Series and Parallel Resistor Calculator Overview

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. It is useful 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 has more resistors than the input fields allow, calculate one group first, then use that equivalent value in the next step.

Resistors in Series

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

Series Resistor Example

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 in Parallel

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)

Parallel Resistor Example

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.

Series vs Parallel Resistors

Supported Resistance Units

How to Use the Calculator

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 obvious series groups and parallel groups first, then replace each group with its equivalent resistance. Repeat until the network is reduced to one equivalent value.

Mixed Network Example

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

Power and Tolerance Notes

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 each resistor value.

When using multiple resistors to share power, do not assume current or heat will divide equally unless the values, tolerances, mounting, and thermal environment support it. For high-power circuits, verify resistor temperature and derating from the datasheet.

Common Mistakes to Avoid

When Equivalent Resistance Is Not Enough

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 frequency, a simple DC equivalent resistance may not describe the complete circuit behavior.

FAQ

Why is parallel resistance lower than the smallest resistor?

Adding a parallel branch gives current another path. More current flows for the same voltage, so the equivalent resistance is lower.

Why is series resistance higher than each resistor?

In a series path, every resistor adds more opposition to the same current flow, so the total resistance is the sum of all values.

Can I use two resistors to make a value I do not have?

Yes. Resistors can be combined in series or parallel to approximate a needed value. Check tolerance and power rating after combining them.

Do resistors in parallel always share current equally?

Only if their resistance values are equal. Otherwise, the lower resistance branch carries more current.

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