Series & Parallel Resistor Calculator
This resistor calculator computes the equivalent resistance for any number of resistors connected in series or parallel. For series circuits, the total equals the sum of all values (Rtotal = R1 + R2+ …). For parallel circuits, the total is found from the reciprocal formula (1/Rtotal = 1/R1 + 1/R2 + …). Enter your values below for an instant result.
Series & Parallel Resistor Calculator
Enter resistor values in ohms (Ω). Add or remove resistors to calculate the equivalent resistance for series or parallel configurations.
In a series circuit, resistors are connected end-to-end. The total resistance equals the sum of all individual resistances: Rtotal = R1 + R2+ …
Quick-add common values:
Equivalent Resistance (series)
600 Ω(600.00 Ω)
Resistor breakdown:
Frequently Asked Questions
How do I calculate resistors in series?
To calculate the total resistance of resistors in series, add all individual resistances together: R_total = R1 + R2 + R3 + … + Rn. For example, three resistors of 100 Ω, 200 Ω, and 300 Ω in series give a total of 600 Ω. The total is always larger than any single resistor in the chain because series connections increase resistance.
How do I calculate resistors in parallel?
To calculate the equivalent resistance of resistors in parallel, use the reciprocal formula: 1/R_total = 1/R1 + 1/R2 + 1/R3 + … + 1/Rn, then take the reciprocal of the result. For example, two 100 Ω resistors in parallel give 1/(1/100 + 1/100) = 1/0.02 = 50 Ω. The total resistance is always less than the smallest individual resistor in the parallel combination.
What is the two-resistor parallel shortcut formula?
For exactly two resistors in parallel, the reciprocal formula simplifies to the product-over-sum shortcut: R_total = (R1 × R2) / (R1 + R2). For example, 100 Ω and 150 Ω in parallel gives (100 × 150) / (100 + 150) = 15000 / 250 = 60 Ω. This is faster to compute by hand than the full reciprocal method and is commonly used in practical electronics work.
What is the difference between series and parallel resistors?
In a series circuit, resistors are connected end-to-end so the same current flows through all of them and the total resistance is the sum of all values. In a parallel circuit, resistors share the same two nodes, so the same voltage appears across all of them and the total resistance is lower than any individual resistor. Series circuits increase resistance and divide voltage; parallel circuits decrease resistance and divide current.
When should I use series vs. parallel resistors?
Use series resistors when you need to limit current (such as a current-limiting resistor for an LED), create a voltage divider, or achieve a resistance higher than any available standard value. Use parallel resistors when you need a resistance lower than any available value, when you want to distribute power dissipation across multiple components, or when you need more precise non-standard values by combining standard parts.
Can I mix series and parallel resistors in the same circuit?
Yes. A circuit with both series and parallel sections is called a series-parallel combination circuit. To solve it, first identify and simplify the parallel groups into single equivalent resistances, then treat those equivalents as series elements and sum them. Work from the innermost nested combination outward. This calculator handles either pure series or pure parallel; for mixed configurations, break the circuit into groups and use the calculator for each group, then combine the results.
What happens if one resistor is zero ohms (a wire) in parallel?
A zero-ohm resistance in parallel short-circuits the entire parallel combination — the total resistance becomes 0 Ω because current bypasses all other resistors through the zero-ohm path. In practice, connecting a wire across any parallel combination reduces its resistance to zero. This is why the calculator requires all parallel resistors to be greater than 0 Ω.
How do I find a non-standard resistance value using standard resistors?
To get a resistance higher than any available standard value, connect two standard resistors in series. To get a lower resistance, connect them in parallel. For example, to get approximately 750 Ω using 1 kΩ resistors: two 1 kΩ in parallel give 500 Ω, and adding a third 1 kΩ (250 Ω from two more in parallel) in series gives 750 Ω. Common E12 series values (100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820 Ω and decades thereof) cover most needs with simple combinations.
Series and Parallel Resistor Guide
Series Resistor Formula
When resistors are connected in series, the same current flows through every resistor and the total (equivalent) resistance is the simple sum of all individual resistances:
Rtotal = R1 + R2 + R3 + … + Rn
For example, connecting a 100 Ω, 200 Ω, and 300 Ω resistor in series gives a total resistance of 600 Ω. The total is always larger than any individual resistor in the chain.
