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The Series and Parallel Resistor Calculator calculates the total resistance of up to 10 resistors connected in series or parallel. Enter each resistance value in ohms (Ω), kilohms (kΩ), or megohms (MΩ) to display the total resistance immediately.
Enter your parameters below to calculate results.
The Series and Parallel Resistor Calculator calculates the equivalent resistance of resistors connected in series, in parallel, or as part of a simple mixed network. Use it when combining available resistor values, checking circuit current, designing voltage dividers, choosing LED current-limiting resistors, and simplifying resistor networks.
Enter the resistor values and select the connection type. The calculator returns the total equivalent resistance in the selected unit, such as ohms, kilohms, or megohms. If a network contains more resistors than the available input fields, calculate one group first, then use that equivalent value in the next step.
Resistors are in series when they are connected end to end in a single current path. The same current flows through every resistor in the chain, and the total voltage is divided among the resistors.
The equivalent resistance of series resistors is the sum of all resistor values:
Rtotal = R1 + R2 + R3 + ... + Rn
Suppose three resistors are connected in series:
R1 = 3 Ω, R2 = 6 Ω, R3 = 8 Ω
Rtotal = 3 + 6 + 8 = 17 Ω
The equivalent resistance is higher than any individual resistor because every resistor adds opposition to the same current path.
Resistors are in parallel when they share the same two electrical nodes. Each resistor has the same voltage across it, while the current divides among the available branches.
The general formula for parallel resistance is:
1 / Rtotal = 1 / R1 + 1 / R2 + 1 / R3 + ... + 1 / Rn
For two resistors in parallel, the formula can be simplified to:
Rtotal = (R1 × R2) / (R1 + R2)
Suppose two resistors are connected in parallel:
R1 = 3 Ω, R2 = 6 Ω
1 / Rtotal = 1 / 3 + 1 / 6 = 1 / 2
Rtotal = 2 Ω
The equivalent resistance is lower than either individual resistor because adding a parallel branch gives current another path.
| Connection | Current | Voltage | Total Resistance |
|---|---|---|---|
| Series | Same through every resistor. | Divides across the resistors. | Greater than any individual resistor. |
| Parallel | Divides among branches. | Same across every branch. | Lower than the smallest branch resistance. |
| Unit | Name | Value in Ohms |
|---|---|---|
| Ω | ohm | 1 Ω |
| kΩ | kilohm | 1000 Ω |
| MΩ | megohm | 1000000 Ω |
Choose whether the resistors are connected in series or parallel. Enter each resistor value and select the correct unit. Leave unused fields blank. The calculator converts all entered values to a common unit, applies the selected formula, and returns the equivalent resistance.
For a mixed resistor network, simplify the circuit in stages. Calculate clearly identifiable series and parallel groups first, then replace each group with its equivalent resistance. Repeat until the network is reduced to one equivalent value.
Suppose R1 = 100 Ω is in series with a parallel group of R2 = 200 Ω and R3 = 300 Ω.
First calculate the parallel group:
Rparallel = (200 × 300) / (200 + 300) = 120 Ω
Then add the series resistor:
Rtotal = 100 + 120 = 220 Ω
Equivalent resistance is not the only design requirement. Each resistor must also have a suitable power rating, voltage rating, tolerance, temperature coefficient, and package size. In series circuits, the same current flows through each resistor, but the voltage and power can be different. In parallel circuits, the same voltage appears across each branch, but branch current and power depend on the resistance of each resistor.
When using multiple resistors to share power, do not assume that current or heat will be distributed equally unless the values, tolerances, mounting, and thermal environment support it. For high-power circuits, verify resistor temperature and derating from the datasheet.
| Mistake | Correct Approach |
|---|---|
| Adding parallel resistor values directly. | Use the reciprocal formula for parallel resistors. |
| Using the reciprocal formula for series resistors. | Series resistors add directly. |
| Mixing Ω, kΩ, and MΩ without conversion. | Convert units before calculating or use calculator unit selectors carefully. |
| Assuming equal power sharing in parallel. | Calculate branch current and power for each resistor. |
| Ignoring resistor tolerance. | Use tolerance analysis when exact resistance matters. |
For precision analog circuits, high-voltage dividers, current-sense networks, power resistors, and safety-related circuits, check more than the nominal equivalent resistance. Consider resistor tolerance, temperature drift, voltage coefficient, noise, parasitic inductance, power derating, creepage, clearance, and PCB layout.
In AC and RF circuits, resistor networks may also be affected by capacitance and inductance. At high frequencies, a simple DC equivalent resistance may not describe the complete circuit behavior.
Adding a parallel branch gives current another path. More current flows for the same voltage, so the equivalent resistance is lower.
In a series path, every resistor adds more opposition to the same current flow, so the total resistance is the sum of all values.
Yes. Resistors can be combined in series or parallel to approximate the required value. Check tolerance and power rating after combining them.
Only if their resistance values are equal. Otherwise, the branch with lower resistance carries more current.
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