Ohm's Law describes the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. It states that voltage equals current multiplied by resistance: V = I × R. This fundamental law applies to all resistive circuits.

Ohm's Law Calculator — Free Online Calculator

Free Ohm's law calculator. Enter any two values of voltage (V), current (I), resistance (R), or power (P) to find the other two. Includes formulas and reference chart.

Voltage (V) (V)

Current (I) (A)

Resistance (R) (Ω)

Power (P) (W)

How to Use This Calculator

Enter any two known electrical values — voltage (V), current (I), resistance (R), or power (P) — and the calculator will compute the remaining two values using Ohm's Law and the power equation.

The Formula Explained

Ohm's Law states that voltage equals current times resistance: V = I × R. Combined with the power equation P = V × I, you can derive any two unknowns from any two knowns. The 12 key formulas are: V = I×R, V = P/I, V = √(P×R), I = V/R, I = P/V, I = √(P/R), R = V/I, R = V²/P, R = P/I², P = V×I, P = V²/R, P = I²×R.

Ohm's Law: The Foundation of Electrical Engineering

Ohm's Law is the most important equation in all of electrical engineering. Named for German physicist Georg Simon Ohm who published the relationship in 1827, it describes how voltage, current, and resistance interact in a simple circuit. V = I × R, or equivalently I = V / R and R = V / I. Add the power formula P = V × I and you can derive four more relationships: P = I² × R, P = V² / R, V = sqrt(P × R), and I = sqrt(P / R). These seven equations form the complete toolkit for analyzing any DC or resistive AC circuit.

The beauty of Ohm's Law is its simplicity and universality. Whether you are calculating the current through a LED indicator on a microcontroller board or the power dissipated in a 500 kW industrial heating element, the same V = I × R applies. Circuits get more complex with parallel/series combinations, reactive components, and non-linear devices, but Ohm's Law remains the foundation underneath all the complexity.

Worked Example: LED Current Limiting Resistor

You have a 5V microcontroller output and want to drive a standard red LED that has a forward voltage of 2.0V and wants 20 mA of current. The resistor must drop the extra voltage (5 − 2 = 3V) while limiting current to 20 mA.

Applying Ohm's Law: R = V / I = 3V / 0.020A = 150 ohms. Use a standard 150-ohm resistor. Power dissipated in the resistor: P = V² / R = 9 / 150 = 0.06 watts = 60 mW. A standard 1/8 watt (125 mW) resistor is fine, 1/4 watt (250 mW) is safer with 4x margin.

If you used a 100-ohm resistor instead, current would be I = 3 / 100 = 30 mA, which exceeds the 20 mA spec and overdrives the LED, shortening its life. If you used a 300-ohm resistor, current would be 10 mA — safe but the LED is dim. 150 ohms is the sweet spot for this LED.

Worked Example: Battery Internal Resistance

A 12V car battery measured under no load reads 12.6V. When you crank the starter (which draws about 200 amps), the voltage drops to 10.5V. What is the battery's internal resistance?

The voltage drop is 12.6 − 10.5 = 2.1V. With 200A flowing, Ohm's Law gives R = V / I = 2.1 / 200 = 0.0105 ohms, or 10.5 milliohms. That is the total internal resistance of the battery.

A healthy battery has internal resistance below 20 milliohms for a typical car battery. If you measure 50 milliohms or higher, the battery is degraded — it might still read 12.6V at rest but cannot deliver the current needed to start the engine. This is why automotive parts stores sell battery load testers: they apply a known load and measure the voltage drop to calculate internal resistance, which reveals battery health far better than resting voltage alone.

Worked Example: Power Dissipation in a Heating Element

An electric stove heating element is rated 2,400W at 240V. What is its resistance, and what happens when the voltage drops to 220V during a brownout?

At rated conditions: R = V² / P = 240² / 2400 = 24 ohms. At 220V: P = V² / R = 220² / 24 = 2,017W. That is 16% less power, so the element heats 16% slower. Current: I = V / R = 220 / 24 = 9.17A instead of 10A at rated voltage.

Note how power scales with voltage squared. A 10% voltage drop produces a 19% power drop (0.90² = 0.81). This is why incandescent bulbs dim dramatically during brownouts and why resistive heaters become noticeably slower. Switched-mode power supplies (computers, modern electronics) compensate internally and maintain constant output power, which is why they tolerate voltage variations that incandescent bulbs do not.

Common Ohm's Law Mistakes

1. Confusing voltage "across" with voltage "at". Ohm's Law uses the voltage across a specific resistor, not the source voltage. In a series circuit with multiple resistors, each resistor sees a fraction of the source voltage.

