SamCalculator

Ohm's Law Calculator

Calculate voltage, current, resistance, and power instantly using Ohm's Law equations with advanced electrical engineering insights and live visualizations.

Standard Ohm's Law

Enter any two of voltage, current, resistance, or power — the calculator solves the other two using V = I × R and P = V × I.

Fill any two — leave the rest blank

Real-world templates

What Is Ohm's Law?

Ohm's Law is the single most important relationship in electrical engineering. Discovered by Georg Simon Ohm in 1827, it states that the current flowing through a conductor between two points is directly proportional to the voltage across them and inversely proportional to the resistance — captured by the compact equation V = I × R. Pair it with the power identity P = V × I and almost every electrical question reduces to one of six algebraic rearrangements.

This calculator solves all four quantities — voltage, current, resistance, and power — from any two you supply. It also handles power-focused calculations, an electrical unit converter, AC versus DC analysis with power factor, and series / parallel resistor networks. Pair it with our voltage drop calculator, horsepower calculator, or unit converter when working across electrical and mechanical systems.

How Ohm's Law Works

Voltage drives the current

Voltage is electrical pressure — the potential difference between two points. Raise the voltage across a fixed resistance and the current rises in direct proportion. Halve the voltage, halve the current.

Resistance opposes the flow

Resistance limits how much current can flow at a given voltage. Double the resistance and the current falls by half — that's the inverse relationship at the heart of Ohm's Law.

Power is voltage × current

Every watt of electrical power equals one volt acting on one amp. Whether the load is a heater, motor, or LED, you can always trade voltage for current at the same total wattage.

Resistors dissipate heat

The power lost in a resistor equals I²R (or equivalently V²/R). High current squared multiplies fast, which is why thick wires run cool but thin wires glow red on the same current.

Core Ohm's Law Formulas

Every result this calculator produces comes from one of these eight closed-form equations. Voltage is measured in volts (V), current in amperes (A), resistance in ohms (Ω), and power in watts (W).

Voltage

V = I × R

Voltage equals current times resistance — the canonical form of Ohm's Law.

Current

I = V ÷ R

Current is voltage divided by resistance. Used to find I when V and R are known.

Resistance

R = V ÷ I

Resistance is voltage divided by current. Used to size resistors for a target current.

Power

P = V × I

Power equals voltage times current. The simplest of the three power forms.

Power (I²R)

P = I² × R

When you know current and resistance — current squared scales fast.

Power (V²/R)

P = V² ÷ R

When you know voltage and resistance. Common in resistor heat-sink sizing.

How to Use This Calculator

  1. 1

    Pick a calculation mode

    Use Standard for everyday V / I / R / P math, Power for I²R or V²/R dissipation problems, Converter to translate between prefixes (mV, kV, mA, kΩ, kW…), AC/DC for three-phase or single-phase power, and Circuit Analysis for series or parallel resistor networks.

  2. 2

    Enter any two values

    In Standard or Power mode, type any two of voltage, current, resistance, or power — and leave the other two blank. The calculator solves the rest automatically using the appropriate Ohm's Law formula.

  3. 3

    Choose the right units

    Each input has its own unit selector — millivolt to kilovolt, microamp to ampere, ohm to megaohm, milliwatt to kilowatt. Pick the prefix closest to your real measurement to avoid clumsy scientific notation.

  4. 4

    Read the step-by-step solution

    The result card shows every formula used to derive each quantity, the substituted numbers, and the final answer — making it easy to learn the relationship, not just the answer.

  5. 5

    Use the visualizations

    An Ohm's Law wheel highlights all four quantities, a circuit diagram shows the live values in context, and the AC waveform displays the phase relationship between voltage and current for any power factor below 1.

Key Electrical Concepts

Voltage

Voltage is the electrical potential difference between two points — measured in volts. Think of it as the "pressure" that pushes electrons through a circuit. Batteries and power supplies maintain a constant voltage; generators produce alternating voltage 50 or 60 times per second.

Current

Current is the rate of electric charge flow — measured in amperes. One amp equals roughly 6.24 × 10¹⁸ electrons crossing a given point each second. AC current alternates direction; DC current always flows the same way.

