Ohms Law Formula Guide | V, I, R and Power

Ohm's Law formula example

What is the Ohm's Law formula?

V = I × R (Voltage equals Current times Resistance)

Find	Formula	Example
Voltage (V)	V = I × R	2A × 10Ω = 20V
Current (I)	I = V / R	20V ÷ 10Ω = 2A
Resistance (R)	R = V / I	20V ÷ 2A = 10Ω

For all Ohms Law formulas, the full 12-formula wheel below covers voltage, current, resistance, and power.

→ Use the Ohm's Law Calculator for instant calculations.

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The Three Ohm's Law Formulas

Core Relationship

Ohm's Law describes the relationship between voltage, current, and resistance in an electrical circuit:

V = I × R

This single equation gives us three formulas:

To Find	Formula	Unit	Symbol
Voltage	V = I × R	Volts	V
Current	I = V / R	Amperes	A
Resistance	R = V / I	Ohms	Ω

Understanding the Variables

Variable	Name	Unit	Description
V	Voltage	Volts (V)	Electrical pressure or potential difference
I	Current	Amperes (A)	Flow of electrons through a conductor
R	Resistance	Ohms (Ω)	Opposition to current flow

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Ohm's Law Wheel (Formula Reference)

Complete Ohm's Law Wheel

The Ohm's Law wheel shows all 12 formulas for calculating voltage, current, resistance, and power:

Voltage (V) Formulas:

V = I × R
V = P / I
V = √(P × R)

Current (I) Formulas:

I = V / R
I = P / V
I = √(P / R)

Resistance (R) Formulas:

R = V / I
R = P / I²
R = V² / P

Power (P) Formulas:

P = V × I
P = I² × R
P = V² / R

Quick Reference Table

Known Values	Find V	Find I	Find R	Find P
I and R	V = I×R	—	—	P = I²×R
V and R	—	I = V/R	—	P = V²/R
V and I	—	—	R = V/I	P = V×I
P and I	V = P/I	—	R = P/I²	—
P and R	V = √(P×R)	I = √(P/R)	—	—
P and V	—	I = P/V	R = V²/P	—

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Power Formulas (Extended Ohm's Law)

Three Power Equations

Combine Ohm's Law with the power formula P = V × I:

Formula	When to Use	Example
P = V × I	Know voltage and current	120V × 10A = 1200W
P = I² × R	Know current and resistance	(10A)² × 12Ω = 1200W
P = V² / R	Know voltage and resistance	(120V)² ÷ 12Ω = 1200W

Power Triangle

 P
 / \
 / \
 V × I

Cover what you want to find:

• Cover P → Multiply V × I
• Cover V → Divide P ÷ I
• Cover I → Divide P ÷ V

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DC Circuit Calculations

Single Resistor Circuit

Given: 12V battery, 4Ω resistor

Find	Calculation	Result
Current	I = V/R = 12V ÷ 4Ω	3A
Power	P = V×I = 12V × 3A	36W

Series Resistor Circuit

For resistors in series: R_total = R₁ + R₂ + R₃ + ...

Given: 24V source, R₁ = 4Ω, R₂ = 8Ω

Step	Calculation	Result
Total resistance	R = 4Ω + 8Ω	12Ω
Current	I = 24V ÷ 12Ω	2A
V across R₁	V₁ = 2A × 4Ω	8V
V across R₂	V₂ = 2A × 8Ω	16V

Parallel Resistor Circuit

For resistors in parallel: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...

Given: 12V source, R₁ = 4Ω, R₂ = 6Ω

Step	Calculation	Result
Total resistance	1/R = 1/4 + 1/6 = 5/12 → R = 2.4Ω	2.4Ω
Total current	I = 12V ÷ 2.4Ω	5A
I through R₁	I₁ = 12V ÷ 4Ω	3A
I through R₂	I₂ = 12V ÷ 6Ω	2A

→ Use Parallel Resistor Calculator for complex combinations.

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AC Circuit Applications

Ohm's Law with Impedance

For AC circuits, resistance (R) becomes impedance (Z):

V = I × Z

Where impedance includes resistance and reactance:

Z = √(R² + X²)

Component	Reactance Formula	Notes
Resistor	X_R = 0	Pure resistance
Inductor	X_L = 2πfL	Increases with frequency (f = 60Hz in US)
Capacitor	X_C = 1/(2πfC)	Decreases with frequency (f = 60Hz in US)

AC Circuit Example

Given: 120V AC, R = 6Ω, X_L = 8Ω (inductive load at 60Hz)

Step	Calculation	Result
Impedance	Z = √(6² + 8²) = √100	10Ω
Current	I = 120V ÷ 10Ω	12A
Power factor	PF = R/Z = 6/10	0.6 (lagging)
Real power	P = V×I×PF = 120×12×0.6	864W

→ Learn more: Impedance and Reactance Guide

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Worked Examples

Example 1: Find Voltage

Given: A circuit has 5A of current flowing through a 24Ω resistor.

Find: Voltage across the resistor

Solution:

V = I × R
V = 5A × 24Ω
V = 120V

Answer: The voltage is 120V.

Example 2: Find Current

Given: A 240V US circuit with a 60Ω heating element.

