Parallel Resistor Calculator
Calculate equivalent resistance for multiple resistors connected in parallel. Enter resistor values and a supply voltage to also calculate total current, branch currents, voltage and power dissipation.
Parallel Resistor Inputs
Branch Results
| Resistor | Resistance | Voltage | Branch Current | Power |
|---|---|---|---|---|
| Enter resistor values and calculate. | ||||
Parallel Resistor Formula
Resistors connected in parallel share the same two electrical nodes. Because the voltage across each branch is the same, each resistor carries a different current depending on its resistance.
Rtotal = 1 / (1/R1 + 1/R2 + ... + 1/Rn)
Branch current: Iᵢ = V / Rᵢ
Total current: Itotal = I1 + I2 + ... + In
Branch power: Pᵢ = V² / Rᵢ
Total power: Ptotal = V × Itotal
For two resistors, the reciprocal equation can be simplified to:
How Parallel Resistors Work
When resistors are connected in parallel, both ends of every resistor are connected to the same two nodes. This means that the voltage across every resistor is identical.
Current, however, divides between the branches. A lower-value resistor carries more current, while a higher-value resistor carries less current.
Same Voltage
Every resistor connected across the same two nodes has the same voltage across it.
Divided Current
Total current splits between the parallel branches according to their resistance values.
Lower Resistance
Adding another resistor in parallel provides another current path and reduces the equivalent resistance.
Two Resistors in Parallel
The special two-resistor equation is often the quickest way to calculate an equivalent resistance.
Example: 100 Ω and 100 Ω
For two equal 100 Ω resistors:
Rtotal = 10000 / 200
Rtotal = 50 Ω
Therefore, two equal resistors connected in parallel produce an equivalent resistance equal to half the value of either resistor.
Worked Parallel Resistor Examples
Example 1: Two 1 kΩ Resistors
Two 1 kΩ resistors are connected across a 12 V supply.
Rtotal = 500 Ω
Itotal = 12 / 500
Itotal = 24 mA
Each resistor has 12 V across it and carries 12 mA. Each resistor dissipates 144 mW.
Example 2: 100 Ω and 220 Ω
A 100 Ω resistor and a 220 Ω resistor are connected in parallel across 12 V.
Rtotal = 22000 / 320
Rtotal ≈ 68.75 Ω
The 100 Ω branch carries 120 mA while the 220 Ω branch carries about 54.55 mA.
Common Parallel Resistor Examples
| Resistors | Equivalent Resistance | At 12 V | Total Power |
|---|---|---|---|
| 100 Ω ∥ 100 Ω | 50 Ω | 240 mA | 2.88 W |
| 1 kΩ ∥ 1 kΩ | 500 Ω | 24 mA | 0.288 W |
| 100 Ω ∥ 220 Ω | 68.75 Ω | 174.55 mA | 2.095 W |
| 100 Ω ∥ 220 Ω ∥ 330 Ω | ≈50.77 Ω | ≈236.36 mA | ≈2.836 W |
| 10 Ω ∥ 100 Ω ∥ 1 kΩ | ≈9.0 Ω | ≈1.333 A | 16 W |
Current Division in Parallel Resistors
One of the most important properties of a parallel resistor network is current division. Every branch has the same voltage, so Ohm’s law determines the current through each resistor.
For example, with 100 Ω and 200 Ω connected across 10 V:
I2 = 10 / 200 = 50 mA
Itotal = 100 mA + 50 mA
Itotal = 150 mA
The lower-resistance 100 Ω branch carries twice as much current as the 200 Ω branch.
Power Dissipation in Parallel Resistors
Since every resistor in a parallel network has the same voltage, the easiest branch-power equation is:
A lower resistance at the same voltage produces greater power dissipation. This is important when selecting physical resistor power ratings.
Example
A 100 Ω resistor connected across 12 V dissipates:
P = 144 / 100
P = 1.44 W
A resistor with an appropriate power rating must therefore be selected for the actual circuit. The calculated dissipation is not itself a recommended component rating.
Series vs. Parallel Resistors
| Property | Series | Parallel |
|---|---|---|
| Total resistance | R1 + R2 + ... | Reciprocal sum |
| Current | Same through every resistor | Divides between branches |
| Voltage | Divides between resistors | Same across every branch |
| Adding resistor | Increases total resistance | Decreases total resistance |
| Total current at fixed voltage | Decreases as resistance increases | Increases as resistance decreases |
Applications of Parallel Resistors
Practical Design Notes
- The equivalent resistance of positive resistors in parallel is always below the smallest individual resistor.
- Every parallel branch sees the same ideal voltage.
- Check the power dissipation of every individual resistor, not just the total network power.
- Resistor tolerances affect the actual equivalent resistance and branch-current distribution.
- PCB trace resistance, contact resistance and wiring can introduce small additional effects in practical circuits.
- Very low equivalent resistance can result in substantial current demand from the power supply.
- When combining resistors to distribute power, consider thermal conditions as well as nominal resistance.
Related Electronics Calculators
Frequently Asked Questions
How do you calculate resistors in parallel?
For resistors connected in parallel, calculate the reciprocal of the total resistance by adding the reciprocals of each resistor: 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn. Then take the reciprocal of the result.
What is the formula for total resistance in parallel?
The general formula is 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn. For two resistors, the equivalent resistance can also be calculated as Rtotal = (R1 × R2) / (R1 + R2).
Is parallel resistance always lower than the smallest resistor?
For two or more positive resistance values connected in parallel, the equivalent resistance is lower than the smallest individual resistor.
What happens to voltage across parallel resistors?
In an ideal parallel circuit, the voltage across every resistor is the same as the supply voltage.
How do you calculate current through each parallel resistor?
Use Ohm’s law for each branch: Ii = V/Ri. The branch current is determined by the common parallel voltage and that resistor’s resistance.
How do you calculate total current in a parallel circuit?
Total current is the sum of all branch currents: Itotal = I1 + I2 + ... + In. It can also be calculated from the equivalent resistance using Itotal = V/Rtotal.
Does adding another resistor in parallel increase or decrease total resistance?
Adding another positive resistance branch in parallel decreases the equivalent resistance because it creates an additional path for current.
What is the equivalent resistance of two resistors in parallel?
For two resistors, Rtotal = (R1 × R2) / (R1 + R2). For example, two 100 Ω resistors in parallel have an equivalent resistance of 50 Ω.
How is power calculated for parallel resistors?
Because each branch has the same voltage, branch power can be calculated using P = V²/R or P = V × I. Total power is the sum of the power dissipated by all branches.