Ohm's Law states that the current (I) through a conductor is directly proportional to the voltage (V) across it and inversely proportional to its resistance (R): V = I × R. Named after German physicist Georg Simon Ohm (1827), it is the most fundamental relationship in circuit analysis and applies to all resistive circuits regardless of whether the driving source is DC or AC.

What are the four Ohm's Law formulas?

The four core formulas are: V = I × R (voltage); I = V / R (current); R = V / I (resistance); P = V × I (power). From these, 12 total formula variants can be derived using the power relationships P = I²R and P = V²/R. Knowing any two of V, I, R, or P allows you to calculate the other two.

How do you calculate current using Ohm's Law?

Current (I) = Voltage (V) divided by Resistance (R): I = V/R. Example: 12V across a 100Ω resistor → I = 12/100 = 0.12A = 120mA. If you know power and voltage: I = P/V. If you know power and resistance: I = √(P/R).

How do you calculate power in an electrical circuit?

Power (P) can be calculated three ways: P = V × I (voltage × current); P = I² × R (current squared × resistance); P = V² / R (voltage squared divided by resistance). Example: 12V circuit drawing 2A → P = 12 × 2 = 24W. Knowing power is important for choosing the correct power rating for resistors and other components.

What is the Ohm's Law wheel or pie chart?

The Ohm's Law wheel is a visual reference showing all 12 formulas for V, I, R, and P arranged in a circle divided into four quadrants. Each quadrant shows the three ways to calculate that quantity using the other three variables. It allows electricians and engineers to quickly look up the correct formula without memorizing all 12 variants.

What is a resistor's power rating and why does it matter?

A resistor's power rating (in watts) is the maximum power it can safely dissipate as heat. Standard ratings are 1/8W, 1/4W, 1/2W, 1W, 2W, 5W, and 10W. If a resistor dissipates more power than its rating, it overheats and may burn out or become a fire hazard. Always choose a resistor rated at least 2× the calculated power dissipation for a safety margin.

Does Ohm's Law apply to AC circuits?

Ohm's Law V = IR applies to purely resistive AC circuits (circuits containing only resistors). For AC circuits with capacitors or inductors, resistance is replaced by impedance (Z), and the formula becomes V = I × Z, where Z is a complex number combining resistance and reactance. For DC analysis and purely resistive AC circuits, standard Ohm's Law applies directly.

What units are used in Ohm's Law?

Voltage (V) is measured in volts (V), millivolts (mV = 0.001V), or kilovolts (kV = 1000V). Current (I) is measured in amperes (A) or milliamperes (mA = 0.001A). Resistance (R) is measured in ohms (Ω), kilohms (kΩ = 1000Ω), or megohms (MΩ = 1,000,000Ω). Power (P) is measured in watts (W), milliwatts (mW), or kilowatts (kW). Ohm's Law formulas require consistent base units (V, A, Ω, W).

Who invented Ohm's Law?

Georg Simon Ohm (1789–1854), a German physicist and mathematician, published his law in 1827 in his treatise 'Die galvanische Kette, mathematisch bearbeitet' (The Galvanic Circuit Investigated Mathematically). Ohm derived the relationship experimentally using hand-made equipment. The unit of electrical resistance, the ohm (Ω), is named in his honor.

What is the difference between voltage, current, and resistance?

Voltage (V) is electrical pressure — the force pushing electrons through a circuit, measured in volts. Current (I) is the flow rate of electrons, measured in amperes (coulombs per second). Resistance (R) is the opposition to current flow, measured in ohms. Water analogy: voltage is water pressure, current is flow rate, and resistance is pipe diameter. Higher pressure (voltage) drives more flow (current); narrower pipe (more resistance) reduces flow.

V · I · R · P · Enter any 2

Ohm's Law
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Enter any two of Voltage, Current, Resistance, or Power — instantly calculate all four. Includes unit scaling, power rating check, and step-by-step formulas.

