Ohms Law Calculator
Calculate voltage, current, resistance, and power using Ohm's Law (V=IR). Essential tool for electrical engineering, electronics projects, and circuit analysis.
Ohm's Law Formulas
Voltage (V)
V = I × R
V = P ÷ I
V = √(P × R)
Current (I)
I = V ÷ R
I = P ÷ V
I = √(P ÷ R)
Resistance (R)
R = V ÷ I
R = V² ÷ P
R = P ÷ I²
Power (P)
P = V × I
P = I² × R
P = V² ÷ R
Related Calculators
About This Calculator
Ohm's Law is the fundamental relationship in electrical circuits, describing how voltage, current, and resistance interact. Named after German physicist Georg Ohm, this principle is essential for anyone working with electronics, from hobbyists building Arduino projects to professional electrical engineers designing power systems.
What is Ohm's Law? Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. The formula V = IR (Voltage = Current × Resistance) forms the basis of all circuit analysis.
Why It Matters:
- Essential for designing any electrical circuit
- Determines component selection and safety
- Calculates power consumption and heat generation
- Required for troubleshooting electrical problems
The Power Relationship: Combined with the power formula (P = VI), Ohm's Law allows you to calculate any electrical quantity when you know two others. The power wheel shows all 12 formulas derived from these fundamental relationships.
This calculator determines voltage, current, resistance, and power from any two known values. For more specific applications, see our Resistor Calculator and Power Calculator.
How to Use the Ohms Law Calculator
- 1Select what you want to calculate (voltage, current, resistance, or power).
- 2Enter any two of the remaining three values.
- 3The calculator automatically computes all values.
- 4Review the formula used for the calculation.
- 5Check the practical information for safety guidance.
- 6Note the wire gauge recommendation if applicable.
- 7Use SI units: Volts (V), Amps (A), Ohms (Ω), Watts (W).
- 8For milliamps, enter as decimals (e.g., 0.020 for 20 mA).
- 9For kilohms, enter as thousands (e.g., 1000 for 1 kΩ).
- 10Verify your results make physical sense.
The Fundamental Formulas
All electrical calculations derive from these basic relationships.
Ohm's Law
V = I × R
Where:
- V = Voltage (Volts)
- I = Current (Amperes)
- R = Resistance (Ohms)
Power Equation
P = V × I
Where:
- P = Power (Watts)
- V = Voltage (Volts)
- I = Current (Amperes)
The Complete Set (12 Formulas)
Voltage (V):
- V = I × R
- V = P ÷ I
- V = √(P × R)
Current (I):
- I = V ÷ R
- I = P ÷ V
- I = √(P ÷ R)
Resistance (R):
- R = V ÷ I
- R = V² ÷ P
- R = P ÷ I²
Power (P):
- P = V × I
- P = I² × R
- P = V² ÷ R
The Ohm's Law Wheel
Visualize all formulas in a circle:
- Inner circle: V, I, R, P
- Outer ring: All calculation formulas
- Know any two, calculate the others
Understanding Units and Prefixes
Electrical quantities span many orders of magnitude.
Base Units
| Quantity | Unit | Symbol |
|---|---|---|
| Voltage | Volt | V |
| Current | Ampere | A |
| Resistance | Ohm | Ω |
| Power | Watt | W |
Common Prefixes
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| Mega | M | 10⁶ | 1 MΩ = 1,000,000 Ω |
| Kilo | k | 10³ | 1 kΩ = 1,000 Ω |
| Milli | m | 10⁻³ | 1 mA = 0.001 A |
| Micro | μ | 10⁻⁶ | 1 μA = 0.000001 A |
| Nano | n | 10⁻⁹ | 1 nA = 0.000000001 A |
Typical Ranges
Voltage:
- Batteries: 1.5V - 12V
- Household (US): 120V
- Household (EU): 230V
- Industrial: 480V - 13,800V
Current:
- LEDs: 10-20 mA
- USB devices: up to 500 mA
- Household appliances: 1-15 A
- Electric vehicles: 100-400 A
Resistance:
- Wire: 0.001 - 1 Ω
- Resistors: 1 Ω - 10 MΩ
- Insulators: > 1 GΩ
Practical Applications
How Ohm's Law applies in real-world scenarios.
LED Circuits
Problem: Power an LED (2V forward voltage, 20mA) from 5V supply
Solution:
- Voltage across resistor: 5V - 2V = 3V
- Current needed: 20 mA = 0.02 A
- R = V ÷ I = 3V ÷ 0.02A = 150 Ω
- P = V × I = 3V × 0.02A = 0.06W (use 1/8W resistor)
Battery Runtime
Problem: How long will a 2000 mAh battery power a 100 mA device?
Solution:
- Runtime = Capacity ÷ Current
- Runtime = 2000 mAh ÷ 100 mA = 20 hours
Heat Calculation
Problem: A 10Ω resistor carries 2A. How much heat?
Solution:
- P = I² × R = 2² × 10 = 40 Watts
- This is significant heat - needs heat sink!
