picture. Electrical power — the rate at which energy is delivered or dissipated, measured in watts — is defined as P = V × I. Substitute Ohm's law into it and you get two more equivalents that save you a step depending on what you know:

• P = V × I — the definition (volts times amps)
• P = I² × R — from substituting V = I × R
• P = V² ÷ R — from substituting I = V ÷ R

Together these four quantities — V, I, R, P — form what's often drawn as the power wheel or VIRP wheel: twelve formulas, one for every way of getting each quantity from a pair of the others. You don't need to memorise all twelve. Know V = I × R and P = V × I, and every other formula is a substitution away. The Ohm's law calculator holds the whole wheel internally, which is why any two inputs are enough to fill in the rest.

Worked example: the resistor for an LED

The most common real reason people meet Ohm's law is to protect a component — usually an LED — from too much current. An LED does not have a fixed resistance you can look up; connect it straight across a supply and it draws whatever current it likes and burns out. The fix is a series resistor that soaks up the leftover voltage and sets the current, and Ohm's law sizes it.

Say you're driving a standard red LED from a 9 V battery. A typical red LED has a forward voltage of about 2 V and wants around 20 mA (0.02 A) of current. The resistor has to drop everything the LED doesn't:

• Voltage across the resistor: 9 V (supply) − 2 V (LED) = 7 V.
• Resistance needed: R = V ÷ I = 7 V ÷ 0.02 A = 350 Ω. The nearest standard value up is 360 Ω (or 390 Ω), and rounding up is the safe direction because a bigger resistor means slightly less current.
• Power the resistor must handle: P = I² × R = 0.02² × 360 = 0.144 W. A standard quarter-watt (0.25 W) resistor copes comfortably; that headroom check is the step beginners skip right before something gets hot.

Every number there came from V = I × R and P = I² × R. Plug the same figures into the Ohm's law calculator — enter 7 V and 0.02 A — and it returns the 350 Ω resistance and the 0.14 W of power in one step. If you'd rather work backwards from a colour-banded resistor you already own, the resistor calculator decodes the bands into ohms so you can check the current it would give.

Why the law sometimes breaks

Ohm's law is an empirical relationship, not a fundamental law of physics like conservation of energy. It describes how a large class of materials — "ohmic" ones — behave, and it's an excellent approximation for them, but plenty of everyday components disobey it.

Temperature changes the resistance

The law holds only while resistance stays constant, and resistance depends on temperature. Push more current through a wire and it heats up; in a metal, that raises its resistance. The tungsten filament in an old incandescent bulb is the textbook case — cold, it might read a few ohms, but glowing white-hot its resistance is ten or more times higher, so the current does not rise in step with the voltage. Plot voltage against current for a filament and you get a curve, not the straight line an ohmic resistor gives.

Semiconductors don't play along at all

LEDs, ordinary diodes and transistors are non-ohmic. A diode passes almost no current until the voltage crosses a threshold (about 0.7 V for silicon, 2 V for a red LED), then current rises steeply — and it blocks current entirely in the reverse direction. There is no single resistance value that describes it. This is exactly why the LED example above uses a separate resistor to set the current: you can't rely on the LED to limit itself the way a plain resistor does.

Real supplies have their own resistance

A battery or power supply isn't a perfect voltage source. It has internal resistance, so the voltage you actually get at the terminals sags a little under load. For small currents it's negligible; for a nearly-flat AA cell driving a motor, the terminal voltage can drop noticeably, and your Ohm's law sums based on the printed 1.5 V will run high. Long thin wires add resistance too — enough to matter over a run, which is what the voltage drop calculator and wire gauge calculator are for.

Using Ohm's law well

A handful of habits keep the arithmetic honest:

• Work in base units. Convert to volts, amps and ohms before you calculate: 20 mA is 0.02 A, 4.7 kΩ is 4,700 Ω, 250 mV is 0.25 V. Mixing prefixes is the number one source of answers that are off by a factor of a thousand.
• Always check the power, not just the resistance. A resistor with the right ohms but too low a wattage rating will cook. Work out P = I² × R and pick a resistor rated at least double it for headroom.
• Sanity-check the size of the answer. A 5 V supply through 1 kΩ gives 5 mA — a sensible small-signal current. If you get 5 A, you've slipped a prefix somewhere.
• Add series resistances, invert parallel ones. Ohm's law works on the total resistance a source sees. Resistors in series add up; in parallel, the combined resistance is smaller than the smallest one.
• Measure, then trust. A multimeter reads all three quantities directly. Measuring the real voltage across a component and the real current through it, then dividing, tells you its actual resistance under working conditions — often more useful than the nominal value.

Common mistakes

Swapping voltage and current. Voltage is measured across a component (a difference between two points); current is measured through it (you break the circuit to insert the meter in line). Confusing which is which scrambles every formula that follows.

Forgetting the prefixes. Typing 20 instead of 0.02 for 20 mA, or 4.7 instead of 4,700 for 4.7 kΩ, throws the result out by orders of magnitude. Pick base units once and stay there.

Assuming resistance is fixed. For a plain resistor it essentially is, but a bulb, a motor or a semiconductor changes its effective resistance with temperature or operating point. Ohm's law still applies moment to moment, but you can't use a cold-measured resistance to predict hot-running current.

Ignoring power ratings. Getting the ohms right but the wattage wrong is a classic — the circuit works for ten seconds, then the resistor discolours and drifts. Sizing power is half the job.

Trusting a nominal supply voltage. A "9 V" battery under load may deliver 8 V or less. When precision matters, base your sums on the measured terminal voltage, not the label.

When the calculation isn't enough

Ohm's law covers steady direct-current (DC) circuits with resistive loads. Once a circuit involves capacitors or inductors, or you're working with alternating current (AC), resistance is replaced by impedance, currents and voltages fall out of step, and you need the reactive-circuit tools instead — the capacitor energy calculator is a starting point for the energy-storage side. For anything involving mains voltage, wiring a property, or a fault you don't understand, this is where a qualified electrician earns their fee: the maths is the easy part, and mains electricity is unforgiving of a wrong assumption. Use Ohm's law to understand and to design low-voltage hobby circuits with confidence; don't use it to talk yourself into touching household wiring.

For the calculation itself — voltage, current, resistance and power from any two knowns, with the formula it used shown alongside — the Ohm's law calculator handles it instantly. To go further into the circuit, the resistor colour-code guide and the voltage drop guide pick up where a single Ohm's law step leaves off.