Series & Parallel Resistor Calculator

Series or parallel: what the layout changes

A resistor opposes the flow of current. When several are combined, the circuit behaves like a single resistor called the equivalent resistance, noted R_eq. In series, the components are placed end to end: the same current flows through each of them and the oppositions add up, so R_eq = R₁ + R₂ + … + R_n, where R₁ to R_n are the values in ohms of the resistors in the layout.

In parallel, the components share the same two nodes: the voltage is identical across all of them, but the current splits between several paths. In this case it is the conductances (the 1/R values) that add up, hence 1/R_eq = 1/R₁ + 1/R₂ + … + 1/R_n. Two practical consequences worth remembering: R_eq is always smaller than the smallest of the resistors, and for n identical resistors of value R we simply get R_eq = R / n. For just two resistors, the shortcut R_eq = (R₁ × R₂) / (R₁ + R₂) avoids having to work with inverses.

Worked example: making 150 Ω and 1.55 kΩ

Suppose a red LED (≈ 2 V) powered from 5 V, at 20 mA. Ohm's law gives R = (5 − 2) / 0.02 = 150 Ω. If the drawer only contains 270 Ω and 330 Ω, put them in parallel: R_eq = (270 × 330) / (270 + 330) = 89,100 / 600 = 148.5 Ω, a 1% deviation from the target value, which is negligible compared to the tolerance of the components.

Let's check the power dissipation. The voltage across the combination is 3 V. In the 270 Ω resistor: P = U² / R = 9 / 270 ≈ 33 mW. In the 330 Ω resistor: 9 / 330 ≈ 27 mW. Two 1/4 W resistors are more than sufficient.

1. Series layout, for comparison: 220 Ω + 330 Ω + 1 kΩ = 1,550 Ω, i.e. 1.55 kΩ.
2. Under 12 V, the current is I = 12 / 1,550 ≈ 7.7 mA, the same in all three components.
3. The largest resistor heats up the most: P = R × I² = 1,000 × (0.0077)² ≈ 60 mW in the 1 kΩ resistor.

For the shopping list, a resistor assortment in E12 values covers most of these combinations, and the Ohm's law calculator lets you check current and voltage once R_eq has been found.

Common pitfalls

The first pitfall is the unit: adding 4.7 (read as kΩ) and 470 (read as Ω) without converting gives 474.7 instead of 5,170 Ω. Convert everything to ohms before calculating, or let the calculator's unit selector do the work.

The second pitfall is power. Placing two identical resistors in parallel doubles the allowable power (two 220 Ω 1/4 W resistors give 110 Ω / 0.5 W), but if the values differ, the smaller resistor takes on the larger share of the current and can burn out on its own. Beyond a few hundred milliwatts, switch to power resistors.

Finally, tolerance does not disappear: with 5% components, the combination remains, at worst, within 5% of the calculated value. There is no point aiming for three decimal places. And in a voltage divider, it is the ratio between the two branches that matters more than the absolute value, which leaves room to use standardized E12 or E24 values.