Find: Current flowing through the element

Solution:

I = V / R
I = 240V ÷ 60Ω
I = 4A

Answer: The current is 4A.

Example 3: Find Resistance

Given: A 12V LED strip drawing 0.5A.

Find: Resistance of the strip

Solution:

R = V / I
R = 12V ÷ 0.5A
R = 24Ω

Answer: The resistance is 24Ω.

Example 4: Find Power (All Methods)

Given: 120V circuit with 10Ω load

Method 1 (using V and R):

I = V/R = 120V ÷ 10Ω = 12A
P = V × I = 120V × 12A = 1440W

Method 2 (direct):

P = V²/R = (120V)² ÷ 10Ω = 14400 ÷ 10 = 1440W

Answer: Power consumption is 1440W.

Example 5: Wire Resistance Calculation

Given: 100 feet of 12 AWG copper wire (US typical resistance: 1.588Ω per 1000 ft)

Find: Voltage drop with 15A current

Solution:

Wire resistance = 1.588Ω × (100/1000) × 2 = 0.318Ω (round trip)
V_drop = I × R = 15A × 0.318Ω = 4.77V

Answer: Voltage drop is approximately 4.8V (4.0% of 120V - within an acceptable range for branch circuits depending on feeder drop, though the US NEC ideally recommends less than 3% drop for branch circuits alone for optimal efficiency).

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Common Values Reference

Standard Resistor Values

E12 series (10% tolerance):

Decade	Values
1-10	1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2
10-100	10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82
100-1k	100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820
1k-10k	1k, 1.2k, 1.5k, 1.8k, 2.2k, 2.7k, 3.3k, 3.9k, 4.7k, 5.6k, 6.8k, 8.2k

Typical US Load Resistances

Load Type	Typical Resistance	At Voltage	Power
100W incandescent	144Ω	120VAC	100W
60W incandescent	240Ω	120VAC	60W
1500W space heater	9.6Ω	120VAC	1500W
12V 55W halogen	2.6Ω	12VDC	55W
5V USB charging	2.5Ω	5VDC	10W

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Unit Conversions

Metric Prefixes for Electrical Units

Prefix	Symbol	Multiplier	Example
Mega (M)	MΩ	× 1,000,000	2.2MΩ = 2,200,000Ω
Kilo (k)	kΩ	× 1,000	4.7kΩ = 4,700Ω
Base	Ω	× 1	100Ω
Milli (m)	mA	× 0.001	500mA = 0.5A
Micro (μ)	μA	× 0.000001	100μA = 0.0001A

Quick Conversion Table

mA to A	kΩ to Ω	mV to V
1 mA = 0.001 A	1 kΩ = 1000 Ω	1 mV = 0.001 V
100 mA = 0.1 A	2.2 kΩ = 2200 Ω	100 mV = 0.1 V
500 mA = 0.5 A	4.7 kΩ = 4700 Ω	500 mV = 0.5 V
1000 mA = 1 A	10 kΩ = 10000 Ω	1000 mV = 1 V

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Common Mistakes to Avoid

Mistake	Why It's Wrong	Correct Approach
Mixing units (kΩ with A)	Wrong result	Convert to the same unit system (base units) first
Forgetting wire resistance	Underestimated voltage drop	Include round-trip wire resistance for single-phase
Using R for AC impedance	Ignores reactance	Use Z = √(R² + X²) for AC circuits with motors/coils
Confusing series/parallel	Wrong total resistance	Series: add directly; Parallel: reciprocal sum

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Related Calculators

Calculator	Use When...
Ohm's Law Calculator	Quick V, I, R, P calculations
Parallel Resistor Calculator	Finding combined resistance
Voltage Drop Calculator	Wire sizing and measuring voltage loss
Power Calculator	General electrical power calculations

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Summary

Core Formulas:

• V = I × R (Voltage = Current × Resistance)
• I = V / R (Current = Voltage ÷ Resistance)
• R = V / I (Resistance = Voltage ÷ Current)

Power Formulas:

• P = V × I
• P = I² × R
• P = V² / R

Memory Tip: Use the triangle method - cover what you want to find:

• Cover V → I × R (multiply)
• Cover I → V / R (divide)
• Cover R → V / I (divide)

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FAQ

What is Ohm's Law in simple terms?

Ohm's Law states that current through a conductor is directly proportional to voltage and inversely proportional to resistance. More voltage = more current; more resistance = less current.

What are the units for Ohm's Law?

• Voltage: Volts (V)
• Current: Amperes or Amps (A)
• Resistance: Ohms (Ω)
• Power: Watts (W)

Does Ohm's Law apply to AC circuits?

Yes, but you must use impedance (Z) instead of simple resistance (R) if inductive or capacitive loads exist. Impedance accounts for both pure resistance and reactance from inductors and capacitors.

How do I calculate power using Ohm's Law?

Use any of these equivalent formulas: P = V × I, P = I² × R, or P = V² / R. Choose based on which values you know.

Why is it called "Ohm's" Law?

It is named after German physicist Georg Simon Ohm who first described this relationship in 1827. The unit of measurement for resistance (Ohm, Ω) is also named in his honor.