Ohm's Law: V = IR, With Numbers That Actually Compute
Science · 5 min read · Last updated September 2026
The three forms
Worked example: 12 V battery, 4 Ω resistor. Current I = 12 ÷ 4 = 3 A. Power P = V × I = 12 × 3 = 36 W — the resistor turns 36 joules per second into heat, which is why resistor power ratings matter.
Series and parallel (where intuition breaks)
Series: resistances add. Two 5 Ω resistors in series = 10 Ω, so the same 12 V drives only 12 ÷ 10 = 1.2 A.
Parallel: 1/R = 1/R₁ + 1/R₂. Two 5 Ω in parallel = 2.5 Ω, so 12 ÷ 2.5 = 4.8 A — parallel paths increase total current because each path sees the full voltage.
| Configuration | Total R | Current at 12 V | Power |
|---|---|---|---|
| Single 4 Ω | 4 Ω | 3.0 A | 36 W |
| Two 5 Ω in series | 10 Ω | 1.2 A | 14.4 W |
| Two 5 Ω in parallel | 2.5 Ω | 4.8 A | 57.6 W |
Practical uses
Choosing an LED series resistor (supply voltage minus LED drop, divided by desired current), checking whether a wire gauge can carry a motor's inrush current, or verifying a power-supply spec. The Ohm's Law Calculator solves any missing variable; the Resistor Color Code tool decodes the bands on the part itself.
Try the calculators
Worked example: Ohm's Law Calculator at its default inputs
Take the default setup on Ohm's Law Calculator: no fields changed, nothing tuned to a nice round number. Run in the site's own engine, those values produce the answer below.
| Input | Default |
|---|---|
| Voltage (V) | 12 |
| Current (A) | 2 |
Result: Resistance: 6.00 Ω | Power: 24.00 W
The steps behind that answer
- Formula: V = I × R, P = V × I
- Step 1: R = V / I = 12 / 2 = 6.00 Ω
- Step 2: P = V × I = 12 × 2 = 24.00 W
Voltage (V) — three values, three answers
Hold every other field still and move only voltage (v).
| Voltage (V) | Result |
|---|---|
| 6 | Resistance: 3.00 Ω | Power: 12.00 W |
| 12 | Resistance: 6.00 Ω | Power: 24.00 W |
| 18 | Resistance: 9.00 Ω | Power: 36.00 W |
The middle row is the default. The outer two show how far the answer drifts when voltage (v) is wrong by half or by a half in the other direction.
Related guides
The three forms you actually use
Voltage equals current times resistance, current equals voltage divided by resistance, and power equals voltage times current. Every other form is algebra on those three. Writing them down before substituting numbers prevents the most common mistake, which is dividing by the wrong quantity.
Power also appears as current squared times resistance and as voltage squared divided by resistance. Those two are handy when the value you know is current or voltage rather than both.
Series and parallel change the rules
In series, resistances add and the same current flows through each element, so voltage divides across them. In parallel, voltage is common and the currents add, so the equivalent resistance is smaller than the smallest branch.
Two equal resistors in parallel give half the resistance, not double. That single fact explains most incorrect answers about household wiring and loudspeaker loads.
Real components are not ideal
A resistor has a tolerance, a wire has resistance per metre, and a supply has internal resistance that drops voltage under load. At low currents these are noise; at high currents they decide whether the circuit works.
Heat matters too: resistance rises with temperature in most conductors, so a component that measures correctly cold can behave differently when it is running.
Wire gauge is the practical version of this. A cable rated for a current at one length may overheat at another, because resistance rises with length and heating rises with the square of the current.
Frequently asked questions
What is Ohm's law in simple words?
Current through a resistor equals voltage across it divided by its resistance. Double the voltage and current doubles; double the resistance and current halves.
How do I calculate current from voltage and resistance?
Divide voltage by resistance: I = V ÷ R. A 12 V supply across 4 Ω gives 3 amperes.
How do I calculate power with Ohm’s law?
P = V × I, which also equals I²R or V²/R. On the 12 V, 3 A example: 36 watts of heat.
Why does parallel resistance come out lower than either resistor?
Each parallel path carries current independently at the full voltage, so total current adds while voltage stays the same — which means the effective resistance must be lower. Two equal resistors in parallel give exactly half the resistance.
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