Parallel Resistance Calculator
Calculate the equivalent resistance of resistors connected in parallel. Add up to 10 resistors, view the total resistance, individual resistor conductances, and a visual breakdown. Perfect for electronics students, hobbyists, and engineers.
What Is Parallel Resistance?
When resistors are connected in parallel, they share the same voltage across their terminals. The total or equivalent resistance of a parallel circuit is always less than the smallest individual resistor in the circuit.
The formula for calculating equivalent resistance in a parallel circuit is:
1/Req = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rn
For two resistors in parallel:
Req = (R₁ × R₂) / (R₁ + R₂)
Conductance (G) is the reciprocal of resistance:
G = 1/R (measured in Siemens, S)
In a parallel circuit, the total current is the sum of the currents through each branch, and the voltage across each branch is the same.
How Does the Parallel Resistance Calculator Work?
The calculator follows these steps:
- Step 1: You enter the resistance values for each resistor in your parallel circuit.
- Step 2: The calculator converts each resistance to conductance (G = 1/R).
- Step 3: It sums all the conductances to find the total conductance.
- Step 4: It converts the total conductance back to resistance (R = 1/G).
- Step 5: If a voltage source is provided, it calculates the current through each resistor (I = V/R).
You can add up to 10 resistors, choose your preferred unit (ohms, kilohms, or megohms), and view individual resistor conductances and currents.
Why Use This Parallel Resistance Calculator?
- Multiple Resistors: Add up to 10 resistors in parallel.
- Unit Flexibility: Choose between ohms (Ω), kilohms (kΩ), and megohms (MΩ).
- Conductance Display: Optionally show conductance for each resistor.
- Current & Power: Calculate current and power dissipation when a voltage source is provided.
- Free & Private: No registration, no data storage.
❓ Parallel Resistance Calculator FAQ
What is the formula for resistors in parallel?
1/Req = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rn. The equivalent resistance is always less than the smallest individual resistor.
How do I calculate the equivalent resistance of two resistors in parallel?
Req = (R₁ × R₂) / (R₁ + R₂). This is the product-over-sum formula, which is derived from the reciprocal formula.
Why is the equivalent resistance of parallel resistors always less than the smallest resistor?
In a parallel circuit, current can flow through multiple paths, effectively increasing the total conductance. Since resistance is the inverse of conductance, the total resistance decreases.
What is conductance?
Conductance (G) is the reciprocal of resistance: G = 1/R, measured in Siemens (S). It represents how easily current flows through a component. In parallel circuits, conductances add together.
What happens if I add more resistors in parallel?
The equivalent resistance decreases. Each additional resistor provides another path for current to flow, which increases the total conductance and lowers the total resistance.
What if all resistors in parallel have the same value?
If all n resistors have the same resistance R, then Req = R/n. For example, two 100Ω resistors in parallel give Req = 50Ω.
How do I calculate current in a parallel circuit?
Total current Itotal = V / Req. The current through each resistor is In = V / Rn. The total current is the sum of all branch currents.
What is the voltage across each resistor in a parallel circuit?
In a parallel circuit, the voltage across each resistor is the same and equals the source voltage. This is a fundamental property of parallel circuits.
How do I convert kilohms to ohms?
1 kΩ = 1000 Ω. To convert, multiply the value in kilohms by 1000. This calculator handles unit conversions automatically.
What is the difference between series and parallel circuits?
In a series circuit, current flows through each resistor one after another, and the total resistance is the sum of all resistors. In a parallel circuit, current is divided among multiple paths, and the equivalent resistance is less than the smallest resistor.
Can I use this calculator for more than 10 resistors?
This calculator supports up to 10 resistors. For more than 10, you can use the reciprocal formula manually or with a more advanced tool.
What is the unit of conductance?
Conductance is measured in Siemens (S), named after the German inventor Werner von Siemens. One siemens is equal to one ampere per volt (A/V).
How does the calculator handle zero or negative resistance values?
Resistance values must be positive. A zero resistance would represent a short circuit, which would make the equivalent resistance zero. Negative resistance is not valid for passive components.
What is the power dissipation in a parallel resistor?
Power dissipated in each resistor is P = V² / R or P = I² × R. The total power is the sum of the power dissipated by each resistor. This calculator shows power when a voltage source is provided.
Can I use this calculator for AC circuits?
This calculator is designed for DC circuits with resistors. For AC circuits with capacitors and inductors, you would need to use impedance calculations.