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Formula
V = I × R, P = V × I = I² × R = V² ÷ R
- V
- voltage (potential difference) across the component, in volts
- I
- current through the component, in amperes
- R
- resistance of the component, in ohms
- P
- power dissipated by the component, in watts
What Ohm’s law says
Ohm’s law describes how voltage, current and resistance relate in an electrical conductor. Voltage (V) is the electrical “push”, measured in volts. Current (I) is the flow of charge, measured in amperes (amps). Resistance (R) is how strongly a component opposes that flow, measured in ohms (Ω). For an ordinary resistor the three are linked by one equation:
V = I × R
Rearranged, I = V ÷ R and R = V ÷ I. Add the definition of electrical power, P = V × I, and you get the four quantities that this Ohm’s law calculator handles. Know any two and the other two follow. That is why electronics references draw the “power wheel” with twelve formulas around it: V² ÷ R, I² × R, P ÷ I, √(P × R) and so on are all the same two laws rearranged.
How to use the Ohm’s law calculator
- In I know, choose the pair of values you have, for example voltage and resistance. There are six possible pairs, and the calculator shows only the two fields you need.
- Type the two values and pick the unit next to each. Prefixes are built in, so you can enter 4.7 kΩ, 20 mA or 250 mV directly without converting.
- The result shows the first unknown as the main answer and the second underneath, with the formula and your numbers for each.
- To work from a different pair, change the I know selection. Only two values are ever used, because three or four could contradict each other.
Results come back with a sensible prefix. 0.0025 A is shown as 2.5 mA and 47,000 Ω as 47 kΩ, so you can match them to the markings on real parts.
How to calculate Ohm’s law by hand
Suppose a 16 Ω heating element runs from a 24 V supply.
- Current: I = V ÷ R = 24 ÷ 16 = 1.5 A
- Power: P = V × I = 24 × 1.5 = 36 W
You can check the power two other ways. P = I² × R = 1.5² × 16 = 36 W, and P = V² ÷ R = 576 ÷ 16 = 36 W. All three agree because they are the same relationship.
Working with unit prefixes
Most mistakes come from prefixes, so convert to base units before you divide:
| Prefix | Symbol | Multiply by | Example |
|---|---|---|---|
| micro | µ | 0.000001 | 50 µA = 0.00005 A |
| milli | m | 0.001 | 20 mA = 0.02 A |
| kilo | k | 1,000 | 4.7 kΩ = 4,700 Ω |
| mega | M | 1,000,000 | 1 MΩ = 1,000,000 Ω |
A handy shortcut: volts ÷ kilohms gives milliamps directly. 9 V ÷ 3 kΩ = 3 mA.
Current and power for common resistor values
This table shows the current through, and power dissipated by, standard resistor values on 5 V (USB and logic) and 12 V (automotive and LED strip) supplies. The values were computed with the same formulas as the calculator.
| Resistor | Current at 5 V | Power at 5 V | Current at 12 V | Power at 12 V |
|---|---|---|---|---|
| 100 Ω | 50 mA | 250 mW | 120 mA | 1,440 mW |
| 220 Ω | 22.73 mA | 113.6 mW | 54.55 mA | 654.5 mW |
| 330 Ω | 15.15 mA | 75.76 mW | 36.36 mA | 436.4 mW |
| 470 Ω | 10.64 mA | 53.19 mW | 25.53 mA | 306.4 mW |
| 1 kΩ | 5 mA | 25 mW | 12 mA | 144 mW |
| 4.7 kΩ | 1.064 mA | 5.319 mW | 2.553 mA | 30.64 mW |
| 10 kΩ | 0.5 mA | 2.5 mW | 1.2 mA | 14.4 mW |
Common through-hole resistors are rated at ¼ W (250 mW). The 100 Ω resistor on 12 V would dissipate 1.44 W, far more than it can handle.
Real-life uses
Sizing an LED resistor
Subtract the LED’s forward voltage from the supply voltage, then use R = V ÷ I with the LED current you want. Then check the resistor’s power with P = I² × R and pick a rating comfortably above it.
Watts to amps for appliances
For heaters, kettles and incandescent lamps, current = power ÷ voltage. That tells you whether several appliances will trip a 15 A household circuit. To see what running them costs, use the kWh calculator and the electricity cost calculator.
Voltage drop across a resistor or wire
Multiply the current by the resistance. A wire run with 0.2 Ω of total resistance carrying 10 A drops 2 V, which is significant on a 12 V system.
Checking a measurement
If a multimeter shows 3.3 V across a resistor marked 1 kΩ, the current must be about 3.3 mA. A very different reading points to a wrong part or a fault.
Common mistakes
- Mixing prefixes. Dividing 5 V by “4.7” when the resistor is 4.7 kΩ gives an answer 1,000 times too large.
- Using the supply voltage instead of the voltage across the part. In a series circuit, each resistor sees only its share of the supply.
- Applying Ohm’s law to non-ohmic parts. An LED or a cold bulb filament does not have a fixed resistance. The result describes only the conditions you entered.
- Ignoring power ratings. The current may be right while the resistor overheats. Always check P.
- Treating AC motors like resistors. Inductive loads draw current that is out of phase with the voltage, so V × I overstates the real power.
Glossary
- Voltage (V): energy per unit charge between two points, in volts (1 V = 1 J/C).
- Current (I): rate of charge flow, in amperes (1 A = 1 C/s).
