Ohm's Law Explained: Formula, Examples and Calculator

If you have ever wondered why a wire gets hot, why a resistor limits current, or how to calculate the right resistor for an LED circuit, you need Ohm's Law. It is the single most fundamental relationship in all of electronics, and once you understand it, a huge amount of circuit behaviour suddenly makes sense.

This guide explains Ohm's Law from the ground up — what it says, where it comes from, how to use it in real calculations, and the practical implications it has for every circuit you design or troubleshoot.

What Is Ohm's Law?

Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. It was formulated by German physicist Georg Simon Ohm in 1827 after extensive experiments with metal wires of different lengths and thicknesses.

Mathematically, Ohm's Law is expressed as: V = I x R

Where: V is voltage in Volts (V), I is current in Amperes (A), and R is resistance in Ohms (symbol: Omega).

This deceptively simple equation has three variables. If you know any two, you can calculate the third. This is what makes Ohm's Law so powerful — it is the key that unlocks most basic circuit analysis.

Understanding the Three Variables

Voltage (V) — The Electrical Pressure

Voltage is the electrical potential difference between two points in a circuit. Think of it as pressure: just as water flows from high pressure to low pressure, electrical current flows from high voltage to low voltage. Voltage is measured in Volts and is often described as the 'electromotive force' that pushes charge through a circuit.

Common voltage levels you will encounter: 1.5V (single AA battery), 3.7V (LiPo cell), 5V (USB power, Arduino supply), 9V (standard battery), 12V (car battery, DC power supplies), and 230V (European mains).

Current (I) — The Flow Rate

Current is the rate at which electric charge flows through a conductor. It is measured in Amperes (or Amps). One Ampere equals one Coulomb of charge passing a point per second. In practical electronics, you will often work with milliamps (mA, thousandths of an Amp) — an LED might draw 20mA, a microcontroller might draw 50mA.

Current flows from the positive terminal of a power source, through the circuit, and back to the negative terminal. In conventional notation, current flows in the opposite direction to electron flow, which can be confusing at first but rarely matters for calculations.

Resistance (R) — The Opposition

Resistance is the property of a material or component that opposes the flow of current. It is measured in Ohms. A high resistance means less current can flow for a given voltage; a low resistance allows more current to flow.

Every material has some resistance, even excellent conductors like copper wire. Insulators like rubber or glass have extremely high resistance. Resistors are components specifically designed to introduce a known, controlled resistance into a circuit.

The Three Forms of Ohm's Law

Because V = I x R has three variables, it can be rearranged to solve for each:

• To find Voltage: V = I x R (multiply current by resistance)

• To find Current: I = V / R (divide voltage by resistance)

• To find Resistance: R = V / I (divide voltage by current)

A common memory aid is the 'Ohm's Law triangle': draw a triangle with V at the top, I at bottom-left and R at bottom-right. Cover the variable you want to find — the remaining two show the operation (side by side = multiply, stacked = divide).

Worked Examples

Example 1: Finding Current

Problem: A 9V battery is connected to a 470 Ohm resistor. How much current flows?

Using I = V / R: I = 9 / 470 = 0.0191 Amps = 19.1 mA

This is a safe, reasonable current for most small electronics circuits.

Example 2: Calculating Resistor for an LED

Problem: You want to connect a red LED (forward voltage 2.0V, max current 20mA) to a 5V supply. What resistor do you need?

First, find the voltage drop across the resistor: 5V - 2.0V = 3.0V. Then: R = V / I = 3.0 / 0.020 = 150 Ohms. Choose the nearest standard resistor value: 150 Ohm or 220 Ohm (the latter is safer, reducing current to about 13.6mA).

Example 3: Calculating Power Dissipation

Problem: A 220 Ohm resistor carries 20mA of current. How much power does it dissipate?

First find voltage: V = I x R = 0.020 x 220 = 4.4V. Then power: P = V x I = 4.4 x 0.020 = 0.088 Watts = 88mW. A standard 1/4W (250mW) resistor is more than sufficient.

Ohm's Law and Power

Ohm's Law naturally extends to power calculations. Electrical power (P) is measured in Watts and represents the rate of energy consumption or dissipation. The basic power formula is: P = V x I

Combining with Ohm's Law gives two additional power formulas: P = I^2 x R (power as a function of current and resistance) and P = V^2 / R (power as a function of voltage and resistance).

These formulas are critical for selecting the correct power rating for resistors, choosing appropriate wire gauges, and calculating battery life.

Where Ohm's Law Applies (and Where It Does Not)

Ohm's Law applies to ohmic conductors — materials where resistance remains constant regardless of voltage or current. Most metals at constant temperature are ohmic. Carbon film resistors and metal film resistors are designed to be as ohmic as possible.

However, many important electronic components are non-ohmic — their resistance changes with conditions:

• LEDs and diodes: Have a non-linear V-I relationship. Current increases dramatically once threshold voltage is exceeded.

• Transistors: Have complex V-I characteristics that depend on control signals.

• Thermistors: Resistance changes significantly with temperature.

• Light-dependent resistors (LDRs): Resistance varies with light intensity.

For these components, Ohm's Law can still be applied locally at a specific operating point, but it cannot be used to predict behaviour across their full range.

Series and Parallel Circuits

Resistors in Series

When resistors are connected in series (end to end), the total resistance is simply the sum: R_total = R1 + R2 + R3... The same current flows through each resistor, but the voltage is divided between them (this is a voltage divider).

Resistors in Parallel

When resistors are connected in parallel (both ends connected together), the total resistance is lower than any individual resistor. For two resistors: 1/R_total = 1/R1 + 1/R2. The voltage across each resistor is the same, but the current divides between them.

Understanding series and parallel resistor configurations is fundamental to circuit design and is used constantly when calculating voltage dividers, pull-up and pull-down resistors, and LED arrays.

Practical Applications in DIY Electronics

• Calculating LED resistor values for any supply voltage

• Sizing pull-up and pull-down resistors for digital inputs

• Determining wire gauge for a given current load

• Selecting power resistors for voltage dividers in sensor circuits

• Calculating battery life: if a circuit draws 50mA from a 2000mAh battery, runtime = 2000/50 = 40 hours

Common Mistakes with Ohm's Law

• Forgetting to convert milliamps to amps before calculating (20mA = 0.020A, not 20)

• Ignoring internal resistance of batteries, which reduces terminal voltage under load

• Applying Ohm's Law to components like LEDs and diodes as if they were simple resistors

• Not accounting for temperature effects on resistance in precision circuits

Conclusion

Ohm's Law — V = I x R — is the bedrock of circuit analysis. It is the first equation every electronics student learns and the one every engineer uses daily. Master its three forms, practise with real calculations, and you will have the foundation to understand, design, and troubleshoot virtually any basic circuit.

For more foundational electronics guides, visit the Circuit Diary Blog, and explore hands-on projects where you can apply Ohm's Law in practice on our Home page.