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
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.
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.
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, so 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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