The formula this page uses
Series: R = R₁ + R₂ + … Parallel: 1/R = 1/R₁ + 1/R₂ + … Two in parallel: R = R₁R₂/(R₁ + R₂)
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Total Resistance Calculator
Solve total resistance problems with clear steps, notation, and a final check.
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Calculate without using AI.
Evaluate the governing formula locally in your browser. Define each known quantity once, then change values to test another case instantly.
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Total Resistance Calculator explained
The short version
- Series resistances add; parallel resistances add as reciprocals. Every network is built from those two rules.
- Work from the innermost group outward, replacing each group with one equivalent resistor as you go.
- A series total is bigger than its biggest part; a parallel total is smaller than its smallest part.
What each part means
SymbolWhat it means
R₁, R₂, R₃ — Individual resistancesIn ohms. Convert every value to the same unit before combining.
R_eq — Equivalent resistanceThe single resistor that would behave identically at the terminals.
arrangement — Series or parallelSeries means one path through both; parallel means the two ends are joined to the same pair of nodes.
I, V — Current and voltageOnce R_eq is known, Ohm's law gives whichever of these you need.
Show your work: a full example
- The networka 6 Ω resistor in series with a 12 Ω and a 4 Ω that are in parallel, on 18 V
- Do the innermost group first1/12 + 1/4 = 1/12 + 3/12 = 4/12
- Flip itthe parallel pair is equivalent to 3 Ω
- Now the outer group is a simple series pair6 + 3 = 9 Ω total
- Total current18 ÷ 9 = 2 A
- Voltage splitthe 6 Ω drops 2 × 6 = 12 V, leaving 6 V across the parallel pair
- Split that 6 V between the branches6/12 = 0.5 A and 6/4 = 1.5 A, and 0.5 + 1.5 = 2 A ✓
A second, different case
- A different case: two parallel pairs in series(10 Ω ∥ 10 Ω) in series with (30 Ω ∥ 60 Ω), on 25 V
- First pair, equal resistors halve10 ÷ 2 = 5 Ω
- Second pair, using product over sum30 × 60 ÷ 90 = 1800 ÷ 90 = 20 Ω
- Add the two blocks in series5 + 20 = 25 Ω
- Current25 ÷ 25 = 1 A
- Voltage across each block1 × 5 = 5 V and 1 × 20 = 20 V, adding back to 25 V
- Read itthe 20 Ω block takes four times the voltage of the 5 Ω block, even though every resistor inside it is larger than 10 Ω
Copy-ready example
a 6 Ω resistor in series with a 12 Ω and a 4 Ω that are in parallel, on 18 V
The network
Questions about the Total Resistance Calculator
How do I tell whether two resistors are in series or parallel?
Follow the wire. If current has to pass through the first to reach the second with no junction between them, they are in series. If both ends of one connect to both ends of the other, they are in parallel and share the same voltage.
What is a fast sanity check on a mixed network?
Compare the answer with the largest and smallest resistors present. The total of the worked example is 9 Ω, which sits below the 12 Ω branch because part of the network is parallel, and above the 4 Ω branch because part of it is series.
Do I need to convert kΩ and MΩ first?
Yes, or mix consistently. 4.7 kΩ + 10 kΩ = 14.7 kΩ is fine, but the moment you divide a voltage by it you must be clear that the current comes out in milliamps rather than amps.
Does a wire's own resistance matter?
Usually not against hundreds of ohms, but it does against very low values. A 0.1 Ω lead in series with a 2 Ω parallel block shifts the total by 5%, which is why precision measurements use four-wire connections.