Ohm's Law: Voltage, Current, Resistance, and Power
Ohm's Law calculator solving V = IR, I = V/R, and R = V/I, plus the power formulas P = VI, P = I2R, and P = V2/R, with a worked example and reference tables.
I = V / R
Common conversions
| Input | Result |
|---|---|
| 120 V, 60 Ω | I = 2 A, P = 240 W |
| 240 V, 24 Ω | I = 10 A, P = 2,400 W |
| 12 V, 4 Ω | I = 3 A, P = 36 W |
| 5 V, 100 Ω | I = 0.05 A, P = 0.25 W |
| 120 V, 2 A | R = 60 Ω, P = 240 W |
| 240 V, 15 A | R = 16 Ω, P = 3,600 W |
| 48 V, 10 A | R = 4.8 Ω, P = 480 W |
| 9 V, 0.5 A | R = 18 Ω, P = 4.5 W |
The math behind it
- I = V / R = 120 / 60
- I = 2 A
- P = V × I = 120 × 2
- P = 240 W = 0.24 kW
Everything you need to know
Ohm's Law is the single relationship every electrical calculation on this site is built on. It states that current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance: V = I × R. Once you know any two of voltage, current, and resistance, the third follows directly, and adding the power formulas lets you find power from any two of the four quantities.
The three quantities and how they relate
Voltage (V), measured in volts, is the electrical pressure pushing current through a circuit. Current (I), measured in amps, is the rate of charge flow that results from that pressure. Resistance (R), measured in ohms (Ω), is the opposition a conductor offers to that flow. Raise voltage with resistance fixed and current rises with it. Raise resistance with voltage fixed and current falls. The three rearrangements, V = IR, I = V/R, and R = V/I, are the same equation solved for a different unknown, and a simple triangle with V on top and I and R on the bottom is a common way to remember all three at once.
Power: the fourth quantity
Combine Ohm's Law with the basic power formula, P = V × I, sometimes called Watt's Law, and two more useful forms fall out by substitution. Replace V with I × R to get P = I² × R, useful when you know current and resistance but not voltage, common when sizing a resistor for a known current. Replace I with V/R to get P = V² / R, useful when you know voltage and resistance but not current, common when checking a fixed appliance's power draw from its element resistance and supply voltage.
Where Ohm's Law connects to kW calculations
Every kW formula on this site, from single-phase amps to three-phase kVA, is Ohm's Law and its power forms with extra terms layered on for AC phase relationships and power factor. A DC circuit's power formula, kW = (V × A) / 1000, is exactly P = V × I divided by 1,000 to convert watts to kilowatts. Understanding Ohm's Law first makes every other formula on the site read as a variation on the same idea rather than a separate thing to memorize.
When Ohm's Law does not apply
Ohm's Law strictly describes linear, resistive components at a constant temperature, wires, resistors, and heating elements. It does not hold for non-ohmic devices: diodes and LEDs have a current that rises far faster than voltage past a threshold, incandescent filaments change resistance substantially as they heat up, and gas-discharge lamps and saturating transformer cores have resistance that shifts with operating point. For these components, a manufacturer's datasheet curve replaces the simple V = IR line.
Common applications
Choosing a resistor or heating coil starts with Ohm's Law: pick the resistance that draws the target current at the supply voltage, then check P = I²R against the component's power rating to avoid overheating it.
Measuring voltage and current at a suspect component and comparing the implied resistance (R = V/I) against its rated value is a standard first step in tracing a fault, a shorted winding, a corroded connection, or a failed component.
Before installing a resistor or wire in a circuit, P = I²R or P = V²/R confirms it won't exceed its power rating and overheat, a routine check in both hobby electronics and professional panel design.
A conductor's resistance per foot, multiplied by circuit current, gives the voltage drop over a long run using V = IR, the calculation behind NEC recommendations to keep voltage drop under 3-5% on branch circuits.
Common mistakes
Incandescent filaments and some heating elements can have 10x higher resistance hot than cold. Using the cold nameplate resistance in Ohm's Law calculations understates operating current and power by a wide margin.
Diodes, LEDs, and gas-discharge lamps don't follow a straight-line V/I relationship. Treating them as a fixed resistance produces current estimates that are wrong by an order of magnitude near their operating point.
A 120 V AC outlet is an RMS value; its peak voltage is about 170 V. Plugging the peak value into Ohm's Law instead of RMS overstates calculated current and power by about 41%.
Confusing mΩ with Ω, or mA with A, shifts a result by a factor of 1,000. Always convert to base units, volts, amps, and ohms, before applying V = IR.
Frequently asked questions
What is Ohm's Law?+
Voltage equals current times resistance: V = I × R. It describes how much current flows through a conductor for a given voltage and resistance, and it can be rearranged to solve for current (I = V/R) or resistance (R = V/I).
Does Ohm's Law apply to LEDs and diodes?+
No, LEDs and diodes are non-ohmic. Their current rises sharply once voltage crosses a threshold (often 1.8-3.3 V) instead of rising in a straight line with voltage, so a fixed resistance value doesn't describe them accurately.
How do I find power from voltage and resistance without measuring current?+
Use P = V² / R. A 120 V element with 40 Ω of resistance draws P = 120² / 40 = 360 W without ever needing a current measurement.
How do I find power from current and resistance without measuring voltage?+
Use P = I² × R. A 3 A current through a 15 Ω resistor dissipates P = 3² × 15 = 135 W.
How many amps flow through a 60 Ω resistor at 120 V?+
2 amps. I = V / R = 120 / 60 = 2 A, drawing 240 W of power.
What is the resistance of a 100 W, 120 V light bulb?+
About 144 Ω, found from R = V² / P = 120² / 100 = 144 Ω. This is the bulb's hot operating resistance, which is higher than its cold resistance.
Is resistance always constant for a given component?+
No, resistance changes with temperature for most real materials. A metal filament's resistance can rise 10-15x between cold and full operating temperature, which is why Ohm's Law calculations use the resistance at the actual operating condition, not the cold nameplate value.
Why does lower resistance draw more current at the same voltage?+
Because I = V / R: with voltage fixed, current and resistance are inversely proportional. Halving resistance doubles current, which is why a short circuit (resistance near zero) produces a current spike large enough to trip a breaker.
What happens to power if voltage doubles but resistance stays the same?+
Power quadruples. Since P = V² / R, doubling voltage while resistance is unchanged multiplies power by 2² = 4, not by 2, which is why overvoltage is far more damaging to resistive components than the voltage increase alone suggests.
How does Ohm's Law relate to the kW formulas used elsewhere on this site?+
Every kW formula is Ohm's Law's power form, P = V × I, with a 1,000 divisor for kilowatts and, for AC, extra terms for power factor and three-phase geometry. See the kW formulas reference for the full set built on this same base equation.