Ohm's Law Explained: V = IR With Examples
A clear guide to Ohm's Law (V = IR) explaining voltage, current and resistance, how to rearrange the formula, worked examples, the power wheel and non-ohmic components.
Ohm's Law is the single most important relationship in all of electronics. It ties together the three quantities every circuit depends on — voltage, current, and resistance — into one elegant equation that you can rearrange to solve almost any basic electrical problem. Whether you are a student meeting circuits for the first time, a hobbyist sizing a resistor for an LED, or an electrician sanity-checking a load, mastering Ohm's Law unlocks the rest of the subject. This guide explains the meaning behind V = IR, works through clear examples, and shows how the Ohm's Law calculator handles the arithmetic for you.
The three quantities: voltage, current and resistance
Before the formula makes sense, you need a feel for what each quantity represents. The classic water-pipe analogy makes them intuitive.
- Voltage (V), measured in volts, is the electrical "pressure" that pushes charge through a circuit. In the water analogy it is the pressure driving water through a pipe. Symbol: V (sometimes E for electromotive force).
- Current (I), measured in amperes (amps), is the rate at which charge flows. It is the volume of water flowing past a point each second. Symbol: I, from the French intensité.
- Resistance (R), measured in ohms (Ω), is how much the circuit opposes the flow. It is the narrowness of the pipe restricting the water. Symbol: R.
Voltage drives, current flows, and resistance limits. Ohm's Law is simply the precise mathematical statement of how these three relate.
The Ohm's Law formula: V = IR
Ohm's Law states that the current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. Written in its most common form, the Ohm's Law formula is:
V = I × R
In words, voltage equals current multiplied by resistance. Because it is a single equation with three variables, you can rearrange it to find whichever quantity is unknown:
| To find | Formula | In words |
|---|---|---|
| Voltage (V) | V = I × R | current times resistance |
| Current (I) | I = V ÷ R | voltage divided by resistance |
| Resistance (R) | R = V ÷ I | voltage divided by current |
A popular memory aid is the "Ohm's Law triangle": write V on top with I and R below it. Cover the quantity you want, and the position of the remaining two shows whether to multiply or divide. Cover V and you see I next to R (multiply). Cover I and you see V over R (divide).
How to calculate resistance, voltage and current
Let us work each direction with concrete numbers. These are exactly the kinds of problems the V = IR calculator solves when you enter any two known values.
Finding voltage
A current of 2 amps flows through a 10-ohm resistor. The voltage across it is V = I × R = 2 × 10 = 20 volts.
Finding current
A 12-volt battery is connected across a 6-ohm resistor. The current is I = V ÷ R = 12 ÷ 6 = 2 amps.
Finding resistance
A device draws 0.5 amps from a 9-volt supply. Its resistance is R = V ÷ I = 9 ÷ 0.5 = 18 ohms. This is the classic case of how to calculate resistance when you know the voltage and current.
Adding power: the Ohm's Law wheel
Ohm's Law is often combined with the power equation, P = V × I, where power P is measured in watts. Substituting Ohm's Law into the power formula produces several useful variants, sometimes drawn together as the "Ohm's Law wheel."
| Quantity | Using V and I | Using I and R | Using V and R |
|---|---|---|---|
| Power (P) | P = V × I | P = I² × R | P = V² ÷ R |
| Voltage (V) | V = P ÷ I | V = I × R | V = √(P × R) |
| Current (I) | I = P ÷ V | I = V ÷ R | I = √(P ÷ R) |
These let you find power directly when you know any two of voltage, current, and resistance. For example, that 2-amp current through a 10-ohm resistor dissipates P = I² × R = 4 × 10 = 40 watts of heat.
A practical example: choosing a resistor for an LED
Ohm's Law turns up constantly in real circuits. Imagine you want to power an LED that needs about 20 milliamps (0.02 A) and drops 2 volts across itself, running from a 5-volt supply. The series resistor must drop the remaining 5 − 2 = 3 volts. Its value is R = V ÷ I = 3 ÷ 0.02 = 150 ohms. You would also check the power it dissipates: P = V × I = 3 × 0.02 = 0.06 watts, comfortably within a standard quarter-watt resistor's rating. This single calculation protects the LED from burning out and is a textbook use of V = IR.
Series and parallel circuits
Ohm's Law applies to whole circuits and to individual components, but you must use matching values. In a series circuit, the same current flows through every component, and the total resistance is the sum of the individual resistances. The supply voltage divides across the components in proportion to their resistance.