- Resistance (R): opposition to current, in ohms (1 Ω = 1 V/A).
- Power (P): rate of energy conversion, in watts (1 W = 1 V × 1 A = 1 J/s).
- Conductance (G): the reciprocal of resistance, in siemens (S).
- Ohmic: a component whose resistance stays constant, so a graph of current against voltage is a straight line.
For the mechanical side of energy and power, see the kinetic energy calculator and the force calculator.
Worked examples
Current through a resistor
A 330 Ω resistor connected across a 9 V battery. How much current flows, and how much power does the resistor dissipate?
Inputs: I know = Voltage and resistance; Voltage (V) = 9; Voltage (V) unit = Volts; Resistance (R) = 330; Resistance (R) unit = Ohms
I = V ÷ R = 9 V ÷ 330 Ω = 27.2727 mA P = V² ÷ R = (9 V)² ÷ 330 Ω = 245.455 mW
Answer: With voltage 9 V and resistance 330 Ω: current = 27.2727 mA, power = 245.455 mW.
Resistance of a heater element
A 1,500 W space heater on a 120 V US outlet. What current does it draw, and what is the hot resistance of its element?
Inputs: I know = Voltage and power; Voltage (V) = 120; Voltage (V) unit = Volts; Power (P) = 1500; Power (P) unit = Watts
I = P ÷ V = 1.5 kW ÷ 120 V = 12.5 A R = V² ÷ P = (120 V)² ÷ 1.5 kW = 9.6 Ω
Answer: With voltage 120 V and power 1.5 kW: current = 12.5 A, resistance = 9.6 Ω.
LED series resistor in milliamps and kilohms
15 mA through a 1.2 kΩ resistor. What voltage drops across it, and what power rating does it need?
Inputs: I know = Current and resistance; Current (I) = 15; Current (I) unit = Milliamperes; Resistance (R) = 1.2; Resistance (R) unit = Kilohms
V = I × R = 15 mA × 1.2 kΩ = 18 V P = I² × R = (15 mA)² × 1.2 kΩ = 270 mW
Answer: With current 15 mA and resistance 1.2 kΩ: voltage = 18 V, power = 270 mW.
Edge case: power and resistance only
A 50 W signal into an 8 Ω loudspeaker. Voltage and current come from square roots: V = √(P × R).
Inputs: I know = Resistance and power; Resistance (R) = 8; Resistance (R) unit = Ohms; Power (P) = 50; Power (P) unit = Watts
V = √(P × R) = √(50 W × 8 Ω) = 20 V I = √(P ÷ R) = √(50 W ÷ 8 Ω) = 2.5 A
Answer: With resistance 8 Ω and power 50 W: voltage = 20 V, current = 2.5 A.
Assumptions and limitations
- Ohm's law applies to ohmic (linear) components such as ordinary resistors, where resistance stays constant as the voltage changes. LEDs, diodes and lamps whose filament heats up are not ohmic, so a single R only describes one operating point.
- Values are DC values, or RMS values for purely resistive AC loads. Circuits with capacitors, inductors or motors also have reactance and a power factor, which this calculator does not model.
- All four quantities must be greater than zero. Enter exactly two of them; the other two are calculated.
- Results are shown to 6 significant figures with the SI prefix that suits their size (µA, mA, A; mΩ, Ω, kΩ, MΩ; mW, W, kW). Conductance (1 ÷ R) is given in siemens.
- The power shown is the power the component turns into heat or work. Choose a resistor rated well above it (commonly at least double).
Frequently asked questions
What is Ohm's law in simple terms?
The current through a resistor is proportional to the voltage across it. Double the voltage and the current doubles; double the resistance and the current halves. In symbols, V = I × R.
How do I calculate current from voltage and resistance?
Divide the voltage by the resistance. 24 V across 16 Ω gives 24 ÷ 16 = 1.5 A. Watch the prefixes. 5 V across 2.2 kΩ is 5 ÷ 2,200 = 0.00227 A, which is 2.27 mA.
How do I convert watts to amps?
For a resistive load, divide the power by the voltage, I = P ÷ V. A 600 W appliance on a 120 V circuit draws 5 A. Enter the power and voltage in the calculator to get the current and the load's resistance at the same time.
What is the Ohm's law triangle or power wheel?
The triangle is a memory aid with V on top and I and R below. Cover the quantity you want and the other two show the operation. The power wheel extends this to 12 formulas that link V, I, R and P. The calculator uses the same equations and shows the one it applied.
Does Ohm's law work for AC circuits?
For purely resistive AC loads such as heaters and incandescent bulbs, yes, using RMS voltage and current. Motors, transformers and electronic power supplies have impedance instead of plain resistance, so V = I × R alone does not describe them.
Why does an LED need a resistor?
An LED's current rises steeply once its forward voltage is reached, so it needs something to set the current. A series resistor drops the remaining voltage. For a 2 V LED at 20 mA on a 9 V supply, R = (9 − 2) ÷ 0.02 = 350 Ω, so a 390 Ω standard value is a safe choice.
Sources
- University Physics Volume 2, 9.4 Ohm's Law — OpenStax (Rice University). Checked October 12, 2026.
- University Physics Volume 2, 9.5 Electrical Energy and Power — OpenStax (Rice University). Checked October 12, 2026.
- The International System of Units (SI Brochure) — Bureau International des Poids et Mesures (BIPM). Checked October 12, 2026.