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→ All 4

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mV/kV

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Watt

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Ohm's Law Calculator

Enter any 2 values → solve for all 4

Voltage

Current

Resistance

Power

⚠️ Enter any 2 values to calculate the other 2.

Visual Reference

Ohm's Law Wheel — All 12 Formulas

Each quadrant shows the three ways to calculate V, I, R, or P from the other variables.

V = Voltage (Volts) → IR · √(PR) · P/I

I = Current (Amps) → V/R · P/V · √(P/R)

R = Resistance (Ω) → V/I · V²/P · P/I²

P = Power (Watts) → VI · I²R · V²/R

All 12 Formulas

Ohm's Law & Watt's Law — Complete Reference

Every formula derived from V = IR and P = VI.

Find V

V = I × R

from I and R

Find V

V = P / I

from P and I

Find V

V = √(P×R)

from P and R

Find I

I = V / R

from V and R

Find I

I = P / V

from P and V

Find I

I = √(P/R)

from P and R

Find R

R = V / I

from V and I

Find R

R = V² / P

from V and P

Find R

R = P / I²

from P and I

Find P

P = V × I

from V and I

Find P

P = I² × R

from I and R

Find P

P = V² / R

from V and R

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The Water Analogy for Ohm's Law

Think of electricity like water in a pipe: Voltage = water pressure (pushes electrons). Current = water flow rate (electrons moving per second). Resistance = pipe diameter (restriction to flow). More pressure (V) drives more flow (I). A narrower pipe (more R) reduces flow. Power = pressure × flow = how much work the water does per second.

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Power Rating — Why It Matters

Every resistor has a maximum power rating. Standard ratings: 1/8W, 1/4W (most common), 1/2W, 1W, 2W, 5W, 10W. Exceeding the rating causes overheating and failure — possibly fire.

Rule of thumb: always choose a resistor rated at 2× the calculated dissipation. A 1Ω resistor with 1A flowing through it dissipates 1W — use a 2W resistor. SMD resistors are typically rated 1/10W to 1/4W due to their small size.

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DC vs AC Circuits

Ohm's Law V = IR applies directly to DC circuits and purely resistive AC circuits. For AC circuits with capacitors or inductors, resistance becomes impedance (Z) — a complex quantity combining resistance (R) and reactance (X).

V = I × Z, where Z = √(R² + X²). For purely resistive circuits (no capacitors, no inductors), impedance Z = resistance R, and standard Ohm's Law applies at any frequency.

Ohm's Law — All Formulas Explained

Ohm's Law and Watt's Law together provide 12 formulas for computing voltage, current, resistance, and power from any two known quantities. These are the most-used formulas in all of electronics and electrical engineering.

The Core Relationships

V = I × R (Ohm's Law — voltage) I = V / R (Ohm's Law — current) R = V / I (Ohm's Law — resistance) P = V × I (Watt's Law — power from V and I) P = I² × R (power from I and R) P = V² / R (power from V and R) Units: V = volts, I = amperes, R = ohms (Ω), P = watts (W) Example: 12V source, 100Ω resistor I = V/R = 12/100 = 0.12 A = 120 mA P = V×I = 12×0.12 = 1.44 W P = I²R = (0.12)²×100 = 1.44 W ✓

Derived Formulas (solving for each variable)

Solving for Voltage (V): V = I × R (from I, R) V = P / I (from P, I) V = √(P × R) (from P, R) Solving for Current (I): I = V / R (from V, R) I = P / V (from P, V) I = √(P / R) (from P, R) Solving for Resistance (R): R = V / I (from V, I) R = V² / P (from V, P) R = P / I² (from P, I) Solving for Power (P): P = V × I (from V, I) P = I² × R (from I, R) P = V² / R (from V, R)

