The Ohm's Law Calculator has three modes to help with different electrical calculations:

1. Basic Ohm's Law Mode:

1. Enter any two values from voltage (V), current (I), or resistance (R)
2. The calculator automatically finds the missing value using V = I × R
3. Power is calculated automatically using P = V × I
4. Results show all four parameters with unit conversions

2. Power Calculations Mode:

1. Enter any two values from V, I, R, or P (power)
2. Click "Calculate All Values" to find the remaining parameters
3. View additional information like energy costs and component ratings

3. Ohm's Law Wheel:

• Click any segment to see the relevant formula
• Visual reference for all Ohm's Law relationships
• Includes power formulas in the outer ring

Ohm's Law is the fundamental relationship between voltage, current, and resistance in electrical circuits:

Where:

• V (Voltage) = Electrical pressure in Volts
• I (Current) = Flow of electrons in Amperes
• R (Resistance) = Opposition to current flow in Ohms

Why it's important:

• Circuit Design: Calculate component values for desired performance
• Safety: Ensure components can handle calculated current and power
• Troubleshooting: Diagnose circuit problems by measuring and calculating
• Power Management: Determine power consumption and heat dissipation
• Universal Application: Works for all DC circuits and resistive AC loads

Fun Fact: Named after German physicist Georg Ohm who published it in 1827!

The calculator uses standard SI (International System) electrical units:

Primary Units:

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

Common Conversions:

Pro Tip: Always convert to base units before calculating to avoid errors!

The calculator provides results with 3 decimal places of precision, which is suitable for most electrical engineering applications.

Accuracy Considerations:

• Mathematical Accuracy: Calculations are exact based on input values
• Real-World Factors: Actual circuits may vary due to:
  • Component tolerances (resistors typically ±5%)
  • Temperature effects on resistance
  • Wire resistance in circuits
  • Contact resistance at connections

Best Practices for Accuracy:

1. Use measured values when available (multimeter readings)
2. Account for tolerances in critical applications
3. Include safety margins (typically 20-50% for power ratings)
4. Consider temperature coefficients for precision work

Example Impact:

A "100Ω" resistor with 5% tolerance can actually be 95Ω to 105Ω, causing up to 5% variation in calculated current.

There are three power formulas, each useful in different situations:

1. P = V × I (Voltage and Current Known)

• Use when: You can measure both voltage and current
• Example: Measuring power consumption with a multimeter
• Application: Battery-powered devices, power supplies

2. P = I² × R (Current and Resistance Known)

• Use when: Current is constant or easily measured
• Example: Calculating resistor power dissipation
• Application: Series circuits, current-limiting resistors

3. P = V² ÷ R (Voltage and Resistance Known)

• Use when: Voltage is constant (like mains power)
• Example: Calculating heater element power
• Application: Household appliances, heating elements

Quick Selection Guide:

Calculating LED resistor values is a common application of Ohm's Law:

Step-by-Step Process:

1. Determine your values:
   • Supply voltage (Vs)
   • LED forward voltage (Vf) - typically 1.8-3.3V
   • LED forward current (If) - typically 10-20mA
2. Calculate voltage across resistor:

   VR = Vs - Vf

3. Calculate resistance using Ohm's Law:

   R = VR ÷ If

4. Choose next higher standard value

Example: Red LED with 9V Battery

• Supply voltage (Vs) = 9V
• LED forward voltage (Vf) = 2V
• LED current (If) = 20mA = 0.02A
• Resistor voltage: 9V - 2V = 7V
• Resistance: 7V ÷ 0.02A = 350Ω
• Use standard value: 390Ω

Power Rating:

P = I² × R = 0.02² × 390 = 0.156W → Use 1/4W resistor

Pro Tip: Always verify the LED datasheet for exact Vf and If values!

Ohm's Law applies differently to AC (Alternating Current) and DC (Direct Current) circuits:

DC Circuits (Simple Ohm's Law):

• V = I × R applies directly
• Voltage and current are constant
• Only resistance opposes current flow
• Examples: Batteries, DC power supplies, LEDs

AC Circuits (Modified for Impedance):

• V = I × Z (where Z is impedance)
• Impedance includes:
  • Resistance (R)
  • Inductive reactance (XL)
  • Capacitive reactance (XC)
• Must consider phase angles
• Power calculations more complex (real, reactive, apparent)

When Standard Ohm's Law Works for AC:

• Purely resistive loads: Heaters, incandescent bulbs
• RMS values: When using RMS voltage and current
• No reactive components: No inductors or capacitors

Important: This calculator is designed for DC circuits and resistive AC loads. For complex AC circuits with inductance or capacitance, use an AC impedance calculator.

