EngineeringFormulaElectrical Engineering
Series & Parallel Resistance Calculator
Calculate the equivalent resistance of resistors connected in series or in parallel.
Combining resistors in series or in parallel produces a single equivalent resistance that behaves the same way in the rest of the circuit. Series and parallel connections combine very differently - series resistance always adds up, while parallel resistance is always less than the smallest individual resistor. Select a configuration, enter at least two resistor values, and this calculator returns the equivalent resistance.
R₁ · Resistance of each resistor being combined - enter at least two; R3 and R4 are optional.
R₂ · Resistance of each resistor being combined - enter at least two; R3 and R4 are optional.
R₃ · Resistance of each resistor being combined - enter at least two; R3 and R4 are optional.
R₄ · Resistance of each resistor being combined - enter at least two; R3 and R4 are optional.
Solution
Enter at least two resistor values to calculate the equivalent resistance.
Rtotal = R1 + R2 + R3 + ...
Formula Sheet
- RtotalEquivalent Resistance
- R₁, R₂, R₃, R₄Individual Resistor
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| Rtotal | Equivalent Resistance | The single resistance that behaves the same way as the whole combination. | Ω, kΩ |
| R₁, R₂, R₃, R₄ | Individual Resistor | Resistance of each resistor being combined - enter at least two; R3 and R4 are optional. | Ω, kΩ, MΩ |
How to Use This Calculator
- 01Select whether the resistors are wired in Series or Parallel.
- 02Enter at least two resistor values in R1 and R2.
- 03Add up to two more resistors in R3 and R4 if you have them - leave them blank if you only have two.
- 04Select Calculate to see the equivalent (total) resistance. If you also know the supply voltage, use the result with Ohm's Law or Electrical Power to check total current and resistor wattage.
How the Formula Works
In a series circuit, current has only one path, so the same current flows through every resistor in turn - the total resistance is simply the sum of the individual resistances: Rtotal = R1 + R2 + R3 + ... Adding another resistor in series always increases the total resistance.
In a parallel circuit, resistors instead share the same two nodes, giving current multiple paths to flow through. Each additional path makes it easier for current to flow overall, so the equivalent resistance is always less than the smallest individual resistor - the reciprocal of the total resistance equals the sum of the reciprocals of each resistor: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ...
Worked Example 01
Three resistors in series
Known
- R1: 100 Ω
- R2: 220 Ω
- R3: 330 Ω
Formula
Rtotal = R1 + R2 + R3 + ...
Substitution
Rtotal = 100 + 220 + 330
Result
Rtotal = 650 Ω
In series, the resistances simply add - three resistors totaling 650 Ω pass the same current in a single loop.
Worked Example 02
Three resistors in parallel
Known
- R1: 100 Ω
- R2: 200 Ω
- R3: 300 Ω
Formula
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ...
Substitution
1/Rtotal = 1/100 + 1/200 + 1/300
Result
Rtotal ≈ 54.55 Ω
In parallel, the equivalent resistance (≈54.55 Ω) is less than even the smallest individual resistor (100 Ω) - every added path makes it easier for current to flow overall.
Applications
- 01Finding the equivalent resistance of a resistor network for circuit analysis
- 02Combining standard resistor values to approximate a non-standard target resistance
- 03Checking total load resistance for a bank of parallel or series-connected components
- 04Reducing a pure resistor group before using Ohm's Law, a voltage divider, or an electrical power calculation
Assumptions
- 01All resistors are ideal (purely resistive, no reactance).
- 02For the series case, the resistors form a single loop with no other branches.
- 03For the parallel case, all resistors share the same two nodes.
Where This Model Stops
- 01Does not support R = 0 (a short circuit) - a zero-resistance branch would force the entire parallel result to zero regardless of the other resistors, which this calculator doesn't model as a distinct case.
- 02Only handles a pure series group or a pure parallel group - mixed series-parallel networks (where some resistors are in series and others in parallel within the same circuit) need to be broken into sub-groups and combined in stages.
- 03Does not model temperature-dependent resistance changes.
- 04Does not calculate tolerance stack-up, nearest E-series resistor values, branch current, or power dissipation automatically.
References
- [1]
Resistors in series and parallel
Standard electrical engineering and physics fundamentals
Series: Rtotal = ΣR. Parallel: 1/Rtotal = Σ(1/R), which reduces to R1R2/(R1+R2) for exactly two resistors.
Frequently Asked Questions
Why is parallel resistance always less than the smallest resistor?
Each parallel branch gives current an additional path, so adding more resistors in parallel can only make it easier for current to flow overall - the combined resistance can never exceed the resistance of the easiest (smallest) individual path.
What if I only have two resistors?
Leave R3 and R4 blank - the calculator works with as few as two resistor values. For exactly two resistors in parallel, this general formula gives the same result as the common "product over sum" shortcut, R1×R2/(R1+R2).
How do I handle a network with both series and parallel connections?
Break the network into groups that are purely series or purely parallel, calculate each group's equivalent resistance separately, then combine those equivalent values in a further step. This calculator handles one pure group at a time.
Does this tell me the current or resistor wattage?
No. It gives equivalent resistance only. Once you have Rtotal, combine it with the supply voltage in Ohm's Law to find current, then use P = I²R or P = V²/R to check resistor power ratings.