Ohm's Law Explained: Formula, Examples and Calculator
Ohm's Law is the single most important equation in electronics. Whether you're designing a power supply, debugging a faulty circuit, or choosing the right resistor for an LED, you'll use Ohm's Law constantly. This guide breaks it down with practical, real-world examples.
Ohm's Law in one line: Voltage equals current times resistance, written V = I × R. Rearrange it to find whatever you're missing: I = V / R for current, R = V / I for resistance. Everything else on this page is applying those three forms.
The Formula: V = I × R
Ohm's Law states that the voltage (V) across a conductor is equal to the current (I) flowing through it multiplied by its resistance (R). This relationship was discovered by Georg Simon Ohm in 1827 and remains the foundation of electrical engineering.
- V = Voltage in volts (V)
- I = Current in amperes (A)
- R = Resistance in ohms (Ω)
You can rearrange the formula to solve for any variable:
| To find | Use | When you know |
|---|---|---|
| Voltage (V) | V = I × R | Current and resistance |
| Current (I) | I = V / R | Voltage and resistance |
| Resistance (R) | R = V / I | Voltage and current |
| Power (P) | P = V × I | Voltage and current |
Cover the quantity you want with your thumb in the triangle V over I×R, and the arrangement that remains is your formula. It is the fastest way to never misremember which form to use.
Want to skip the arithmetic? The Ohm's Law Calculator solves for any variable and handles the unit conversions for you.
Convert Your Units First
The most common Ohm's Law mistake is not the formula, it is mixing units. The formula only works in base units: volts, amperes and ohms. Convert before you calculate.
| You have | Multiply or divide | To get base unit |
|---|---|---|
| Milliamps (mA) | ÷ 1000 | Amps (A) |
| Microamps (µA) | ÷ 1,000,000 | Amps (A) |
| Kilohms (kΩ) | × 1000 | Ohms (Ω) |
| Megohms (MΩ) | × 1,000,000 | Ohms (Ω) |
| Millivolts (mV) | ÷ 1000 | Volts (V) |
For example, 20 mA is 0.02 A, and 4.7 kΩ is 4700 Ω. Plug those converted values into the formula, not the labelled ones.
Example 1: Calculating LED Current
Suppose you connect a red LED (forward voltage 2V) to a 5V supply through a 150Ω resistor. What current flows through the LED?
The voltage across the resistor is 5V - 2V = 3V. Using Ohm's Law:
I = V / R = 3V / 150Ω = 0.02A = 20 mA
This is the typical operating current for a standard LED, perfect. If you are sizing a resistor for an LED specifically, our LED resistor guide walks through it step by step.
Example 2: Choosing a Resistor
You need to limit current to 100 mA through a 12V motor from a 24V supply. What resistance do you need?
Voltage across resistor: 24V - 12V = 12V
R = V / I = 12V / 0.1A = 120 Ω
Don't forget to check power dissipation: P = V × I = 12V × 0.1A = 1.2W. You'd need at least a 2W resistor.
Example 3: Measuring Unknown Resistance
Your multimeter reads 9V across a component and 45mA through the circuit. What's the resistance?
R = V / I = 9V / 0.045A = 200 Ω
The Power Formulas
Ohm's Law extends naturally to power calculations. The base formula is P = V × I, and by substituting V = IR or I = V/R you get two more forms:
| To find power | Use | When you know |
|---|---|---|
| P = V × I | Voltage and current | The direct version |
| P = I² × R | Current and resistance | Useful for sizing resistors |
| P = V² / R | Voltage and resistance | Useful for heater/load calculations |
The P = I² × R form is especially practical: after you calculate the current through a resistor, you can immediately check whether the resistor's wattage rating is sufficient. A 1/4 W resistor that must dissipate 0.5 W will overheat and eventually fail.
Always choose a power rating at least double the calculated dissipation. A calculated 0.3 W load should go on a 1 W resistor, not a 1/4 W. The extra margin costs almost nothing and prevents heat-related failures.
Common Applications
Voltage Dividers
Two resistors in series create a voltage divider. The output voltage depends on the ratio of the resistors, derived directly from Ohm's Law. Voltage dividers are one of the most common uses of Ohm's Law in practice, and the full walkthrough is in our voltage divider tutorial.
Current Sensing
A small "sense resistor" in a circuit develops a voltage proportional to current flow. By measuring this voltage and applying I = V / R, you can determine the current without breaking the circuit. Current sense resistors are typically low-value (0.1 to 1 Ω) to avoid dropping significant voltage from the main circuit.
Resistor Selection
Choosing a resistor for a circuit is Ohm's Law in its most common applied form. Calculate R = V / I for the resistance you need, then P = I² × R for the wattage rating. If you need to identify a physical resistor you already have, the resistor color code guide covers how to read the bands.
Troubleshooting
If a circuit draws more current than expected, Ohm's Law helps you identify whether a resistance has decreased (short circuit) or if a voltage source is misbehaving. If a load receives less voltage than expected, the "missing" voltage is being dropped across something you did not intend, and V = IR across each component tells you where.
Limitations of Ohm's Law
Ohm's Law applies perfectly to ideal resistors and to many real-world conductors under normal conditions. However, some components are "non-ohmic", their resistance changes with voltage, current, or temperature:
- Diodes and LEDs have a nonlinear voltage-current relationship
- Thermistors change resistance with temperature
- Varistors change resistance with applied voltage
- Superconductors have zero resistance below critical temperature
For these components, Ohm's Law still applies instantaneously, but the effective resistance is not constant.
Tips for Beginners
- Always convert units before calculating (mA to A, kΩ to Ω)
- Draw the circuit diagram and label known values before solving
- Double-check your answer, does the result make physical sense?
- Remember that power dissipation matters as much as the resistance value
Frequently Asked Questions
What is Ohm's Law in simple terms?
Ohm's Law says that the current through a component is directly proportional to the voltage across it and inversely proportional to its resistance. In plain language: more voltage pushes more current, and more resistance holds it back. The formula is V = I × R.
Does Ohm's Law work for AC circuits?
It works for AC when the load is purely resistive. For loads with capacitance or inductance (motors, transformers, speakers), you replace resistance with impedance (Z), giving V = I × Z. The idea is the same, but impedance accounts for how the component reacts to a changing signal.
Why doesn't Ohm's Law work for diodes and LEDs?
Because their resistance is not constant. A resistor has the same resistance at any voltage, but a diode's effective resistance changes dramatically with the applied voltage. These are called non-ohmic components. Ohm's Law still describes the instant-by-instant relationship, but you cannot treat the resistance as a fixed number.
What is the difference between Ohm's Law and the power formula?
Ohm's Law relates voltage, current and resistance (V = I × R). The power formula adds energy into the picture (P = V × I). They are separate relationships that combine neatly, which is how you get forms like P = I² × R.
How do I calculate resistance from voltage and current?
Rearrange to R = V / I. Divide the voltage across the component by the current through it, both in base units. For example, 9 V across a part carrying 0.045 A gives R = 9 / 0.045 = 200 Ω.
Related Guides & Tools
- Ohm's Law Calculator solves for V, I, R or P automatically
- How to Read Resistor Color Codes
- What Resistor Do I Need for My LED?
- Voltage Divider Calculator Tutorial
- RC Time Constant Explained
Ready to put this into practice?
Use our Ohm's Law Calculator