Ohm's Law Explained: Formula, Examples & Calculator

Ohm's Law is the most fundamental formula in electrical engineering and electronics. It describes the relationship between voltage, current, and resistance in an electrical circuit. Whether you are a student learning circuit analysis, a hobbyist building your first simple LED circuit, or an electrical engineer troubleshooting electrical circuits in the field, Ohm's Law is the equation you will use more than any other.

In simple terms: if you know any two of the three values (voltage, current, resistance), Ohm's Law lets you calculate the third.

The Ohm's Law Formula

Ohm's Law states that the voltage across a conductor is directly proportional to the current flowing through it, provided the resistance remains constant. The formula is:

By rearranging this equation, you get all three Ohm's Law formulas:

• Find voltage: V = I × R
• Find current: I = V / R
• Find resistance: R = V / I

These three formulas are the foundation of circuit analysis. Every calculation involving resistors, LEDs, sensors, and motors ultimately comes back to V = I × R.

The Ohm's Law Triangle

The easiest way to remember all three formulas is the Ohm's Law triangle (also called the Ohm's Law pie chart). Place V at the top, I on the bottom left, and R on the bottom right:

To use the triangle:

• Cover V (you want to find voltage) → I × R remains → V = I × R
• Cover I (you want to find current) → V over R remains → I = V / R
• Cover R (you want to find resistance) → V over I remains → R = V / I

This triangle works because the horizontal line represents division: anything above the line is divided by what is below it. It is a simple visual tool that makes using Ohm's Law intuitive, even if you are just starting to learn about electrical circuits.

How to Use Ohm's Law

Using Ohm's Law to solve a circuit problem follows a consistent process:

1. Identify which two values you know (voltage, current, or resistance)
2. Choose the correct formula to find the unknown value
3. Substitute the known values into the equation
4. Calculate the result
5. Verify by plugging all three values back into V = I × R

Let's work through several examples.

Ohm's Law Examples

Example 1: Find the Voltage

Problem: A current of 2A flows through a 150Ω resistor. What is the voltage across the resistor?

Formula: V = I × R

V = 2A × 150Ω = 300V

The voltage dropped across the resistor is 300 volts.

Example 2: Find the Current

Problem: A 9V battery is connected to a 470Ω resistor. What is the current in the circuit?

Formula: I = V / R

I = 9V / 470Ω = 0.019A (19.1mA)

About 19 milliamperes of current flow through the circuit. This is a typical current value for an LED circuit — which is why 470Ω is a common LED resistor value when using a 9V supply.

Example 3: Find the Resistance

Problem: A lamp operates at 12V and draws 0.5A. What is the resistance of the lamp?

Formula: R = V / I

R = 12V / 0.5A = 24Ω

The resistance created by the lamp is 24 ohms.

Example 4: Series Circuit with Two Resistors

Problem: Two resistors (R1 = 220Ω and R2 = 330Ω) are connected in series to a 5V supply. What is the current in the circuit, and what is the voltage drop across each resistor?

Step 1 — Total resistance:

In a series circuit, the total resistance is the sum of all individual resistances:

R_total = 220Ω + 330Ω = 550Ω

Step 2 — Find the current:

I = V / R = 5V / 550Ω = 0.00909A (9.09mA)

Step 3 — Voltage drop across each resistor:

V_R1 = I × R1 = 0.00909A × 220Ω = 2.0V

V_R2 = I × R2 = 0.00909A × 330Ω = 3.0V

Verify: 2.0V + 3.0V = 5.0V ✓

The current is constant through both resistors (9.09mA), but the voltage is divided proportionally — the larger resistor drops more voltage. For more on this, see how to calculate voltage drop across resistors.

Example 5: Parallel Circuit

Problem: Two resistors (R1 = 100Ω and R2 = 200Ω) are connected in parallel across a 12V supply. What is the current through each resistor?

In a parallel circuit, the voltage across each branch equals the supply voltage. So we apply Ohm's Law to each resistor individually:

I_R1 = V / R1 = 12V / 100Ω = 0.12A (120mA)

I_R2 = V / R2 = 12V / 200Ω = 0.06A (60mA)

Total current from the supply:

I_total = 0.12A + 0.06A = 0.18A (180mA)

More current flows through R1 because it has lower resistance — it offers less opposition to the flow of electric current. The voltage across both resistors is the same (12V), but the current through each path depends on the resistance of that path.

