Parallel & Series Resistor Calculator
Combine up to 8 resistors in parallel or series. See the equivalent resistance and the nearest E24 / E96 standard value.
Resistors
Equivalent resistance
3.2 kΩ
R1 + R2
Nearest standard
Practical Examples
- Three equal in parallel — Three 1 kΩ in parallel → 333 Ω. The shortcut for N equal resistors in parallel is R/N. Useful when you need to spread current or dissipation across cheap parts.
- Voltage rating in series — Two 1 MΩ in series for a 1 kV probe → 2 MΩ total, and the voltage drop is shared. Each resistor only sees half the rail, so standard 500 V parts survive a kilovolt rail.
- Hit a non-standard target — Need 3.2 kΩ but no E24 stock? 2.2 kΩ + 1 kΩ in series gives exactly 3.2 kΩ. Or 4.7 kΩ ∥ 10 kΩ gives 3.20 kΩ — close enough for almost any analog use.
How series & parallel work
In series, the same current flows through every resistor — so the total resistance is just the sum: Rtotal = R1 + R2 + … Each resistor drops a share of the input voltage proportional to its value.
In parallel, the same voltage sits across every resistor — so currents add, and the total resistance is the reciprocal of the summed reciprocals: 1 / Rtotal = 1 / R1 + 1 / R2 + … The result is always smaller than the smallest resistor in the network.
The two patterns are complementary tools. Series adds — useful for stepping up resistance, dividing voltage, and sharing voltage stress. Parallel divides — useful for stepping down resistance, sharing current, and spreading power dissipation across multiple parts.
Design rules of thumb
- Prefer a single resistor when an E-series value fits — One part is cheaper, smaller on the board, and avoids stacking tolerances. Only combine when no standard value gets you close enough.
- Identify the worst-case dissipator and rate it 2× — Series: the largest resistor dissipates the most. Parallel: the smallest does. Find it, calculate P, and pick a part rated for at least 2× that.
- Avoid wide-ratio pairs in parallel — A 100 Ω in parallel with 100 kΩ ≈ 99.9 Ω — the big resistor barely contributes. If one resistor dominates, drop the other entirely.
- Use 1% (E96) parts when stacking — Tolerance errors don't fully cancel in real circuits. ±1% metal-film is the default for any combination feeding an ADC, op-amp, or voltage reference.
- Mind thermal coupling in precision dividers — Two resistors in physical contact (same package, adjacent on PCB) track temperature together — ratio stays stable. Resistors at different temperatures will drift apart.
- Series for high voltage, parallel for high current — Series splits voltage stress across multiple parts; parallel splits current and heat. Match the topology to which limit you're worried about.
FAQ
When would I parallel resistors instead of just picking one?
Three reasons. First, to hit a non-standard target (two 10 kΩ in parallel give exactly 5 kΩ — no E-series part needed). Second, to share power across multiple components — two ¼ W resistors in parallel can dissipate ½ W combined. Third, when the value you need isn't stocked: any uncommon resistance can be approximated with a parallel combination of standard E-series parts.
How does tolerance combine across series and parallel?
For uncorrelated tolerances (typical for resistors from a reel), the combined tolerance is the root-sum-square (RSS) of individual tolerances weighted by their share of the total. In practice, two ±1% resistors in series give roughly ±1% on the sum, not ±2%, because errors partially cancel. For worst-case design (a single bad batch), assume tolerances add linearly.
Do I need matched power ratings?
In series, the same current flows through every resistor — so the largest resistor dissipates the most power. In parallel, the smallest resistor dissipates the most. Always identify the worst-case resistor and rate it for at least 2× the calculated power (standard derating). Other resistors in the network can be lower-rated.
What does E24 vs E96 mean?
E-series are the standard preferred values manufacturers produce. E24 has 24 values per decade and is the default for ±5% carbon-film resistors. E96 has 96 values per decade and is used for ±1% metal-film resistors. If your target falls between two E24 values, an E96 part is likely available within a fraction of a percent.
Can I mix carbon film and metal film resistors in a combination?
Electrically yes — the formulas don't care. But the combined network inherits the worst characteristics: the higher temperature coefficient, the higher noise, and the looser tolerance. For precision circuits (references, dividers feeding ADCs), match resistor types and tolerances throughout.
How precise can I get by combining standard values?
Very. With two E96 resistors in series or parallel you can typically hit any target within 0.1%. With three, within 0.01%. The limiting factor is component tolerance, not the math — two ±1% resistors won't give a ±0.01% result regardless of how perfectly the nominal values land.
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