Resistance

Resistance opposes current flow and dissipates electrical energy as heat — measured in ohms. Resistor color codes encode the value in coloured bands. Conductors have very low resistance; insulators have extremely high resistance.

Power

Power is the rate at which electrical energy is delivered or consumed — measured in watts. One watt equals one joule per second, or one volt times one amp. Kilowatt-hours (kWh) are the unit your utility bill is denominated in.

AC vs DC

Direct current (DC) flows in one direction — like a battery feeding a flashlight. Alternating current (AC) reverses direction many times per second — the form delivered by your wall outlet because it can be efficiently transformed up and down for long-distance transmission.

Power factor

On AC circuits, power factor is the cosine of the angle between current and voltage. A PF of 1 means current and voltage are in phase (purely resistive load). Lower PF on motors and ballasts increases the apparent power (VA) the source must supply.

Ohm's Law in Real-World Circuits

💡

LED resistor sizing

Run a 3.2 V LED at 20 mA from a 5 V supply: you need a resistor that drops the extra 1.8 V at 20 mA — that's 90 Ω, dissipating 36 mW. A 1/8 W (125 mW) part is more than enough.

🔋

Battery internal resistance

A 12 V lead-acid battery with 10 mΩ internal resistance loses 1 V at 100 A — Ohm's Law in action. This is why cranking voltages sag during engine start.

☀️

Solar panel matching

A 100 W panel rated 18 V will produce roughly 5.5 A at its maximum power point. Knowing this lets you size charge controllers and wiring properly.

🤖

Arduino & microcontrollers

Most microcontroller pins source or sink only 20 mA. Adding a resistor with V/R = 20 mA at 5 V (so R ≥ 250 Ω) protects the pin from over-current damage.

🚗

Automotive electrical

A 12 V car battery feeding a 100 W headlight delivers 8.3 A. The wiring must carry that current continuously without excessive voltage drop.

🏠

Home AC circuits

A 1500 W heater on a 120 V outlet draws 12.5 A — close to the 15 A breaker limit. Knowing the math prevents nuisance trips and overloaded circuits.

🎚️

Amplifiers & speakers

A 100 W amplifier into a 4 Ω speaker produces √(P × R) = 20 V at 5 A. Used to size speaker wire and protect tweeters from over-current.

⚙️

Industrial 3-phase

A 480 V three-phase motor pulling 60 A at 0.85 PF delivers √3 × 480 × 60 × 0.85 ≈ 42 kW real power — sized using the three-phase form of the power equation.

Best Practices for Electrical Calculations

  • ✓Always check units before you calculate. A milli (10⁻³) versus kilo (10³) confusion is a six-orders-of-magnitude mistake — the most common error in junior engineering work.
  • ✓Size resistors for 2× the calculated power. Standard resistors come in 1/8 W, 1/4 W, 1/2 W, 1 W, and 5 W ratings — leave headroom for tolerance, ambient temperature, and surge.
  • ✓Account for wire resistance on long runs. Even a few milliohms per metre adds up — see our voltage drop calculator for cable-aware sizing.
  • ✓Use power factor for AC sources. Most motors and electronic ballasts run between 0.7 and 0.95 PF — apparent power (VA) sizes your service entrance, not real power (W).
  • ✓Verify with a multimeter under load. Calculated values assume ideal components. Real wiring, contacts, and connectors all introduce parasitic resistance — always measure during commissioning.
  • ✓Respect safe voltage levels. Anything above 50 V can deliver a dangerous shock under fault conditions. Use insulated tools, de-energize before working, and follow your local electrical code.

Common Mistakes to Avoid

Mixing units

Computing in milliamps but treating the answer as amps gives an answer 1,000× too large. Pick a unit system and stick with it; the calculator handles prefix conversion so you don't have to.

Forgetting power dissipation

Computing the resistor value for a given current but skipping the I²R wattage check is the fastest way to burn out a 1/8 W resistor. Always check whether the resistor can dissipate the heat.

Using DC formulas on AC

Pure DC math ignores reactance and power factor. For AC inductive or capacitive loads, apparent power (V × I) can be 20–40% larger than real power. Use the AC/DC mode for these calculations.

Confusing series and parallel

Series circuits add resistances; parallel circuits add reciprocals. For two parallel resistors, the total is always less than the smaller of the two — a useful sanity check.