Series configurations naturally increase resistance. Every resistor adds to the total, so adding even a single resistor always raises the equivalent resistance.
A zero-ohm resistor (a short circuit) is valid in series — it contributes nothing to the total. A negative resistance is not physically realizable with standard passive resistors, so the calculator rejects negative values.
Parallel Resistor Formula
When resistors are connected in parallel, all resistors share the same two nodes (same voltage across each). The total equivalent resistance is found using the reciprocal formula:
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + … + 1/Rn
The equivalent resistance of a parallel combination is always less than the smallest individual resistor. Adding more parallel paths provides more routes for current, reducing the total opposition.
For example, two 100 Ω resistors in parallel give 50 Ω — exactly half of one resistor. Three 300 Ω resistors in parallel give 100 Ω — one third of one resistor. This is a useful shortcut: n identical resistors of value R in parallel give R/n.
A zero-ohm resistor in parallel creates a short circuit (total resistance = 0 Ω). The calculator rejects zero and negative values for parallel configurations to prevent division-by-zero errors.
Two-Resistor Shortcut
For the common case of exactly two resistors in parallel, the reciprocal formula simplifies to the product-over-sum shortcut:
Rtotal = (R1 × R2) / (R1 + R2)
This is faster to compute by hand than the reciprocal formula. For instance, 100 Ω and 150 Ω in parallel:
| Product: | 100 × 150 = 15,000 |
| Sum: | 100 + 150 = 250 |
| Result: | 15,000 / 250 = 60 Ω |
For more than two resistors, apply the shortcut iteratively: combine any two resistors into their equivalent, then combine that result with the next resistor, and so on.
When to Use Each Configuration
Choosing between series and parallel depends on your circuit goals:
| Goal | Series | Parallel |
|---|---|---|
| Increase resistance | Yes — always | No — reduces it |
| Reduce resistance | No | Yes — always |
| Same current everywhere | Yes | No — current splits |
| Same voltage everywhere | No — voltage divides | Yes |
| Voltage divider | Yes | No |
| Current limiter (e.g., LED) | Yes | No |
| Load sharing / power distribution | No | Yes |
| Non-standard value from standard parts | For higher value | For lower value |
Series resistors are used to limit current (for example, a current-limiting resistor for an LED), create voltage dividers, and set bias points in amplifier circuits. Because the same current flows through every component, a failure (open circuit) in any series resistor breaks the entire path.
Parallel resistors are used when you need a lower resistance than any available standard value, or when you need to share power dissipation across multiple resistors. Because each parallel resistor is independently connected across the supply, a failure in one does not interrupt the others.
Worked Examples
Example 1: LED Current-Limiting Resistor in Series
You have a 5 V supply and want to drive a red LED (forward voltage 2.0 V, target current 20 mA). The required series resistor is:
Using two 330 Ω resistors in parallel gives 165 Ω — the closest achievable value with common 330 Ω parts. A single standard 150 Ω resistor is also readily available in the E12 series.
Example 2: Achieving a Non-Standard Value
You need exactly 750 Ω but only have 1 kΩ resistors. Connect three 1 kΩ resistors in parallel:
Two 1 kΩ in parallel = 500 Ω. One more 500 Ω (two 1 kΩ in parallel) in series = 1,000 Ω. Mix of configurations lets you build many exact values from a small set of standard parts.
Example 3: Power Distribution
A 1 kΩ resistor must dissipate 1 W across a 31.6 V source, but standard 1/4 W resistors are all you have. Place four 250 Ω resistors (two pairs of 500 Ω in parallel, then those two pairs in series) to achieve 1 kΩ total while each part only dissipates 250 mW. Alternatively, use four 1 kΩ resistors in parallel to get 250 Ω, with each sharing 250 mW — a simpler calculation.
Standard Resistor Values — E12 Series
Resistors are manufactured in standardized value series. The E12 series (12 values per decade, ~10% tolerance) is the most common in general electronics work. Multiplied by powers of 10, these 12 base values cover all decades from 1 Ω to 10 MΩ:
For example, the E12 decade starting at 100 Ω gives: 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820 Ω. The next decade begins at 1.0 kΩ with the same multipliers.
When you need a value that does not appear in the E12 series, combine two standard values in series (for a value larger than either) or in parallel (for a value smaller than either). This calculator helps you verify the result instantly.