“V = IR looks simple, but I never remember which value goes where” — and then the three power formulas pile on. The fix is one organizing principle: any two of voltage, current, resistance and power determine the other two. Once substitution becomes habit, the rearrangements follow on their own.
This article works through voltage, current, resistance and power with fully substituted examples, including a practical LED resistor calculation and the three power formulas — finishing with a free calculator for checking.
The definition: V = I × R
Ohm’s law states voltage = current × resistance:
V = I × R （V in volts, I in amperes, R in ohms）
A water analogy maps directly: voltage is the pressure, current the flow, resistance the narrowness of the hose. Double the pressure doubles the flow — that proportionality is the law.
Any one value follows from the other two:
| Solve for | Formula | Example |
|---|---|---|
| Current I | I = V ÷ R | 9 V ÷ 300 Ω = 0.03 A |
| Voltage V | V = I × R | 0.02 A × 220 Ω = 4.4 V |
| Resistance R | R = V ÷ I | 12 V ÷ 2.5 A = 4.8 Ω |
The last example is from OpenStax’s College Physics 2e: a car headlight drawing 2.5 A from a 12 V battery has a resistance of 4.8 Ω.
Current: 9 V across 300 Ω
I = 9 ÷ 300 = 0.03 A (30 mA)
A milliampere (mA) is a thousandth of an ampere — 0.03 A reads as 30 mA. Kilohms (kΩ) are a thousand ohms. Aligning the prefixes (m = 1/1000, k = 1000) before substituting prevents most digit slips.
The three power formulas
Power P (watts) is the rate of energy consumption, and three equivalent formulas cover whichever two values you have:
| Formula | When to use |
|---|---|
| P = V × I | Voltage and current known (DC conditions here) |
| P = I² × R | Current and resistance known |
| P = V² ÷ R | Voltage and resistance known |
A resistor with 12 V DC and 0.5 A dissipates 6 W. A 10 Ω resistor carrying 2 A dissipates 40 W. Actual component selection also needs rated power, temperature derating and tolerances. This arithmetic does not assess household wiring safety.
Three common mistakes: entering milliamps as amperes (20 mA is 0.02 A — divide by 1000); forgetting the square in P = I²R and the square root when going from P and R back to V (√(P × R)); and applying the DC formulas directly to AC circuits, where RMS values and power factor need separate consideration.
Practical example: choosing an LED resistor
An LED needs a resistor to limit its current. With a 5 V supply and an LED that drops 2 V at 20 mA:
- The resistor takes the remaining voltage: 5 − 2 = 3 V
- The required resistance: R = 3 V ÷ 0.02 A = 150 Ω
A 10 mA target gives R = 3 ÷ 0.01 = 300 Ω for a dimmer circuit. Do not choose an arbitrary nearby value. Check the LED rating, forward-voltage variation, supply and resistor tolerances. At 20 mA, the 150 Ω resistor dissipates 0.06 W.
Verify with the tool
Tools Hub’s Ohm’s Law Calculator takes any two of V, I, R and P and computes the other two, showing the substituted formulas it used. Under-filled, over-filled and negative inputs are each reported clearly.
How to use it (3 steps)
Enter two known values
Fill in any two of the four fields (V, I, R, P) that you know. Leave the rest empty.
Read the other two
The result card shows all four values (V, A, Ω, W) — the two you did not enter are computed automatically.
Check the substituted formulas
The Working panel shows which formulas were used (e.g. R = V ÷ I) with your numbers, so you can see exactly where a hand calculation differed.
The tool featured in this article
Ohm's Law Calculator
Any two of V, I, R and P determine the other two, with substituted working shown. All six combinations, free and browser-based.
To reproduce the examples, enter V = 9 and I = 0.03: the tool shows R = 300 and P = 0.27 with the substitution in the working. For multi-resistor circuits, first combine them in the equivalent resistance calculator, then feed the total here.
Summary
- Ohm’s law V = I × R: any two of the three values determine the third by multiplication or division
- Power has three forms — P = VI, P = I²R, P = V²/R — all equal; pick whichever matches the two values at hand
- An LED resistor is chosen in two steps: subtract the LED’s drop, then divide by the current
- mA is 1/1000 of an A; align prefixes (m, k) before substituting
- The DC formulas apply to simple resistive loads; AC adds RMS values and power factor
FAQ
Why does V = I × R hold?
In conductors, higher voltage pushes electrons more strongly and higher resistance restricts them. Most metal conductors show this as a clean proportionality (called ohmic conductors), observed as current = voltage ÷ resistance.
Which of the three power formulas should I use?
Whichever matches the two values you have: P = VI for voltage and current, P = I²R for current and resistance, P = V²/R for voltage and resistance. All give the same value, so a mismatch means an input error. P = I²R is the direct choice for resistor heating, P = VI for the supply side.
What is mA?
A milliampere — one thousandth of an ampere. Electronics work involves small currents like 20 mA, which is 0.02 A when entered into formulas.
Does Ohm’s law apply to AC circuits?
The basic form V = IR applies to DC with a resistive load. AC circuits add RMS values and, with coils or capacitors, phase (power factor) considerations that go beyond this article.
References
- OpenStax, College Physics 2e, Section 20.2 “Ohm’s Law: Resistance and Simple Circuits” (Ohm’s law V = IR with worked examples): openstax.org
- OpenStax, College Physics 2e, Section 20.4 “Electric Power and Energy” (the three power formulas): openstax.org
Input assumptions
This guide assumes DC and a constant, positive, finite resistance. Zero-valued pairs can leave other quantities underdetermined and need separate treatment.
