Quick answer
For parallel resistors, 1/R = Σ 1/Rᵢ; for series, R = Σ Rᵢ. Two 100 Ω resistors in parallel give 50 Ω, and in series 200 Ω.
Enter at least two resistor values separated by commas. The calculator returns the parallel and series totals.
Related tools: Ohm's Law Calculator: Solve voltage, current or resistance. Watt-Hours Calculator: Energy in watt-hours from power and time, or from amp-hours and voltage. LC Resonant Frequency Calculator: Resonant frequency of an LC circuit.
How to use the Parallel Resistor Calculator
- Type resistances (Ω), for example 100, 220, 470.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Resistances (Ω) | Text, such as 100, 220, 470 | — |
Formula and method
Formula
1/R_parallel = Σ 1/Rᵢ; R_series = Σ Rᵢ
IEEE-754 double precision; shown to at most 6 decimal places.
Resistances must be greater than 0.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Resistances (Ω) = 100, 100.
| Result | Value |
|---|---|
| Parallel resistance | 50 Ω |
| Series equivalent | 200 |
Example 2
Inputs: Resistances (Ω) = 100 220 470.
| Result | Value |
|---|---|
| Parallel resistance | 59.9768 Ω |
| Series equivalent | 790 |
Example 3
Inputs: Resistances (Ω) = 10, 10, 10.
| Result | Value |
|---|---|
| Parallel resistance | 3.3333 Ω |
| Series equivalent | 30 |
The first line is the headline result (parallel resistance). Below it the parallel Resistor Calculator lists series equivalent, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Shortcuts
For two resistors, R = R₁R₂ ÷ (R₁ + R₂). Equal resistors divide by their number: three 300 Ω resistors in parallel give 100 Ω. The parallel total is always smaller than the smallest resistor.
Where this estimate stops applying
At least two values are needed and zero resistance is rejected because it would short the circuit. Tolerances of real resistors shift the result by their percentage.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Resistances (Ω): entering "100" shows "Enter at least 2 numbers." beside that field and no result.
Choosing between the Parallel Resistor Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Ohm's Law Calculator](/engineering/ohm-s-law-calculator/) | Current | |
| [Watt-Hours Calculator](/engineering/watt-hours/) | use | Energy |
| [LC Resonant Frequency Calculator](/engineering/resonant-frequency-lc/) | inductance and capacitance | Resonant frequency |
| [Wattage Calculator](/engineering/wattage/) | Power | |
| [Battery Runtime Calculator](/engineering/battery-runtime-calculator/) | battery capacity, battery voltage and load | Runtime |
Background: electrical circuits
Ohm's law links voltage, current and resistance: V = I × R, so I = V ÷ R and R = V ÷ I. Power is P = V × I, which also equals I² × R and V² ÷ R.
These relations hold for ohmic components, where resistance is constant. Diodes and transistors are non-linear, and in AC circuits with reactive parts impedance (Z) takes the place of resistance. Check component ratings and local electrical code before relying on any calculation.
Assumptions and limitations
- At least two resistors
- Zero resistance rejected
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for resistances (Ω) to confirm this.
Frequently asked questions
Why is parallel resistance lower?
More paths for current.
What about 10 Ω and 1,000 Ω in parallel?
About 9.9 Ω, near the smaller value.
Can I mix both?
Combine series and parallel groups in stages.
What does the Parallel Resistor Calculator calculate?
Equivalent resistance of resistors in parallel and in series. It returns Parallel resistance and Series equivalent.
What formula does the Parallel Resistor Calculator use?
1/R_parallel = Σ 1/Rᵢ; R_series = Σ Rᵢ. Resistances must be greater than 0.
What do I need to enter in the parallel Resistor Calculator?
You enter Resistances (Ω).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. At least two resistors.
What are the limits of this calculator?
At least two resistors. Zero resistance rejected.
What is an example of a parallel Resistor result?
With resistances (Ω) 100, 100, the parallel resistance is 50 Ω.
Can I rely on this calculator for a decision?
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them. For this calculator in particular: At least two resistors.
Related calculators
- Ohm's Law Calculator — Solve voltage, current or resistance.
- Watt-Hours Calculator — Energy in watt-hours from power and time, or from amp-hours and voltage.
- LC Resonant Frequency Calculator — Resonant frequency of an LC circuit.
- Wattage Calculator — Solve power, voltage or current for a DC or resistive load.
- Battery Runtime Calculator — Runtime of a battery under a constant load.
- Parallel Plate Capacitor Calculator — Capacitance of two parallel plates.
- Resistor Color Code Calculator — Resistance value and tolerance from color bands.
- kW to VA Converter — Apparent power in VA from real power and power factor.
- Ah ⇄ Wh Converter — Convert between amp-hours, milliamp-hours and watt-hours.
Sources
- OpenStax, University Physics Volume 2 (Rice University): electricity, circuits and thermodynamics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.