In a parallel circuit, every branch sees the same voltage, while the current splits among the branches. The total resistance is found from 1/Rtotal = 1/R1 + 1/R2 + ... and is always lower than the smallest individual resistor. Apply Ohm's Law branch by branch, using that branch's own voltage and resistance, and the numbers fall out cleanly.
The limits of Ohm's Law
Ohm's Law holds beautifully for "ohmic" materials such as metals and standard resistors at a constant temperature, where resistance stays fixed regardless of voltage. But it is not a universal law of nature. Some components are non-ohmic: their resistance changes with conditions, so current is not simply proportional to voltage.
- Diodes and LEDs conduct only above a threshold voltage and have a highly non-linear current-voltage curve.
- Filament lamps grow more resistive as they heat up, so their resistance rises with current.
- Thermistors are designed to change resistance with temperature.
For these, V = IR still describes the instantaneous relationship at a given operating point, but R is not a single fixed number across the whole range. Recognising when a component is non-ohmic prevents a common class of mistakes.
Units and prefixes you will meet
Real circuits span an enormous range of values, so engineers lean heavily on metric prefixes. Getting them right is essential when plugging numbers into the formula.
| Prefix | Symbol | Multiplier | Common use |
|---|---|---|---|
| milli | m | 0.001 | milliamps (mA) |
| kilo | k | 1,000 | kilohms (kΩ) |
| mega | M | 1,000,000 | megohms (MΩ) |
| micro | µ | 0.000001 | microamps (µA) |
Always convert to base units (volts, amps, ohms) before calculating, then convert back if you want a tidy answer. Mixing milliamps with ohms without converting is one of the most frequent sources of error.
A water analogy that makes Ohm's Law intuitive
Before working through more circuits, it helps to picture electricity as water flowing through pipes, because the analogy maps onto Ohm's Law almost perfectly. Voltage is like the water pressure pushing the flow along. Current is like the rate of water flow, the litres per second moving through the pipe. Resistance is like the narrowness of the pipe, restricting how much can flow for a given pressure. Increase the pressure and more water flows; narrow the pipe and less water flows. That is exactly what V = IR describes: raise the voltage and current rises, raise the resistance and current falls.
This picture also clarifies why components heat up. Forcing water through a narrow constriction creates friction and turbulence; forcing current through a resistance dissipates energy as heat. The tighter the constriction relative to the pressure, the more energy is lost. Keep this image in mind as we work through real numbers, because it turns abstract symbols into something physical you can reason about when a calculation looks surprising.
More worked circuit examples
The best way to internalise Ohm's Law is to grind through varied examples until the rearrangements feel automatic. Below are several complete, worked problems covering the three forms of the equation.
Example 1, find the current. A 12-volt car battery feeds a dashboard bulb with a resistance of 48 ohms. Current equals voltage divided by resistance, so I = 12 / 48 = 0.25 amps, or 250 milliamps. The bulb is dim and draws little current because its resistance is high relative to the supply.
Example 2, find the resistance. A heating element runs from the UK mains at 230 volts and draws 10 amps. Resistance equals voltage divided by current, so R = 230 / 10 = 23 ohms. Heating elements deliberately use low resistance so they pull substantial current and dissipate plenty of heat.
Example 3, find the voltage. A current of 0.5 amps flows through a 100 ohm resistor in a signal circuit. Voltage equals current times resistance, so V = 0.5 × 100 = 50 volts. This is the voltage drop developed across that resistor, a figure you will use constantly when analysing larger circuits.
| Example | Known values | Formula used | Answer |
|---|---|---|---|
| 1 | V = 12 V, R = 48 Ω | I = V / R | 0.25 A |
| 2 | V = 230 V, I = 10 A | R = V / I | 23 Ω |
| 3 | I = 0.5 A, R = 100 Ω | V = I × R | 50 V |
Notice the pattern: cover the quantity you want in the V = IR triangle, and what remains tells you whether to multiply or divide. If you would like to check any of these instantly, the Ohm's Law calculator solves for any of the four quantities once you enter the two you know.
Electrical power: watts, the fourth quantity
Ohm's Law links voltage, current, and resistance, but the quantity that often matters most in practice is power, measured in watts. Power tells you the rate at which a component converts electrical energy into heat, light, or motion, and it determines whether a part will run cool or burn out. The fundamental power equation is P = V × I, power equals voltage times current. Because Ohm's Law lets you substitute, two further forms are extremely useful: P = I² × R and P = V² / R.
