Ohm's Law (V = I × R) is the starting point for every electrical calculation. This guide covers the formula, all three rearrangements, worked examples, and the most common mistakes engineers and students make.
If you have ever asked why a fuse blows, why a wire gets hot, or how to choose the right resistor for an LED circuit, the answer always starts with Ohm's Law. The formula V = I × R is the single most used equation in electrical engineering — and once you understand what it actually means, a huge range of problems become straightforward. This guide breaks down Ohm's Law completely: the formula, all three rearrangements, how each variable behaves in a real circuit, a set of worked examples you can follow step by step, and the most common mistakes people make when applying it. Whether you are a student studying for an exam, a hobbyist wiring an electronics project, or a professional double-checking a calculation, you will find exactly what you need here. You can also jump straight to the Ohm's Law Calculator if you just need a quick result.
Quick Answer
Ohm's Law states that voltage (V) equals current (I) multiplied by resistance (R): V = I × R. Rearrange it to find current (I = V ÷ R) or resistance (R = V ÷ I). It applies to linear, resistive components at a constant temperature.
Ohm's Law describes the relationship between three fundamental electrical quantities: voltage, current, and resistance. It was formulated by German physicist Georg Simon Ohm in 1827 and remains the backbone of circuit analysis today.
Voltage (V), measured in Volts, is the electrical potential difference between two points — think of it as the pressure that pushes electrons through a conductor. Current (I), measured in Amperes (amps), is the rate at which charge flows. Resistance (R), measured in Ohms (Ω), is how strongly a material opposes that flow.
The relationship is simple and linear: double the voltage and you double the current; double the resistance and you halve the current. That linear relationship is precisely what makes Ohm's Law so powerful — and also what defines the limits of where it applies.
V = I × RVVoltage in Volts (V)ICurrent in Amperes (A)RResistance in Ohms (Ω)Worked Example
Problem: A 12V battery drives current through a 6Ω resistor. What is the current?
Solution: Rearranging: I = V ÷ R = 12 ÷ 6 = 2A. The current through the circuit is 2 amperes.
Because V = I × R is a simple algebraic relationship, you can rearrange it to solve for whichever quantity you don't know. The three forms are equally valid:
To find Voltage: V = I × R To find Current: I = V ÷ R To find Resistance: R = V ÷ I
A common memory tool is the Ohm's Law triangle: draw a triangle with V at the top, I on the bottom left, and R on the bottom right. Cover the variable you want to find — what remains shows the operation. Cover V → I × R. Cover I → V ÷ R. Cover R → V ÷ I.
In practical work, you will use the current form (I = V ÷ R) most often when sizing components for a circuit. The resistance form (R = V ÷ I) is useful when you know how much current you want to allow and need to choose a resistor value. The voltage form is common in troubleshooting — if you measure current and know resistance, you can calculate the expected voltage drop.
Table 1: Ohm's Law rearrangements — use whichever matches the variable you need to find.
| Unknown | Formula | Units | Use Case |
|---|---|---|---|
| Voltage (V) | V = I × R | Volts | Calculate voltage drop across a component |
| Current (I) | I = V ÷ R | Amperes | Find current in a branch or circuit |
| Resistance (R) | R = V ÷ I | Ohms (Ω) | Choose a resistor to limit current |
Follow these steps every time you use Ohm's Law to ensure you get the right answer and avoid unit errors.
Ohm's Law gives you voltage, current, and resistance. But in real circuits, you also need to know power — how much energy is consumed per second (measured in Watts). The power formula connects directly to Ohm's Law:
P = V × I (power equals voltage times current)
Combine this with Ohm's Law and you get two more useful forms:
P = I² × R (useful when you know current and resistance) P = V² ÷ R (useful when you know voltage and resistance)
These power formulas are critical for selecting components. A resistor rated at 0.25W (quarter watt) will overheat and fail if the circuit demands 0.5W of power dissipation — even if the voltage and current values look correct individually. The watts-to-amps calculator handles these conversions quickly.
Table 2: Ohm's Law worked examples at common voltage levels. All assume a single resistive load.
| Voltage (V) | Resistance (Ω) | Current (A) | Power (W) |
|---|---|---|---|
| 5 | 100 | 0.05 (50mA) | 0.25 |
| 12 | 6 | 2.0 (2A) | 24 |
| 24 | 48 | 0.5 (500mA) | 12 |
| 120 | 1000 | 0.12 (120mA) | 14.4 |
| 240 | 2400 | 0.1 (100mA) | 24 |
Ohm's Law applies to any individual component in a circuit. But circuits often have multiple components. The total resistance depends on how the components are arranged.
Series circuits: Resistances add directly. Two 10Ω resistors in series give 20Ω total. Current is the same through every component; voltage divides across them.
Parallel circuits: Total resistance is lower than any individual resistor. For two equal resistors R, the total is R/2. For unequal resistors: 1/R_total = 1/R1 + 1/R2. Voltage is the same across every branch; current divides.
Understanding this matters when you're reading the AWG wire sizing guide — wire resistance adds in series with every load on the circuit, causing voltage drop that reduces available voltage at the end of a long cable run.
Ohm's Law in its basic form (V = IR) applies to purely resistive AC loads. AC circuits with inductors and capacitors require impedance (Z) instead of resistance — the generalised form becomes V = IZ, where Z is a complex number representing both magnitude and phase.
Resistance (R) opposes current in DC and resistive AC circuits with no phase shift. Impedance (Z) is the broader quantity that includes resistance plus reactance (opposition from capacitors and inductors, which is frequency-dependent). In a purely resistive circuit, Z = R.
The symbol I comes from the French word "intensité" (intensity of current), introduced by André-Marie Ampère. The unit Ampere is named after him. The letter C was already reserved for capacitance.
Yes. Copper wire has a small but measurable resistance per unit length. Multiply the wire resistance (in Ohms) by the current (in Amps) to get the voltage drop (in Volts). This is exactly what a voltage drop calculator uses — and why the AWG wire sizing guide recommends upsizing wire for long runs.
From I = V ÷ R, if resistance doubles and voltage stays constant, current is halved. This is a linear inverse relationship — a fundamental property of ohmic conductors.
Put the concepts above to work with these free, browser-based tools.
Ohm's Law — V = I × R — is brief enough to memorise in ten seconds and powerful enough to underpin an entire career in electrical engineering. The key skill is not memorising the formula but knowing when and how to rearrange it, keeping your units consistent, and recognising the cases where it doesn't apply directly. From selecting a current-limiting resistor to calculating voltage drop across a cable run, this law appears in every electrical task you will ever tackle. For hands-on calculations, use the Ohm's Law Calculator — or continue building your electrical knowledge with the AWG wire sizing guide, which shows how wire resistance interacts with load calculations in real installations. All articles in this cluster are listed on the Technical Guides hub.