2. Applying DC formulas to reactive AC circuits. Capacitors and inductors have impedance (frequency-dependent), not simple resistance. Use V = I × Z for reactive circuits and include phase angle calculations.

3. Forgetting that resistance is not constant for all components. Incandescent bulb resistance is much lower when cold than when hot. Semiconductor junctions have non-linear V-I curves. Ohm's Law assumes linear resistance.

4. Missing units. V = I × R only works with V in volts, I in amps, R in ohms. If you use mA and kilohms, the product is still in volts but you need to remember the unit scaling.

5. Ignoring power dissipation. Just because current and voltage work out does not mean the component can handle the power. Always calculate power and verify component ratings.

Ohm's Law Cheat Sheet

Basic: V = I × R, I = V / R, R = V / I.

Power: P = V × I, P = I² × R, P = V² / R.

Voltage from power: V = sqrt(P × R), V = P / I.

Current from power: I = sqrt(P / R), I = P / V.

Resistance from power: R = V² / P, R = P / I².

Unit prefixes to memorize: milli (m) = 1/1000, kilo (k) = 1000, micro (µ) = 1/1,000,000, mega (M) = 1,000,000. So 1 kΩ = 1000 Ω, 1 mA = 0.001 A, 1 µF = 0.000001 F, 1 MΩ = 1,000,000 Ω.

Historical and Standards Context

Georg Simon Ohm published his work in 1827 in the book "Die galvanische Kette, mathematisch bearbeitet" (The Galvanic Circuit Investigated Mathematically). His work was initially rejected by the scientific establishment but eventually recognized as fundamental. The unit of resistance was named the ohm in his honor at the 1881 International Electrical Congress.

Modern standards: the ohm is defined in SI units as 1 volt per ampere, and the volt is defined in terms of the Josephson effect (a quantum mechanical phenomenon). These definitions give extraordinary precision — better than parts per billion — enabling accurate calibration of measurement instruments worldwide. Any digital multimeter you buy today traces its calibration back to these fundamental physical constants.

Ohms law: V = I x R and its four useful rearrangements

Written by Munir Ahmed, founder of VoltFlow. Reviewed against NIST electrical units handbook, IEEE 100 dictionary, standard electrical engineering textbooks. See our editorial standards, methodology, and electrical-safety disclaimer. Last reviewed May 2026.

Ohms law is the foundation. Voltage equals current times resistance. From this single relationship and the power equation, you can solve any pure-resistance DC problem and the resistive component of any AC problem. The calculator above does all 12 useful rearrangements (V, I, R, P from any two known values).

The formula and what it does

V = I x R P = V x I P = V^2 / R P = I^2 x R

The first equation is Ohms law itself. The other three combine Ohms law with the power equation P = V x I. Together they let you compute any one of V, I, R, P if you know any other two.

Worked example

Scenario: A heating element draws 12.5 A on 120 V. Find its resistance and power.

R = V / I = 120 / 12.5 = 9.6 ohm. P = V x I = 120 x 12.5 = 1500 W. Verify: P = I^2 x R = 156.25 x 9.6 = 1500 W. Matches a typical 1500 W toaster.

Common mistakes to avoid

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Frequently asked questions

Does Ohms law apply to AC?

For purely resistive AC loads, yes. For inductive or capacitive loads, you use complex impedance Z instead of R, and the math involves phase angles. The basic V = I x Z still holds; just the numbers are complex.

What is the difference between resistance and impedance?

Resistance is the DC opposition to current. Impedance includes resistance plus reactance (frequency-dependent inductive or capacitive opposition). At DC, impedance equals resistance. At AC frequencies, they can differ.

Why does resistance change with temperature?

Conductor resistance rises with temperature. Copper: about 0.4 percent per degree C. Tungsten (lightbulbs): a lot more (incandescent filament cold resistance is 1/10 of hot resistance). Semiconductors usually decrease resistance with heat.

How do I use Ohms law for parallel resistors?

For parallel: 1/R_total = 1/R1 + 1/R2 + ... So two 10-ohm resistors in parallel make 5 ohm total. Three 30-ohm resistors in parallel make 10 ohm.

Series resistors?

Add them. R_total = R1 + R2 + R3. Two 10-ohm resistors in series make 20 ohm.

Why is wire resistance important if it is so small?

On long runs at high current, even small resistance causes meaningful voltage drop. 100 ft of 12 AWG copper has about 0.2 ohm; at 20 A that drops 4 V (3.3 percent on a 120 V circuit), right at the NEC recommendation limit.