Unit Conversions

Voltage: 1 kV = 1,000 V; 1 mV = 0.001 V Current: 1 A = 1,000 mA; 1 mA = 0.001 A Resistance: 1 kΩ = 1,000 Ω; 1 MΩ = 1,000,000 Ω Power: 1 kW = 1,000 W; 1 mW = 0.001 W Always convert to base units (V, A, Ω, W) before calculating. Example: 5V, 20mA = 0.020A R = V/I = 5/0.020 = 250Ω P = V×I = 5×0.020 = 0.1W = 100mW

Frequently Asked Questions

Ohm's Law states V = I × R — voltage equals current times resistance. Named after Georg Simon Ohm (1827), it is the most fundamental relationship in electronics. It means: more voltage pushes more current; more resistance reduces current. Knowing any two of V, I, or R lets you calculate the third. Adding Watt's Law (P = VI) gives you power as a 4th variable.

V = I × R; I = V / R; R = V / I; P = V × I. From these, 12 total variants can be derived. Our calculator accepts any 2 of V, I, R, P and solves for the other 2 using the appropriate formula. Entering different pairs shows you which formula is being applied.

I = V / R. Example: 12V supply, 100Ω resistor → I = 12/100 = 0.12A = 120mA. If you know power and voltage: I = P/V. If you know power and resistance: I = √(P/R). Enter any two known values in our calculator and it will pick the correct formula automatically.

Three ways: P = V × I; P = I² × R; P = V² / R. All three give the same answer when using consistent values. Example: 12V, 2A → P = 24W. Same: I=2A, R=6Ω → P = 4×6 = 24W. Same: V=12V, R=6Ω → P = 144/6 = 24W. Use the formula that matches your two known values.

A visual reference with 4 quadrants (V, I, R, P), each showing the 3 formulas to calculate that value. Cover the variable you want and the formula is revealed. It's the standard reference used by electricians and electronics students to avoid memorizing all 12 variants. See our wheel above — each quadrant shows the three ways to solve for V, I, R, and P respectively.

Maximum power a resistor can safely dissipate as heat. Common ratings: 1/8W, 1/4W, 1/2W, 1W, 2W, 5W. If exceeded, the resistor overheats and may fail or cause fire. Rule: use a resistor rated at least 2× calculated power. Example: circuit dissipates 0.4W → use 1W rated resistor. Our calculator shows the recommended rating automatically.

Yes, for purely resistive AC circuits (resistors only, no capacitors or inductors). For AC circuits with capacitors or inductors, resistance becomes impedance Z = √(R² + X²), and V = I × Z. For household AC through a pure resistor (like a heater), standard V = IR applies directly using RMS (root mean square) voltage and current values.

Base units: Volts (V), Amperes (A), Ohms (Ω), Watts (W). Common prefixes: mV=0.001V, kV=1000V; mA=0.001A; kΩ=1000Ω, MΩ=1,000,000Ω; mW=0.001W, kW=1000W. Always convert to base units before calculating. Our calculator handles unit conversion automatically — select mA, kΩ, etc. from the unit dropdowns.

Georg Simon Ohm (1789–1854), a German physicist, published the law in 1827. He derived it experimentally using hand-built equipment. Initially his work was rejected by the German scientific community, but it was later vindicated. The unit of resistance (ohm, Ω) is named in his honor. James Watt (1736–1819) preceded Ohm with power relationships, giving us P = VI.

Voltage (V) = electrical pressure that drives electrons. Current (I) = rate of electron flow (coulombs per second = amperes). Resistance (R) = opposition to flow. Water analogy: voltage = pump pressure, current = flow rate, resistance = pipe narrowness. Higher voltage drives more current through the same resistance. More resistance reduces current for the same voltage.

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Ohm's LawCalculator

Ohm's Law Wheel — All 12 Formulas

Ohm's Law & Watt's Law — Complete Reference

The Water Analogy for Ohm's Law

Ohm's Law — All Formulas Explained

The Core Relationships

Derived Formulas (solving for each variable)

Unit Conversions

Frequently Asked Questions

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Ohm's Law
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