Parallel Resistor Calculator

Calculate equivalent resistance for resistors connected in parallel using 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...

Resistor Configuration

R1
R2

Equivalent Resistance Results

0.000000 μΩ
Equivalent Resistance (R_total)
0.000000
Megohm
0.000000
Kilohm
0.000000 Ω
Ohm
0.000
Milliohm
0 μΩ
Microhm

Formula: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ... (for parallel resistors)

Example Calculation

LED Current Limiting Example

Circuit: Three current limiting resistors in parallel for LED array

R₁: 220 Ω (for red LED)

R₂: 330 Ω (for green LED)

R₃: 470 Ω (for blue LED)

Calculation

1/R_total = 1/R₁ + 1/R₂ + 1/R₃

1/R_total = 1/220 + 1/330 + 1/470

1/R_total = 0.00454 + 0.00303 + 0.00213 = 0.0097

R_total = 1/0.0097 = 103.1 Ω

Parallel vs Series

Parallel Resistors

1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...

Total resistance decreases

Series Resistors

R_total = R₁ + R₂ + R₃ + ...

Total resistance increases

Resistance Units

Ohm (Ω)Base unit
Kilohm (kΩ)10³ Ω
Megohm (MΩ)10⁶ Ω
Milliohm (mΩ)10⁻³ Ω
Microhm (μΩ)10⁻⁶ Ω

Parallel Resistor Tips

Parallel resistors follow the reciprocal sum formula

All resistors have the same voltage across them

Total current is the sum of individual currents

Parallel connection decreases total resistance

Lower resistance resistors carry more current

Used for current division and redundancy

Understanding Parallel Resistors

What are Parallel Resistors?

Parallel resistors are resistors connected side by side in a circuit, where each resistor has the same voltage across its terminals. The equivalent resistance is calculated using the reciprocal formula: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...

Key Characteristics

  • Same voltage across all resistors (V₁ = V₂ = V₃ = V_source)
  • Total current is sum of individual currents (I_total = I₁ + I₂ + I₃)
  • Equivalent resistance is always less than the smallest resistor
  • Current divides inversely proportional to resistance

Mathematical Derivation

V = I₁ × R₁ = I₂ × R₂ = I₃ × R₃

I₁ = V/R₁, I₂ = V/R₂, I₃ = V/R₃

I_total = I₁ + I₂ + I₃

I_total = V/R₁ + V/R₂ + V/R₃

I_total = V × (1/R₁ + 1/R₂ + 1/R₃)

V/R_total = V × (1/R₁ + 1/R₂ + 1/R₃)

1/R_total = 1/R₁ + 1/R₂ + 1/R₃

Common Applications

  • Current divider circuits
  • LED current limiting (multiple paths)
  • Shunt resistors for current measurement
  • Heating elements with multiple zones
  • Redundant circuit paths for reliability