Wire Sizing
Problem: 12V system drawing 10A over 20 feet
Solution:
- Maximum voltage drop: typically 3% = 0.36V
- R = V ÷ I = 0.36V ÷ 10A = 0.036 Ω
- For 40 feet total wire: 0.036 ÷ 40 = 0.0009 Ω/ft
- Use resistance tables: 10 AWG wire needed
Fuse Selection
Problem: Select fuse for 120V, 1000W appliance
Solution:
- I = P ÷ V = 1000W ÷ 120V = 8.33A
- Add 25% safety margin: 8.33 × 1.25 = 10.4A
- Use 15A fuse (next standard size up)
Series and Parallel Circuits
Ohm's Law applies differently to circuit configurations.
Series Circuits
Components connected end-to-end:
Current: Same through all components I_total = I₁ = I₂ = I₃
Voltage: Divides across components V_total = V₁ + V₂ + V₃
Resistance: Adds up R_total = R₁ + R₂ + R₃
Example: Three 100Ω resistors in series
- R_total = 300Ω
- At 12V: I = 12V ÷ 300Ω = 40mA
- Each resistor drops: 40mA × 100Ω = 4V
Parallel Circuits
Components connected across same points:
Voltage: Same across all components V_total = V₁ = V₂ = V₃
Current: Divides through components I_total = I₁ + I₂ + I₃
Resistance: Reciprocal formula 1/R_total = 1/R₁ + 1/R₂ + 1/R₃
Example: Three 100Ω resistors in parallel
- 1/R = 1/100 + 1/100 + 1/100 = 3/100
- R_total = 100/3 = 33.3Ω
- At 12V: I = 12V ÷ 33.3Ω = 360mA
Quick Rules
- Series: Resistance increases, current decreases
- Parallel: Resistance decreases, current increases
- Two equal resistors in parallel: R_total = R ÷ 2
Safety Considerations
Electricity can be dangerous. Understand the risks.
Voltage Danger Levels
| Voltage | Risk Level | Notes |
|---|---|---|
| < 12V | Low | Safe for most situations |
| 12-50V | Moderate | Can be dangerous if wet |
| 50-120V | High | Dangerous, can cause injury |
| > 120V | Very High | Life-threatening |
Current Effects on Human Body
| Current | Effect |
|---|---|
| 1 mA | Barely perceptible |
| 5 mA | Painful shock |
| 10-20 mA | Muscle lock, can't let go |
| 50-100 mA | Ventricular fibrillation |
| > 100 mA | Often fatal |
Note: It's current that kills, but voltage drives it through resistance.
Wire Gauge Selection
| AWG | Max Current | Typical Use |
|---|---|---|
| 24 | 0.5 A | Signal wires |
| 22 | 1 A | Low power |
| 20 | 2 A | Electronics |
| 18 | 5 A | Extension cords |
| 14 | 15 A | House circuits |
| 12 | 20 A | Kitchen circuits |
| 10 | 30 A | Dryers, AC |
Heat and Power Dissipation
Heat generated: P = I² × R
Rule of thumb: Resistors should be rated 2× the calculated power
Heat effects:
- Resistors > 0.5W: Consider heat sinking
- ICs: Check thermal specs
- Wire: Undersized wire = fire hazard
Common Component Values
Reference values for practical design.
Standard Resistor Values (E12 Series)
10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82
Multiply by powers of 10: 100Ω, 1kΩ, 10kΩ, etc.
Common Resistor Applications
| Value | Common Use |
|---|---|
| 330Ω | LED with 5V |
| 470Ω | LED with 5V (dimmer) |
| 1kΩ | Pull-up/down, general |
| 4.7kΩ | I²C pull-up |
| 10kΩ | Input protection |
| 100kΩ | High-impedance |
Power Supply Voltages
| Voltage | Application |
|---|---|
| 1.5V | AA/AAA battery |
| 3.3V | Modern logic |
| 3.7V | Li-ion battery |
| 5V | USB, TTL logic |
| 9V | 9V battery |
| 12V | Automotive, PC |
| 24V | Industrial |
| 48V | Telecom (PoE) |
Power Consumption Reference
| Device | Typical Power |
|---|---|
| LED | 20-100 mW |
| Arduino | 250 mW |
| Raspberry Pi | 2.5-7 W |
| Laptop | 30-90 W |
| Desktop PC | 200-500 W |
| Electric kettle | 1500-3000 W |
Pro Tips
- 💡Always double-check your decimal points - mA vs A is a 1000x difference.
- 💡When in doubt, use a larger wire gauge for safety.
- 💡Heat dissipation is proportional to I² - doubling current quadruples heat.
- 💡Measure twice, connect once - verify calculations before powering on.
- 💡Use fuses rated slightly above expected current for protection.
- 💡Resistance increases with temperature for most metals.
- 💡LED circuits always need current-limiting resistors.
- 💡Power supplies should be rated 20-50% above expected load.
- 💡For batteries, current capacity (mAh) determines runtime.
- 💡High voltage requires proper insulation and safety procedures.
- 💡Use the metric prefix that makes numbers easy to read (4.7kΩ not 4700Ω).
- 💡Ground yourself when working with sensitive electronics.
Frequently Asked Questions
Voltage is the "pressure" that pushes electrons through a circuit (measured in Volts). Current is the actual flow rate of electrons (measured in Amperes). A common analogy: voltage is like water pressure, current is like flow rate, and resistance is like pipe diameter.
