Parallel Resistor Calculator

Equivalent resistance for 2–10 resistors in parallel or series

Operating Mode

Target Variable

Resistor values

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When filled, paste values override R1–Rn. Supports 4K7 shorthand.

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Quick Answer

Parallel resistors: 1/R = 1/R1 + 1/R2 + … (for two resistors use (R1×R2)/(R1+R2)). Series resistors add: R = R1 + R2 + …

Documentation

How to use this parallel resistor calculator

Leave Parallel selected (default) for resistors that share the same two nodes.
Enter R1 and R2 with Ω / kΩ / MΩ units, or add more resistors (up to 10).
Read the equivalent resistance, formula steps, and circuit diagram.
Switch to Series when resistors share one current path.
Use Missing R to solve for an unknown resistor given a target Req.
Optional: paste 1k, 2.2k, 4.7k to override the individual fields.

Last reviewed: 2026-07-21 — formulas verified against product-over-sum and reciprocal sum test cases.

Parallel resistance formula

Resistors in parallel share the same two nodes. Current splits among branches; total resistance is always less than the smallest individual value.

1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

Two resistors: product-over-sum

Rtotal = (R1 × R2) / (R1 + R2)

Example: 100 Ω ∥ 200 Ω → (100 × 200) / (100 + 200) = 66.7 Ω

Three or more resistors

Sum the reciprocals, then invert. Example: 1 kΩ ∥ 2 kΩ ∥ 4 kΩ → 1/R = 0.001 + 0.0005 + 0.00025 = 0.00175 → R ≈ 571 Ω

Equal resistors in parallel

For N identical resistors of value R: Rtotal = R / N

Two 1 kΩ → 500 Ω
Three 1 kΩ → 333 Ω
Four 1 kΩ → 250 Ω

Series mode (same tool)

Rtotal = R1 + R2 + R3 + ... + Rn

Same current through all parts; total is always greater than the largest resistor. Example: 100 + 220 + 330 = 650 Ω.

Find a missing resistor

In Missing R mode:

Parallel: 1/Req = 1/Rknown_eq + 1/Rmissing → solve for Rmissing (target must be below the known parallel equivalent).
Series: Rmissing = Req − ΣRknown (target must exceed the known sum).

Current and power in each branch

With a known voltage across a parallel network:

Branch current: I_n = V / R_n
Branch power: P_n = V² / R_n (lowest R dissipates the most power)

For branch-current problems from a known total current, use the Current Divider Calculator.

Series vs parallel (quick contrast)

	Series	Parallel
Current	Same through all	Splits by conductance
Voltage	Divides across parts	Same across all
Total R	Sum (larger)	Reciprocal sum (smaller)

For definitions, diagrams, and classroom-style examples, see Series vs Parallel Circuits. For theory of Req, see Equivalent Resistance Guide. Nested networks such as R1 + (R2 ∥ R3) belong in the Series-Parallel Circuit Solver.

Tolerance (accurate statement)

Worst-case: two 5% resistors in series or parallel can still reach ±5% at the extremes.
Statistical (RSS) averaging can reduce expected error only if errors are independent and random — do not treat “≈3.5%” as a guaranteed result.

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Design Notes

Combining resistors is an invaluable trick in professional prototyping. When you don't have the exact E96 precision value needed for an Op-Amp gain stage, you can parallel two higher-value resistors to hit the exact target. Furthermore, dropping high voltages or handling high power (e.g., snubber circuits) is often better done by stringing multiple smaller 1/4W resistors in series, which spreads the heat and significantly increases the maximum voltage rating (dielectric breakdown limits).

Common Mistakes

1
Thinking parallel resistors can increase the total resistance. Adding a resistor in parallel ALWAYS decreases the equivalent resistance.
2
Ignoring the power rating split. If 1W is flowing into two unequally sized parallel resistors, the lower resistance one takes the majority of the heat.
3
Failing to account for parasitic inductance when placing wirewound resistors in parallel for high-frequency RF dummy loads.

Engineering Handbox

1. Two-resistor shortcut: R = (R1 × R2) / (R1 + R2) 2. R = (10000 × 4700) / (10000 + 4700) 3. R = 47,000,000 / 14,700 = 3197.9 Ω

VerificationEquivalent parallel resistance ≈ 3.2 kΩ (always less than the smallest resistor).

Knowledge Base

What is a parallel resistor calculator?

A parallel resistor calculator finds the equivalent resistance when two or more resistors share the same two nodes. Enter your values (e.g., 1k, 4.7k, 10k) and get the total instantly. For two resistors use R = (R1 × R2) / (R1 + R2). The result is always less than the smallest individual resistor.

What is a series resistor calculator?

A series resistor calculator adds resistor values in a single current path: R_total = R1 + R2 + R3 + ... + Rn. Example: 100 Ω + 220 Ω + 470 Ω = 790 Ω. Series combinations are used for voltage division, current limiting, and reaching non-standard E-series values. Switch this tool to Series mode when you need that calculation.

What is the formula for parallel resistors?

The reciprocal of the total resistance equals the sum of reciprocals: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn. The result is always smaller than the smallest individual resistor. For two resistors, use the shortcut: R_total = (R1 x R2) / (R1 + R2).

What is the shortcut formula for two parallel resistors?

For exactly two resistors in parallel: R_total = (R1 x R2) / (R1 + R2). This is called the product-over-sum method. Example: 10k and 4.7k in parallel = (10000 x 4700) / (10000 + 4700) = 3197 ohms (approximately 3.2k).

How do I find a missing resistor for a target Req?

Use Missing R mode. Enter the known resistors and the target equivalent resistance. In parallel, Rmissing = 1 / (1/Req − 1/Rknown_eq). In series, Rmissing = Req − ΣRknown. The target must be reachable with a positive resistor value.

What happens when I put identical resistors in parallel?

N identical resistors of value R in parallel give R_total = R / N. Two 10k resistors in parallel = 5k. Three 10k resistors in parallel = 3.33k. This is also useful for increasing power handling across packages.

Does adding a resistor in parallel increase or decrease total resistance?

Adding a resistor in parallel ALWAYS decreases the total resistance, no matter how large the added resistor is. You are providing an additional path for current, which reduces total opposition.

How does power distribute in parallel resistors?

In a parallel circuit, voltage across all resistors is the same, but current splits inversely with resistance. Power in each resistor: P = V² / R. The LOWER value resistor dissipates MORE power. Always check that each resistor can handle its individual power share.

How do I calculate a mixed series-parallel network?

This tool solves pure parallel or pure series lists. For nested networks such as R1 + (R2 ∥ R3), use the Series-Parallel Circuit Solver, or simplify groups by hand: innermost parallel/series first, then work outward.

Does tolerance stack up in series or parallel?

Worst-case tolerance for series or parallel combinations of equal-tolerance resistors remains the same percentage as a single resistor (e.g., two 5% parts can still be ±5% at the extremes). Only if errors are independent and randomly distributed may the statistical (RSS) combined error be smaller — that is not a guaranteed 3.5% result for two 5% parts.

When should I use series resistors instead of a single higher value?

Use series resistors when: (1) You need a non-standard value not in your kit. (2) High voltage applications: each resistor only sees a fraction of the total voltage. (3) Power spreading across multiple packages. (4) PCB layout constraints favor multiple smaller parts.

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Guides & Related Tools

Current Divider

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Series vs Parallel Guide

Definitions, formulas & comparison

Equivalent Resistance Guide

How to find Req step by step

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