Ohm's Law Calculator — Voltage, Current, Resistance & Power

What is Ohm's Law?

Ohm's Law is one of the most fundamental relationships in electrical engineering and physics. It describes how voltage, current, and resistance are related in an electrical circuit. Formulated by German physicist Georg Simon Ohm in 1827, the law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance — provided the temperature and other physical conditions remain constant.

Ohm's Law applies to a vast range of real-world situations: designing resistor networks, selecting fuses, calculating power dissipation in heating elements, sizing wires for safe current capacity, troubleshooting circuits, and much more. Any time two of the four fundamental electrical quantities — voltage (V), current (I), resistance (R), and power (P) — are known, the other two can be derived.

Ohm's Law Formula

The classic statement of Ohm's Law gives resistance as the ratio of voltage to current:

Where:

• R — Resistance in ohms (Ω)
• V — Voltage (potential difference) in volts (V)
• I — Current in amperes (A)

This relationship tells us that for a given voltage, a higher resistance results in lower current. Conversely, for a given resistance, increasing the voltage increases the current proportionally.

Voltage Formula

Rearranging Ohm's Law to solve for voltage:

This form is used to calculate the voltage drop across a resistor or wire when the current and resistance are known. For example, a 10 Ω resistor carrying 2 A of current will have a 20 V drop across it.

Power Equation

Power (P) is the rate at which electrical energy is converted to another form (heat, light, mechanical work). The fundamental power equation is:

Combining this with Ohm's Law (V = I × R) yields additional power formulas that allow power to be calculated from any two of the three quantities V, I, R.

All Derived Formulas

With four quantities (V, I, R, P) and their interrelationships, there are twelve useful formulas in total. The table below summarizes them all. Our calculator covers all six possible input pair combinations.

How to Use the Ohm's Law Calculator

1. Select the unit system. Choose Metric SI for standard international units or American for presets common in North American practice (milliamps for small currents, kilohms for resistance, etc.).
2. Choose what to solve for. In the "Solve For" dropdown, select which two quantities you already know. The calculator will automatically show only those two input fields and hide the others.
3. Enter your values. Type the numerical value into each visible input field and select the appropriate unit prefix from the adjacent dropdown (e.g., mV, kΩ, mA).
4. Click Calculate. The results panel on the right will instantly display the two computed quantities along with full unit breakdowns and a shareable link.
5. Use Reset to clear all fields and start a new calculation.

The calculator automatically converts all SI prefix values (μ, m, k, M, G) to base units before computing, so you never need to do unit conversions manually.

Metric vs American Measurement Systems

Ohm's Law itself uses the same physics everywhere in the world — only the commonly preferred units differ between regions.

Metric SI System

The International System of Units (SI) is used in scientific work and most countries worldwide. Base units are the volt (V), ampere (A), ohm (Ω), and watt (W). SI prefixes allow convenient expression of very large or very small quantities:

• Voltage: μV (microvolt), mV (millivolt), V (volt), kV (kilovolt)
• Current: μA (microampere), mA (milliampere), A (ampere), kA (kiloampere)
• Resistance: mΩ (milliohm), Ω (ohm), kΩ (kilohm), MΩ (megaohm), GΩ (gigaohm)
• Power: μW (microwatt), mW (milliwatt), W (watt), kW (kilowatt), MW (megawatt)

American Practice

In North American electronics and electrical work, certain unit combinations are standard defaults:

• Small signal circuits typically use mA (milliamps) for current and kΩ (kilohms) for resistance.
• Power electronics and household circuits use A (amps) and Ω (ohms).
• Low-power devices (sensors, LEDs, microcontrollers) are often specified in mW (milliwatts).

Selecting the American preset in this calculator adjusts the default unit selections to match these conventions, making data entry faster for North American users.

Ohm's Law for Anisotropic Materials

The simple scalar form of Ohm's Law (V = IR) applies to isotropic conductors — those whose electrical properties are the same in all directions, such as most metals. For anisotropic materials (where conductivity varies with direction), Ohm's Law must be expressed in its general tensor form:

Where:

• J — Current density vector (A/m²)
• σ — Conductivity tensor (a 3×3 matrix for anisotropic materials)
• E — Electric field vector (V/m)

In anisotropic materials such as certain crystals, layered composites, and semiconductors under a magnetic field (the Hall effect), the current density need not be parallel to the electric field. The resistivity tensor ρ is the matrix inverse of the conductivity tensor σ. This generalization is essential in solid-state physics, materials science, and the design of advanced electronic components.

For practical circuit calculations — resistors, wires, household appliances — the simple scalar Ohm's Law is always sufficient.

FAQs

Does Ohm's Law apply to all materials?

No. Ohm's Law applies to ohmic conductors — materials where resistance remains constant regardless of the applied voltage or current. Most metals behave ohmically at constant temperature. Non-ohmic devices include diodes (current flows easily in one direction but not the other), transistors, and electrolytes. For these components, the V–I relationship is nonlinear and Ohm's Law cannot be directly applied.

What is the difference between voltage and current?

Voltage (electric potential difference) is the "pressure" that drives electrons through a circuit — analogous to water pressure in a pipe. Current is the actual flow of electric charge — analogous to the flow rate of water. Resistance is the opposition to that flow. A high voltage with a high resistance may produce only a small current, just as high water pressure through a narrow pipe gives a limited flow rate.

What happens to current when resistance doubles?

From Ohm's Law (I = V / R): if resistance doubles while voltage remains constant, the current is exactly halved. This linear inverse relationship is one of the key practical insights of Ohm's Law for circuit design.

Can Ohm's Law be used for AC circuits?

Yes, with an important extension. In AC circuits, resistance is replaced by impedance (Z), which is a complex number accounting for both resistance (R) and reactance (X, from capacitors and inductors). The generalized Ohm's Law for AC is V = I × Z, where V and I are phasors. For purely resistive AC circuits, impedance equals resistance and the simple form applies directly.

How do I calculate power dissipation in a resistor?

Power dissipated as heat in a resistor can be found using any of three equivalent formulas, depending on what you know:

• P = V × I — if you know voltage and current
• P = I² × R — if you know current and resistance
• P = V² / R — if you know voltage and resistance

All three formulas are derived by combining P = V × I with V = I × R.

What is the Ohm's Law "magic triangle"?

The "magic triangle" (or "Ohm's Law wheel") is a mnemonic tool. Cover the quantity you want to find with your finger:

• Cover V → the remaining symbols show I × R
• Cover I → the remaining symbols show V / R
• Cover R → the remaining symbols show V / I

This tool is widely taught in introductory electronics courses. Our calculator extends this idea to all four quantities (V, I, R, P) and handles unit conversions automatically.

Why is my calculated power very high or very low?

Check your unit prefixes. A common mistake is entering resistance in kΩ but selecting the base Ω unit, or entering current in mA but selecting A. Always verify that the unit selected in the dropdown matches the scale of the number you typed. For example, if your resistor is 4.7 kΩ, enter 4.7 and select kΩ — not 4700 with Ω.

What is the relationship between Ohm's Law and Joule's Law?

Joule's Law states that the power dissipated in a conductor is P = I² × R. This is directly derived by substituting V = I × R into P = V × I, giving P = (I × R) × I = I² × R. Joule's Law quantifies resistive heating — the phenomenon behind electric heaters, incandescent light bulbs, and fuses. It is fully consistent with and derivable from Ohm's Law.