Wire gauge selection is critical for safety and efficiency. Use this guide based on your calculated current:

AWG Wire Current Capacity (Copper, 60°C insulation):

Important Considerations:

• Safety margin: Use 80% rule (wire rated for 125% of continuous current)
• Voltage drop: Longer runs need larger wire
• Temperature: Higher temps require derating
• Bundling: Multiple wires together need derating

Example: For 15A continuous load, use 12 AWG (rated 30A × 0.8 = 24A capacity)

This error occurs when you enter three values that are mathematically inconsistent with Ohm's Law:

Common Causes:

1. Unit confusion:
   • Entering milliamps (mA) instead of amps (A)
   • Using kilohms (kΩ) instead of ohms (Ω)
   • Example: 12V, 10mA, 1000Ω → Should be 12V, 0.01A, 1200Ω
2. Measurement errors:
   • Multimeter on wrong range
   • Poor connections affecting readings
   • Component tolerances
3. Rounding issues:
   • Using rounded values from previous calculations
   • Solution: Use more decimal places

How to Fix:

1. Enter only 2 values and let the calculator find the third
2. Double-check units - convert everything to base units
3. Verify measurements with a multimeter
4. Account for tolerances in real components

Quick Check:

Manually verify: Does V = I × R? For example:

• V = 12V, I = 2A, R = 6Ω
• Check: 2A × 6Ω = 12V ✓

Electrical safety is paramount when working with circuits. Here are essential safety guidelines based on your calculations:

Voltage Safety Levels:

• < 50V DC / < 30V AC: Generally safe (still use caution)
• 50-1000V: Dangerous - can cause severe shock
• > 1000V: High voltage - special training required

Current Danger Levels (through human body):

• 1 mA: Barely perceptible
• 5 mA: Maximum safe current
• 10-20 mA: Painful, muscular control lost
• 30 mA: Respiratory paralysis
• > 75 mA: Cardiac fibrillation likely

Component Safety:

• Power Rating: Use 2× calculated power for safety margin
• Voltage Rating: Components rated for 2× operating voltage
• Fusing: Always fuse at 125% of normal current
• Heat Management: Power > 1W needs heat dissipation

Best Practices:

1. Always disconnect power before modifying circuits
2. Use one hand when testing live circuits
3. Wear safety glasses when soldering
4. Keep workspace dry and insulated
5. Have fire extinguisher rated for electrical fires

Remember: It's not voltage that kills, it's current - but voltage drives the current!

Temperature significantly affects resistance, which impacts all Ohm's Law calculations:

Temperature Coefficient Formula:

R₂ = R₁[1 + α(T₂ - T₁)]

Where α is the temperature coefficient of resistance

Common Temperature Coefficients:

Practical Impact:

• Copper wire at 20°C: 100Ω
• Same wire at 70°C: 100 × [1 + 0.00393 × 50] = 119.65Ω
• Current reduction: Nearly 20% less current!

Applications to Consider:

• Power resistors: Resistance increases as they heat up
• Motor windings: Higher resistance when hot reduces efficiency
• Precision circuits: Use low-tempco resistors
• Outdoor equipment: Account for seasonal variations

The Ohm's Law wheel is a visual tool that shows all relationships between V, I, R, and P at a glance:

How to Read the Wheel:

1. Center circle: Shows the basic Ohm's Law equation (V = I × R)
2. Inner segments: Each shows one parameter (V, I, R, or P)
3. To find a value: Cover it with your finger - the visible formula gives the answer

Example Uses:

• Finding Voltage: Cover V → see I × R
• Finding Current: Cover I → see V ÷ R
• Finding Resistance: Cover R → see V ÷ I
• Finding Power: Multiple formulas available in outer ring

12 Key Formulas in the Wheel:

Pro Tip: Print the wheel and keep it at your workbench for quick reference!

Once you calculate power using Ohm's Law, determining electrical costs is straightforward:

Cost Calculation Formula:

Cost = Power (kW) × Time (hours) × Rate ($/kWh)

Step-by-Step Process:

1. Calculate power: Use P = V × I or other formulas
2. Convert to kilowatts: Divide watts by 1000
3. Determine usage hours: Daily, monthly, or yearly
4. Find your rate: Check electricity bill (typically $0.10-$0.15/kWh)

Example: Space Heater Cost

• Voltage: 120V, Current: 12.5A
• Power: 120V × 12.5A = 1,500W = 1.5kW
• Daily use: 8 hours
• Rate: $0.12/kWh
• Daily cost: 1.5 × 8 × $0.12 = $1.44
• Monthly cost: $1.44 × 30 = $43.20

Common Appliance Costs (at $0.12/kWh):

Ohm's Law applies differently in series and parallel circuits:

Series Circuits (Components in a Line):

• 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)

Parallel Circuits (Multiple Paths):

• Voltage: Same across all branches (V_total = V₁ = V₂ = V₃)
• Current: Divides between branches (I_total = I₁ + I₂ + I₃)
• Resistance: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃

Quick Formulas:

• Two resistors in parallel: R_total = (R₁ × R₂) ÷ (R₁ + R₂)
• N identical resistors in parallel: R_total = R ÷ N

Practical Applications:

• Series: Christmas lights, voltage dividers
• Parallel: House wiring, car headlights
• Mixed: Most real circuits combine both

Ohm's Law is an essential tool for diagnosing circuit problems:

Basic Troubleshooting Process:

1. Calculate expected values using Ohm's Law
2. Measure actual values with a multimeter
3. Compare results to identify problems
4. Isolate the fault using logical deduction

Common Problems and Indicators:

Diagnostic Examples:

• LED not lighting:
  • Measure voltage across LED
  • If 0V: Check connections/polarity
  • If full supply voltage: LED is open
• Motor running slow:
  • Measure current draw
  • Calculate resistance: R = V/I
  • High R indicates worn brushes/poor connections

Safety: Always disconnect power before changing connections!