Trusting nameplate voltage

Real installed voltage often sags 5–10% under load. Size circuits for the worst-case voltage, not the ideal nameplate, especially for motors that draw 5–8× running current at start.

Ignoring temperature

Resistance rises with temperature (~0.39%/°C for copper). On hot days or in confined enclosures, a circuit calculated cold can carry significantly different current when fully warmed up.

Why Ohm's Law Matters

Almost every electrical decision — from picking a current-limiting resistor for an LED to sizing the service entrance of a building — comes back to Ohm's Law. Get the math wrong and components burn up, breakers trip, batteries drain prematurely, or — in the worst case — wires overheat and start fires. Get it right and everything just works.

Beyond circuit design, Ohm's Law is the foundation for measurement: ammeters, voltmeters, ohmmeters, and oscilloscopes all rely on the same equations. Understanding the relationships qualitatively also catches errors before they reach the bench: if a calculated current is 100× larger than your intuition expects, you almost certainly have a unit or rearrangement mistake.

Built for electrical engineers, electronics hobbyists, electricians, students, and anyone learning circuit fundamentals.

Formulas cross-checked against standard electrical engineering references — see our methodology and editorial policy. Educational only — always confirm critical designs with a licensed electrician and your local electrical code.

Frequently Asked Questions

Ohm's Law is the foundational rule of electrical engineering: the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. It is expressed as V = I × R, where V is voltage in volts, I is current in amperes, and R is resistance in ohms. Power is then derived as P = V × I.

Voltage equals current multiplied by resistance: V = I × R. If you know power and current, V = P ÷ I. If you know power and resistance, V = √(P × R). This calculator solves any of these forms automatically — enter any two of voltage, current, resistance, or power and it returns the other two.

Resistance equals voltage divided by current: R = V ÷ I. If you know power and current, R = P ÷ I². If you know voltage and power, R = V² ÷ P. The right form depends on which two quantities you already have — the calculator above picks the appropriate formula for you.

Current is the rate at which electric charge flows through a conductor. It is measured in amperes (A), where one amp equals one coulomb of charge passing a given point per second — roughly 6.24 × 10¹⁸ electrons per second. Direct current (DC) flows in one direction; alternating current (AC) reverses direction many times per second.

Resistance is a material's opposition to current flow, measured in ohms (Ω). It depends on the conductor's resistivity, length, and cross-section, plus its temperature. Conductors like copper have very low resistance; insulators like rubber have extremely high resistance. Resistors are components manufactured to have a specific, predictable resistance value.

Power is the rate at which electrical energy is delivered or consumed, measured in watts. One watt equals one joule per second, or equivalently one volt acting on one amp. The three common forms are P = V × I, P = I² × R, and P = V² ÷ R — all algebraically equivalent. Power tells you how much heat a resistor dissipates and how much energy a load consumes per second.

The core Ohm's Law formula is V = I × R, with its two rearrangements I = V ÷ R and R = V ÷ I. Combined with the power identity P = V × I, you can derive five more useful forms: P = I² × R, P = V² ÷ R, V = √(P × R), I = √(P ÷ R), and R = P ÷ I². Together they let you solve any pair of (V, I, R, P) inputs for the other two.

DC (direct current) flows in one direction with constant polarity, as from a battery or solar panel. AC (alternating current) reverses direction at a fixed frequency — 50 Hz in most of the world, 60 Hz in North America. AC is used for grid distribution because it can be efficiently stepped up to high voltage for long-distance transmission and stepped back down for use. DC dominates in electronics, batteries, and increasingly in solar systems.

All calculations use exact algebra — no rounding until the final display step. Floating-point precision is more than sufficient for any practical electrical work (about 15 significant digits). Real-world accuracy is then limited by your input precision and unmodeled effects like wire resistance, contact resistance, and temperature variation — not by the calculator itself.

Ohm's Law underlies virtually every electrical calculation done by engineers, electricians, electronics hobbyists, and physicists. It determines fuse and breaker sizes, wire gauges, resistor values, power supply ratings, motor selection, battery sizing, and countless other design decisions. Understanding it qualitatively also catches errors before they cause damage — if a current is 100× larger than expected, you almost certainly have a unit confusion or rearrangement mistake.

Related Calculators