Series and Parallel Resistor Calculator
Combine resistors in series, in parallel, or in a nested network you type as a formula such as 100 + (220 | 330). You get the equivalent resistance, a schematic, every step of the working and — if you add a supply voltage — the voltage, current and power in each resistor. Two more modes solve voltage and current dividers. Free, no sign-up.
Use + for series and | for parallel; | binds tighter than +, and brackets group. Values take k, M, m or the RKM code: 4.7k, 2k2, 4R7.
Add a voltage to see the current, voltage and power in each resistor.
Results
232 Ω
Equivalent resistance
3
Resistors
4.31 mS
Total conductance
51.72 mA
Total current
620.7 mW
Total power
The working
- Parallel: 1 ÷ (1/220 Ω + 1/330 Ω) = 132 Ω
- Series: 100 Ω + 132 Ω = 232 Ω
Each resistor with this supply
| Resistor | Resistance | Voltage across | Current through | Power |
|---|---|---|---|---|
| R1 | 100 Ω | 5.172 V | 51.72 mA | 267.5 mW |
| R2 | 220 Ω | 6.828 V | 31.03 mA | 211.9 mW |
| R3 | 330 Ω | 6.828 V | 20.69 mA | 141.3 mW |
How to Use the Series and Parallel Resistor Calculator
- 1. Pick how the resistors are joined. Series and Parallel take a list of values. Nested takes a formula for networks that mix both. The two divider modes handle the common two-resistor cases.
- 2. Enter the resistances. Each has its own unit menu from mΩ to GΩ. In a formula, write values as 470, 4.7k or 2M2; the letter can stand in for the decimal point, as on component markings.
- 3. Optionally add a supply voltage. With 12 V across the network, the table lists the voltage across, the current through and the power in every resistor.
- 4. Read the equivalent resistance and the working. The schematic redraws as you type, and the steps work from the innermost group outwards.
The Rules
| Connection | Equivalent resistance | What is shared |
|---|---|---|
| Series | R = R₁ + R₂ + R₃ + … | The same current flows through each resistor |
| Parallel | 1/R = 1/R₁ + 1/R₂ + 1/R₃ + … | The same voltage is across each resistor |
| Two in parallel | R = R₁R₂ ÷ (R₁ + R₂) | The product-over-sum shortcut |
| n equal in parallel | R = R₁ ÷ n | Each carries 1/n of the current |
Resistances add in series because the current has to pass through every one of them, so the total opposition is the sum. In parallel, each resistor gives the current another path, and it is the conductances (1/R, in siemens) that add — which is why the combined resistance is always smaller than the smallest resistor in the group.
Worked Example: A Nested Network on 12 V
The starting formula is 100 + (220 | 330): a 100 Ω resistor in series with a 220 Ω and a 330 Ω resistor in parallel, connected across 12 V.
- Parallel part: 1 ÷ (1/220 + 1/330) = 1 ÷ (0.004545 + 0.003030) = 132 Ω.
- Whole network: 100 Ω + 132 Ω = 232 Ω.
- Total current: 12 V ÷ 232 Ω = 51.72 mA, and total power 12 V × 51.72 mA = 620.7 mW.
- The 100 Ω resistor carries all 51.72 mA and drops 5.172 V (267.5 mW). The remaining 6.828 V is across both parallel resistors: 220 Ω takes 31.03 mA (211.9 mW) and 330 Ω takes 20.69 mA (141.3 mW).
The two parallel currents add back to 51.72 mA, and the four powers add to the 620.7 mW the supply delivers: a quick check that nothing was dropped.
Voltage and Current Dividers
A voltage divider is two resistors in series across a supply, with the output taken across the lower one: Vout = Vin × R₂ ÷ (R₁ + R₂). With 12 V across 10 kΩ and 5 kΩ, the output is 12 × 5 ÷ 15 = 4 V. The calculator also runs it backwards: for a 5 V supply, a 3.3 V output and R₁ = 1 kΩ, R₂ = 1.941 kΩ, and a 1.96 kΩ part from the E96 series gives 3.31 V. A divider's output is only that value if the load draws far less current than the divider itself; a load in parallel with R₂ pulls the output down.
A current divider is two resistors in parallel sharing a total current. Each branch gets the other resistor's share: I₁ = I × R₂ ÷ (R₁ + R₂). Splitting 100 mA over 100 Ω and 300 Ω sends 75 mA through the smaller resistor and 25 mA through the larger, with 7.5 V across both.
Check the answer's size
A parallel result must be smaller than the smallest resistor, and a series result must be larger than the largest. If yours is not, the formula was entered the wrong way round. Real resistors also have a tolerance (often ±5% or ±1%), so a calculated 132 Ω is an expected value, not a guaranteed one.
Frequently Asked Questions
- How do you calculate resistors in parallel?
- Add the reciprocals and invert the result: 1/R = 1/R₁ + 1/R₂ + …. For two resistors, R = R₁R₂ ÷ (R₁ + R₂); for 220 Ω and 330 Ω that is 72,600 ÷ 550 = 132 Ω. For n identical resistors, divide one value by n.
- Why is the parallel resistance less than the smallest resistor?
- Each extra resistor in parallel gives the current another path, so the total conductance increases and the resistance falls. Even a 1 MΩ resistor in parallel with a 100 Ω one reduces the total slightly below 100 Ω.
- How do I calculate a mixed series-parallel circuit?
- Reduce it from the inside out. Replace each parallel group with its equivalent, then add the series elements, repeating until one value is left. The nested mode does exactly this and shows each step; in the formula, + means series, | means parallel, and brackets group.
- What is a voltage divider used for?
- To get a lower voltage from a higher one — for example to scale a 12 V signal down to what a 3.3 V microcontroller input can read, or to bias a transistor. It is not suitable for powering a load that draws much current, because the output sags as the load grows.
- Do resistors in series share the same current?
- Yes. There is only one path, so the same current flows through every resistor in series, and the supply voltage divides between them in proportion to their resistances. In parallel it is the voltage that is shared and the current that divides.
- How do I make a value that I do not have?
- Combine standard values. Two equal resistors in parallel give half the value, and two in series give double; a series pair with a small trimming resistor can land closer to a target. Check the combination with this calculator and the nearest-value mode of the resistor colour code calculator.