These three power formulas plus the three Ohm's Law formulas together make up the "Ohm's Law wheel" that lets you find any one of the four quantities, voltage, current, resistance, or power, from any two others. The squared terms are worth a second look. Because power depends on the square of the current, doubling the current through a resistor quadruples the heat it must dissipate. This is why an undersized resistor or wire fails so suddenly when current climbs: the heating rises far faster than the current itself.
| To find | If you know V and I | If you know I and R | If you know V and R |
|---|---|---|---|
| Power (P) | P = V × I | P = I² × R | P = V² / R |
| Voltage (V) | — | V = I × R | — |
| Current (I) | — | — | I = V / R |
Worked power examples and choosing component ratings
Power calculations are not academic; they decide which physical part you must buy. Resistors are sold with power ratings such as 1/8 watt, 1/4 watt, 1/2 watt, 1 watt, and upward. Exceed that rating and the resistor overheats, drifts in value, discolours, and eventually fails, sometimes spectacularly.
Power example 1. A 220 ohm resistor carries 30 milliamps, or 0.03 amps. Using P = I² × R, power = 0.03² × 220 = 0.0009 × 220 = 0.198 watts. That is just under a quarter watt, so a 1/4 watt resistor is cutting it dangerously fine; a 1/2 watt part gives a sensible safety margin.
Power example 2. A device drops 5 volts across a 10 ohm resistor. Using P = V² / R, power = 25 / 10 = 2.5 watts. This demands at least a 3 watt or 5 watt resistor, the chunky ceramic kind, not a tiny film resistor.
Power example 3. A mains appliance in the US runs at 120 volts and draws 12.5 amps. Power = V × I = 120 × 12.5 = 1500 watts, a typical limit for a US household circuit, which is exactly why space heaters are usually capped around 1500 watts on a standard 15 amp circuit.
- Always choose a resistor rated for at least double the calculated power, giving headroom for temperature and tolerance.
- Remember that power becomes heat, so high-power resistors may need spacing or a heat sink for airflow.
- For wiring, the same P = I²R logic explains why thicker wire is needed for higher currents: thin wire has more resistance and overheats.
US and UK electrical context
Ohm's Law is universal, but the numbers you plug in differ by country, and that has real safety implications. The United States runs domestic outlets at a nominal 120 volts, while the United Kingdom uses 230 volts. For the same appliance power, the higher UK voltage means lower current, since I = P / V. A 2300 watt kettle draws about 10 amps in the UK but a similar 1500 watt US kettle draws about 12.5 amps, and US kettles are typically less powerful precisely because the lower voltage limits practical current on a standard circuit.
The lower current at higher voltage is one reason UK kettles boil faster; more power can be delivered within safe current limits. It also affects wiring and fusing. UK plugs famously contain their own fuse, commonly 3 amp or 13 amp, sized to the appliance using exactly the P = V × I relationship. US plugs have no built-in fuse and rely solely on the circuit breaker in the panel. Whenever you size a fuse, choose a cable gauge, or pick a power supply, you are applying Ohm's Law and the power equations whether you write them down or not.
| Quantity | Typical US | Typical UK |
|---|---|---|
| Mains voltage | 120 V | 230 V |
| Standard outlet circuit | 15 to 20 A | Ring final, 32 A breaker |
| Current for 1500 W load | 12.5 A | 6.5 A |
| Plug fuse | None (panel breaker only) | 3 A or 13 A in plug |
Common mistakes when applying Ohm's Law
Beginners trip over a predictable set of errors. The most frequent is unit confusion: mixing milliamps with amps or kilohms with ohms inside the same calculation. Always convert everything to base units, amps, volts, and ohms, before you compute, then convert back at the end. A current of 20 milliamps is 0.02 amps, and a resistance of 4.7 kilohms is 4700 ohms; forgetting these conversions throws answers off by factors of a thousand.
- Forgetting that resistance changes with temperature. A filament bulb's cold resistance is far lower than its hot operating resistance, so a single Ohm's Law calculation only captures one operating point.
- Applying Ohm's Law to non-ohmic components. Diodes, transistors, and LEDs do not have a constant resistance, so you cannot treat them as a fixed resistor across their whole range.
- Confusing voltage drop with supply voltage. In a series circuit the supply splits across components, and the voltage you use in V = IR for one resistor is only the drop across that resistor, not the whole supply.
- Ignoring power ratings. A calculation can be electrically correct yet specify a part that will overheat because its wattage was never checked.
