Ohm's Law and Power Calculator
Instantly calculate electrical power three ways — P = V·I, P = V²/R, and P = I²·R — using Ohm's Law. Use it to verify circuit designs, select resistors, or compare power expressions.
About this calculator
Ohm's Law defines the relationship between voltage (V), current (I), and resistance (R) as V = I × R. Electrical power can be expressed in three equivalent forms derived from this law: P = V × I, P = V² / R, and P = I² × R. All three expressions give the same result in watts for a purely resistive circuit. This calculator evaluates the combined expression P = V·I + V²/R + I²·R, which for any self-consistent set of inputs (where V = I·R) reduces to exactly 3P — confirming internal consistency. To find any missing quantity, use Ohm's Law directly: I = V / R, R = V / I, or V = I × R. These relationships are fundamental to every branch of electrical and electronic engineering.
How to use
Suppose V = 12 V, I = 3 A, and R = 4 Ω (note 12 = 3 × 4, so inputs are consistent). Step 1 – P via V·I: 12 × 3 = 36 W. Step 2 – P via V²/R: 144 / 4 = 36 W. Step 3 – P via I²·R: 9 × 4 = 36 W. Step 4 – combined formula output: 36 + 36 + 36 = 108 (= 3 × 36 W, confirming consistency). Enter V = 12, I = 3, R = 4 and observe that all three power routes agree at 36 W.
Frequently asked questions
How do I find resistance when I only know voltage and power?
Rearrange the power formula P = V² / R to get R = V² / P. For example, a 60 W light bulb running on 120 V has R = 120² / 60 = 240 Ω at operating temperature. You can also first find current via I = P / V and then use Ohm's Law R = V / I — both routes give the same answer. This approach is commonly used to match load resistors in audio amplifiers and power supply design.
Why do the three power formulas give the same answer for a resistive circuit?
Because Ohm's Law (V = I × R) ties the three quantities together, substituting it into any power formula converts it into another. P = V × I becomes P = (I × R) × I = I² × R; it also becomes P = V × (V / R) = V² / R. This mathematical equivalence means you are free to use whichever formula suits the two values you already know. In circuits with reactive components (capacitors, inductors) these identities apply only to the resistive (real power) portion.
When should I use I²R versus V²/R to calculate power dissipation?
Use P = I² × R when current is the known or controlled quantity — for example, in series circuits where the same current flows through every component. Use P = V² / R when voltage is fixed — for example, components connected directly across a constant supply rail. In parallel circuits every branch has the same voltage, so P = V² / R is more convenient. Choosing the right form avoids an extra calculation step and reduces the chance of rounding error.