Ohm's Law Calculator

1. Choose what to solve for: voltage, current, resistance or power.
2. Enter the two known values in the input fields. The mode tells you which pair to enter.
3. Read all four results: voltage, current, resistance and power, plus the Joule's law cross-checks.

Ohm's law is one of the most fundamental relationships in electrical science. Published by Georg Simon Ohm in 1827, it states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance.

This single equation can be rearranged to solve for any of its three variables. Combined with the power equation P = V x I, it forms a complete system for basic DC circuit analysis.

For more math and science tools, see the math calculators hub.

The calculator applies exact algebraic rearrangements of two formulas: Ohm's law and the electrical power equation.

1. Select which quantity to solve for.
2. Enter the two known values.
3. The calculator applies the matching formula and derives all four quantities.

Why Three Power Formulas?

P = V x I is the definition of electrical power. By substituting Ohm's law (V = IR or I = V/R) into it, you get P = I²R and P = V²/R. All three give the same answer; the calculator shows all of them as a cross-check.

Example 1: A 12 V battery drives 2 A through a resistor. What is the resistance and power?

R = V / I = 12 / 2 = 6 ohms. Power P = V x I = 12 x 2 = 24 W.

Cross-check: P = I² x R = 4 x 6 = 24 W. P = V² / R = 144 / 6 = 24 W. All agree.

Example 2: A 120 V supply feeds a 60 ohm load. What current flows and how much power is consumed?

I = V / R = 120 / 60 = 2 A. Power P = V x I = 120 x 2 = 240 W.

Example 3: A circuit dissipates 100 W across 4 ohms. What are the current and voltage?

I = sqrt(P / R) = sqrt(100 / 4) = sqrt(25) = 5 A. V = I x R = 5 x 4 = 20 V.

Or equivalently, V = sqrt(P x R) = sqrt(100 x 4) = sqrt(400) = 20 V.

Students often memorize Ohm's law using a triangle diagram: V on top, I and R on the bottom. Cover the letter you want to find and read the formula from the remaining two.

The Power Wheel

A wider diagram arranges all twelve combinations of V, I, R and P in a circle. Each quadrant shows three formulas for one quantity. This calculator implements all of them.

Ohm's law in its basic form (V = IR) applies directly to DC (direct current) circuits and to purely resistive AC circuits.

AC and Impedance

In AC circuits with inductors or capacitors, resistance generalizes to impedance (Z), and the law becomes V = I x Z. Power in AC also involves the power factor. This calculator handles the DC / purely resistive case.

When Ohm's Law Applies

The law holds for ohmic materials where resistance stays constant regardless of voltage. Semiconductors, diodes and other nonlinear devices do not follow Ohm's law at all operating points.

Ohm's law assumes a constant, linear resistance. Several real-world factors change the result you get in practice.

Temperature

Metals increase in resistance as they heat up. A copper wire at 100 degrees C has about 30 percent more resistance than at 20 degrees C, which changes the current for a given voltage.

Material and Geometry

Resistance depends on the conductor material (resistivity), its length and its cross-sectional area. Longer or thinner wires have higher resistance.

Frequency (AC Circuits)

At higher frequencies, skin effect and reactance from inductors or capacitors change the effective impedance, so the simple V = IR form no longer applies directly.

Unit Prefixes

Enter values in base units (volts, amps, ohms, watts) for this calculator. Convert prefixed values first: for example, 4.7 k ohm is 4,700 ohms.

Choosing a Resistor

If you need to limit current to 20 mA (0.02 A) from a 5 V supply, R = V / I = 5 / 0.02 = 250 ohms. The power dissipated is P = V x I = 0.1 W, so a quarter-watt resistor is sufficient.

Sizing Wire and Fuses

Knowing the current a circuit draws tells you the minimum wire gauge and the correct fuse rating. Under-rated wire overheats; an oversized fuse fails to protect the circuit.

Solar Panel and Battery Systems

Ohm's law helps size charge controllers, inverters and wiring in solar installations. For panel output estimates, try the solar panel calculator.

LED Circuits

A current-limiting resistor for an LED is sized with R = (V_supply - V_LED) / I_LED, a direct Ohm's law application.

1. Mixing Units

Using kilohms where ohms are expected gives a result off by a factor of 1,000. Always convert to base units first.

2. Applying It to Nonlinear Devices

Diodes, transistors and LEDs do not have a constant resistance. Ohm's law applies only to ohmic (linear) elements.

3. Forgetting Power Dissipation

A resistor sized by voltage and current must also handle the resulting power. Ignoring P = VI can burn out components.

4. Confusing Series and Parallel

In a series circuit, current is the same through every component. In parallel, voltage is the same across each branch. Applying the wrong value to the wrong formula is a common source of error.

5. Using Peak vs RMS in AC

AC voltages are usually stated as RMS. Using peak voltage instead overstates the effective current and power.

The formulas are exact algebraic relationships from physics. The calculator introduces no rounding beyond display formatting.

Ohm's law states that voltage equals current times resistance: V = I times R. It is one of the most fundamental equations in electrical engineering and physics.

Multiply current (in amps) by resistance (in ohms): V = I times R. For example, 3 A through 10 ohms gives 30 V.

Divide voltage by resistance: I = V / R. For example, 120 V across 60 ohms gives 2 A.

Divide voltage by current: R = V / I. For example, 12 V with 2 A flowing gives 6 ohms.

Multiply voltage by current: P = V times I. For example, 12 V at 2 A gives 24 W.

Joule's first law relates power to current and resistance: P = I squared times R. It is equivalent to P = V times I when combined with Ohm's law.

In its basic form, Ohm's law applies to DC and purely resistive AC circuits. For AC circuits with inductors or capacitors, impedance (Z) replaces resistance and the law becomes V = I times Z.

Voltage in volts (V), current in amperes (A), resistance in ohms (the Greek letter omega), and power in watts (W).

A perfect conductor has zero resistance (superconductors approach this). In practice, all materials have some resistance. This calculator requires positive values.

The power wheel is a circular diagram showing all twelve formulas relating V, I, R and P. Each quadrant gives three ways to find one quantity from two others.

• Ohm's Law - HyperPhysics (Georgia State University HyperPhysics; Ohm's law derivation and explanation).
• Joule's Laws - HyperPhysics (Georgia State University HyperPhysics; power in electrical circuits and Joule heating).
• NIST SI Units - Electrical quantities (National Institute of Standards and Technology; definitions of volt, ampere, ohm and watt).