Ohm's Law Calculator — Solve V, I, R, P

Enter any two of voltage, current, resistance, and power to solve the rest with Ohm's Law. Works for AC and DC circuits with instant results.

Known values
Voltage (V)
Resistance (Ω)
3.0 Acurrent
Power: 36.0 W
Circuit breakdown
QuantityValueFormula
Voltage (V)12.0 VV = I × R
Current (I)3.0 AI = V ÷ R
Resistance (R)4.0 ΩR = V ÷ I
Power (P)36.0 WP = V × I
Derived from the two values you supplied using Ohm's Law and the power formula.
Ohm's Law: V = I × R, I = V ÷ R, R = V ÷ I, and P = V × I. Enter any two of voltage, current, and resistance to derive the remaining values plus power. Results assume a purely resistive DC circuit.

Understanding Ohm's Law and Electrical Power

Ohm's Law is one of the most fundamental relationships in electrical engineering. It states that the voltage across a conductor is equal to the current flowing through it multiplied by its resistance: V = I × R. Voltage (V), measured in volts, is the electrical pressure that pushes charge around a circuit. Current (I), measured in amperes, is the rate at which charge flows. Resistance (R), measured in ohms (Ω), is the opposition a component offers to that flow. The three are tightly linked — change any one and at least one of the others must change too.

Because the relationship is linear, you can rearrange the formula to solve for any single quantity when you know the other two. Current is I = V ÷ R, and resistance is R = V ÷ I. This means a circuit with a 12 V supply and a 4 Ω resistor pushes 3 A of current, exactly as this calculator shows by default. The same three quantities also let you find the power a circuit consumes. Electrical power (P), measured in watts, is the rate at which energy is converted or dissipated, and it is given by P = V × I. For the default example, 12 V × 3 A = 36 W of power is dissipated as heat in the resistor.

The Power Triangle and Its Variants

Power can be expressed in several equivalent forms by substituting Ohm's Law into P = V × I. Replacing V with I × R gives P = I² × R, which is useful when you know current and resistance but not voltage. Replacing I with V ÷ R gives P = V² ÷ R, which is handy when you know voltage and resistance. All three forms describe the same physical quantity, so you can pick whichever matches the values you have on hand. This calculator derives power directly from the two known values you supply, so you never need to remember which variant to use.

When Ohm's Law Applies

Ohm's Law holds exactly for purely resistive components and DC circuits, where voltage and current are constant. In AC circuits with capacitors or inductors, the relationship becomes more complex: the opposition to current is called impedance (Z) rather than resistance, and it depends on frequency. The power formula also changes — real power in an AC circuit is P = V × I × cos(φ), where cos(φ) is the power factor. For everyday DC work, however, such as sizing a resistor for an LED, choosing a fuse, or understanding a battery circuit, the simple V = I × R relationship is accurate and indispensable.

Practical Applications

Ohm's Law is used constantly in electronics and electrical work. It tells you what resistor value you need to limit current to a safe level for an LED, how much current a heater will draw from the mains, and whether a wire is thick enough to carry a given load without overheating. The power calculation is equally practical: it tells you how much heat a component must dissipate, which drives component sizing and cooling decisions. Understanding these four quantities and how they interrelate is the foundation of working safely and effectively with electricity.

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Ohm's Law is the fundamental relationship in electrical engineering that connects voltage, current, and resistance. It states that the voltage across a conductor is directly proportional to the current flowing through it, with the resistance as the constant of proportionality: V = IR. This single equation, together with the power relationship P = IV, lets you solve for any electrical quantity given two others.

The core relationships

From V = IR, three equivalent forms follow: I = V/R (current equals voltage divided by resistance), and R = V/I (resistance equals voltage divided by current). Power, the rate at which energy is converted, is given by P = IV. Substituting Ohm's Law into the power equation yields two more useful forms: P = V²/R and P = I²R. These five relationships let you compute any of the four quantities — voltage, current, resistance, or power — from any two known values.

Understanding the units

Voltage (V) is measured in volts, the electrical potential difference that drives current. Current (I) is measured in amperes, the rate of charge flow. Resistance (R) is measured in ohms, the opposition to current flow. Power (P) is measured in watts, the rate of energy conversion. A simple example: a 12-volt battery connected to a 4-ohm resistor drives a current of I = V/R = 12/4 = 3 amperes, and the resistor dissipates P = IV = 3 × 12 = 36 watts.

AC circuits and impedance

Ohm's Law applies directly to DC circuits and to AC circuits with purely resistive loads, using RMS values. However, AC circuits often contain capacitors and inductors, which introduce reactance. In that case, resistance is replaced by impedance (Z), a complex quantity that combines resistance and reactance, and the relationship becomes V = IZ. The power calculation also becomes more complex, involving the power factor. This calculator handles the resistive case, which is the foundation for understanding the more advanced AC analysis.

Practical applications

Ohm's Law is used everywhere in electronics and electrical engineering: sizing resistors to limit current, calculating voltage drops across wires, determining the power rating a component needs, and designing circuits that deliver the correct voltage and current to a load. Understanding these relationships is essential for safe and effective circuit design, from a simple LED circuit to a complex power distribution system.

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