- Reversing the formula. Dividing when you should multiply is easy under pressure; the V = IR triangle is the quickest guard against it.
Build the habit of writing down your known values with their units, choosing the correct form of the equation, computing in base units, and finally sanity-checking the answer against the water analogy. If a tiny resistor is supposedly dissipating 50 watts, something has gone wrong. With practice, Ohm's Law and the power equations become second nature, and you will reach for them automatically every time you design, repair, or simply understand a circuit.
Worked example: a voltage divider
One of the most common applications of Ohm's Law is the voltage divider, two resistors in series used to produce a smaller voltage from a larger one. Suppose you have a 9-volt supply and you want roughly 3 volts to feed a sensor. Place two resistors in series, R1 on top and R2 to ground, and the output is taken across R2. The output voltage equals the supply multiplied by R2 divided by the sum of R1 and R2.
Pick R1 = 6.8 kilohms and R2 = 3.3 kilohms. The total resistance is 10.1 kilohms, so the current through the chain is I = 9 / 10100 = about 0.89 milliamps. The voltage across R2 is then V = I × R2 = 0.00089 × 3300 = about 2.94 volts, close to our 3 volt target. Notice that the same current flows through both resistors because they are in series, and the supply voltage divides between them in proportion to their resistances. This proportional split is Ohm's Law applied twice, and it underpins countless real circuits from sensor biasing to volume controls.
A practical caution: a voltage divider only holds its output voltage well if whatever you connect to the output draws very little current compared with the divider chain itself. Connect a hungry load and it effectively adds resistance in parallel with R2, pulling the output voltage down. This loading effect is one of the first subtleties every electronics learner meets, and it is best understood by tracing the currents with Ohm's Law rather than memorising a rule.
Measuring with a multimeter
Everything above becomes tangible the moment you pick up a multimeter, the single most useful tool for applying Ohm's Law in the real world. A multimeter measures voltage, current, and resistance directly, letting you verify your calculations against the actual circuit. To measure voltage you place the probes in parallel, across the component, because voltage is a difference between two points. To measure current you must break the circuit and insert the meter in series, so the current flows through it. To measure resistance you isolate the component, ideally with no power applied, and let the meter pass a tiny known current to deduce the resistance.
- Voltage: probes in parallel across the component, with the circuit powered.
- Current: meter in series, circuit broken to insert it, mind the meter's current limit.
- Resistance: power off and component isolated, or you risk a false reading and a blown fuse.
A frequent beginner mistake is leaving the meter on its low-resistance current setting and then touching it across a voltage source, which can blow the meter's internal fuse instantly because the meter looks almost like a short circuit. Always confirm the dial is set to the quantity and range you intend to measure. Used carefully, a multimeter and a grasp of Ohm's Law let you diagnose almost any simple circuit fault, confirming whether a measured voltage drop, current, and resistance agree with V = IR or reveal a broken connection, a wrong component, or an unexpected short.
Frequently asked questions
What does V = IR actually mean?
It means the voltage across a component equals the current flowing through it multiplied by its resistance. Equivalently, current is proportional to voltage and inversely proportional to resistance. It is the fundamental relationship linking the three core electrical quantities in any simple circuit.
How do I calculate resistance from voltage and current?
Rearrange Ohm's Law to R = V ÷ I. Divide the voltage across the component by the current flowing through it. For example, 9 volts driving 0.5 amps gives a resistance of 9 ÷ 0.5 = 18 ohms.
Is Ohm's Law the same as the power formula?
No, but they are closely related. Ohm's Law is V = IR, while the power formula is P = VI. By substituting one into the other you can derive useful combined forms such as P = I²R and P = V²/R, which let you find power directly from resistance.
Does Ohm's Law work for AC circuits?
For purely resistive AC circuits, yes — V = IR applies using RMS values. When capacitors or inductors are involved, resistance is replaced by impedance (Z), and the relationship becomes V = IZ, accounting for the phase difference between voltage and current.
Why doesn't Ohm's Law apply to all components?
Ohm's Law assumes resistance stays constant. Components such as diodes, filament lamps and thermistors are non-ohmic: their resistance changes with voltage, current or temperature, so current is not simply proportional to voltage. For these, the simple fixed-R version of the law does not describe the whole curve.
What is the easiest way to remember the Ohm's Law formulas?
Use the Ohm's Law triangle, with V on top and I and R underneath. Cover the quantity you want to find: if the remaining two sit side by side you multiply, and if one sits above the other you divide. It instantly gives V = IR, I = V/R or R = V/I.