Ohm's Law Calculator
Enter any two values — Voltage, Current, Resistance, or Power — and the solver instantly calculates the remaining two.
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Homeowner Savings Tip: The "Resistance" Money Pit
In your home, resistance is usually your enemy. Corroded outlets, loose wire nuts, or undersized extension cords create excessive resistance. According to Ohm's Law (\(P = I^2 \times R\)), this resistance consumes power and turns it into wasted heat. This not only increases your electric bill but is a leading cause of electrical fires. Periodically checking and tightening connections in high-use circuits can save money and improve safety.
What is Ohm's Law?
Ohm's Law is a fundamental principle of electrical engineering, first published by German physicist Georg Simon Ohm in 1827. It defines the mathematical relationship between three core electrical quantities: Voltage (V), Current (I), and Resistance (R).
The law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. This relationship is expressed as:
When Power (P) is added, using Joule's Law (\(P = V \times I\)), the four quantities V, I, R, and P form a complete system with 12 interchangeable formulas — collectively known as the Ohm's Law Wheel.
The Ohm's Law Wheel
The Ohm's Law Wheel organises all 12 derived formulas into four groups — one for each unknown quantity. Any two known values are sufficient to solve for the remaining two.
The Water Analogy
The easiest way to understand Ohm's Law is the water pipe analogy, which maps electrical concepts to familiar physical experiences:
Voltage is the electrical pressure that drives current through a circuit — just as water pressure pushes water through a pipe.
Current is the rate at which electric charge flows — analogous to the volume of water per second passing through a pipe.
Resistance is how much a conductor opposes current flow — like a narrow pipe restricts water flow. More resistance = less current for the same voltage.
Power is the rate of energy transfer — like the work done by water turning a mill wheel. More pressure and more flow means more power output.
How to Use This Solver
The Smart Solver above implements all 12 formulas from the Ohm's Law Wheel automatically. Here's how it works:
Enter Two Known Values
Type into any two of the four fields: Voltage (V), Current (I), Resistance (R), or Power (P). Leave the unknowns blank.
The Solver Activates
Once two valid values are detected, the solver selects the correct formula from the Ohm's Law Wheel and runs the calculation in real time.
Read the Highlighted Results
Calculated fields are highlighted in orange with a "Calculated" badge so you can instantly identify what the solver generated versus what you entered.
See the Formula Used
The exact formula the solver applied appears below the grid, so you can verify the math or use it manually in your own calculations.
Example Calculations
| Known Values | Result 1 | Result 2 | Formulas Used |
|---|---|---|---|
| V = 120V, I = 10A | R = 12 Ω | P = 1,200 W | \(R = V/I\), \(P = V \times I\) |
| V = 240V, R = 48 Ω | I = 5 A | P = 1,200 W | \(I = V/R\), \(P = V^2/R\) |
| P = 1500W, V = 120V | I = 12.5 A | R = 9.6 Ω | \(I = P/V\), \(R = V^2/P\) |
| P = 300W, I = 5A | V = 60 V | R = 12 Ω | \(V = P/I\), \(R = P/I^2\) |
| I = 2A, R = 100 Ω | V = 200 V | P = 400 W | \(V = I \times R\), \(P = I^2 \times R\) |
| P = 500W, R = 50 Ω | V ≈ 158.1 V | I ≈ 3.16 A | \(V = \sqrt{P \times R}\), \(I = \sqrt{P/R}\) |
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