Electrical Power in Circuits

Ohm's Law also connects to electrical power — the rate at which electrical energy is converted into heat, light, or motion. Power is measured in watts (W) and is calculated using:

P = V × I — Power equals Voltage times Current

By substituting Ohm's Law into the power equation, you get two additional formulas:

Power Example

Problem: A 12V supply drives 0.5A through a circuit. What is the power dissipated?

P = V × I = 12V × 0.5A = 6W

The circuit dissipates 6 watts of power. This is important for choosing the correct power rating for your resistors — a standard 1/4W resistor cannot safely handle 6W of power dissipation. You would need a resistor rated for at least 6W, or redesign the circuit to reduce the current.

Electrical Power Rating

Every resistor has a maximum power rating — the amount of power it can safely dissipate as heat without being damaged. Common ratings are 1/8W, 1/4W, 1/2W, 1W, 2W, and 5W. If the power calculated using Ohm's Law exceeds the resistor's rating, the resistor will overheat and eventually fail.

To determine the power dissipated by a resistor, use P = I² × R or P = V² / R. Always choose a resistor with a power rating at least 50% higher than the calculated power dissipation to provide a safety margin.

What Ohm's Law Can Validate

Ohm's Law is not just for calculation — it is also a powerful tool for validating and troubleshooting electrical circuits:

• Verify measurements: If you measure voltage and current with a multimeter, you can calculate what the resistance should be (R = V / I) and compare it to the actual resistor value. If they don't match, something is wrong — possibly a damaged component, a short circuit, or a bad connection.
• Check circuit design: Before building a circuit, calculate the expected current to make sure it does not exceed the ratings of your components. If V = 12V and R = 10Ω, then I = 1.2A — that's too much current for most small components.
• Diagnose problems: If an LED does not light up, measure the voltage across the resistor. If the voltage is zero, no current is flowing — the circuit is open. If the voltage equals the supply voltage, the LED may be dead or connected backwards.
• Size components: Use Ohm's Law to calculate the correct resistor value for any application. For example, to limit current to 20mA with a 5V supply: R = V / I = 5V / 0.02A = 250Ω. A standard 270Ω resistor would be the closest value.

When Ohm's Law Applies (and When It Doesn't)

Ohm's Law applies to ohmic components — materials and devices where the resistance remains constant regardless of the applied voltage. Resistors, conductors like copper wire, and most simple circuit components are ohmic.

However, some components are non-ohmic — their resistance changes depending on the voltage or current. Examples include:

• Diodes: Allow current to flow in only one direction. Their resistance drops dramatically once the forward voltage threshold is reached.
• Transistors: Used as switches and amplifiers, their behavior is controlled by a small input signal.
• Thermistors: Resistance changes with temperature.
• Light-dependent resistors (LDRs): Resistance changes with light intensity.

For non-ohmic components, Ohm's Law can still be used to calculate the voltage, current, and resistance at a specific operating point, but the relationship between V and I is not a straight line across a wide range of voltages.

Who Was Georg Ohm?

Georg Simon Ohm (1789–1854) was a German physicist and mathematician who discovered the relationship between voltage, current, and resistance in electrical conductors. He published his findings in 1827 in a book titled Die galvanische Kette, mathematisch bearbeitet (The Galvanic Circuit, Investigated Mathematically).

At the time, Ohm's work was largely ignored by the scientific community. It was not until the 1840s and 1850s that his law gained widespread acceptance. In recognition of his contribution, the unit of electrical resistance — the ohm (Ω) — was named after him. Today, Ohm's Law is one of the core principles in electrical engineering and is taught in physics and engineering courses worldwide.

Summary

Ohm's Law describes the relationship between voltage, current, and resistance in any resistive circuit:

The voltage across a resistor is directly proportional to the current flowing through it. If the current doubles, the voltage doubles. If the resistance doubles, the current halves (for the same voltage). This proportional relationship is what makes circuit analysis predictable and is why Ohm's Law remains one of the most fundamental principles in electrical engineering.

Use the Ohm's Law Calculator to quickly solve for voltage, current, or resistance in your circuit. When you move on to Arduino programming, you will use these formulas every time you calculate resistor values for LEDs and sensors.