🔌 Parallel Resistance Calculator

When resistors are connected in parallel, both ends of each resistor join the same two nodes, so every resistor sees the full supply voltage. The current splits between the branches, and the total (equivalent) resistance is always lower than the smallest individual resistor. That is the opposite of a series connection, where resistances simply add up.

Picture conductance as the number of open lanes on a road: more lanes in parallel let traffic flow more easily, so the effective resistance drops. That picture is why parallel wiring is the standard for redundancy. In a house, one blown bulb does not darken the rest, because every fixture is its own lane back to the panel; in electronics the same idea lets a device keep running if one of several parallel cooling fans or LEDs fails.

Parallel wiring is everywhere in real electronics: it is how the lamps in a holiday string, the outlets on a power strip, and the cells in many battery packs are arranged so that each part keeps working if another is removed. Our voltage divider calculator and LED resistor calculator cover the other two classic building blocks.

The table shows a few combinations you will meet constantly, so you can sanity-check the calculator:

If the resistors are all the same value, the pattern is even simpler — just divide one resistor by the number of branches:

The rule for parallel resistors comes from conductance (the inverse of resistance). The total conductance is the sum of the branch conductances:

1 / R_total = 1 / R₁ + 1 / R₂ + … + 1 / R_n

Flip that sum back over and you have the equivalent resistance. Because you are adding positive reciprocals, the result is always smaller than the smallest resistor in the group — adding more parallel paths only makes it easier for current to flow.

For exactly two resistors there is a handy product-over-sum shortcut that avoids the reciprocals entirely: R_total = (R₁ × R₂) / (R₁ + R₂). Try 100 Ω and 200 Ω and you get 20,000 / 300 ≈ 66.7 Ω, matching the table. The calculator uses the general reciprocal sum underneath, which is the same idea extended to any number of branches.

If you also enter a supply voltage, the calculator works out the total current from Ohm's law (I_total = V / R_total) and then the current in each branch (I_n = V / R_n). The branch currents always add back up to the total — a useful check that your wiring is behaving.

A worked example with three unequal resistors makes the pattern concrete: 100 Ω ∥ 200 Ω ∥ 300 Ω gives 1/R = 0.010 + 0.005 + 0.00333 = 0.01833, so R ≈ 54.5 Ω. Notice it lands close to, but a little below, the smallest resistor (100 Ω) — exactly what the conductance rule promises, and a good sanity check when you are hand-verifying the tool.

As a derived metric, the calculator reports every branch current, which tells you whether any single resistor is carrying more than its rated power. For high-precision work, remember that real resistors have a tolerance (typically ±1% to ±5%), so the true equivalent value sits in a small band around the number shown.

A common trap in power electronics is assuming that parallel resistors share current equally. They only do so when their values are identical. With unequal resistors, the smallest-value branch hogs most of the current and dissipates the most heat. Always verify the wattage of the lowest-ohm resistor first: if that branch burns up, the remaining branches suddenly see more current and a cascade failure can follow. In production designs, derating each parallel resistor to at least 50 % of its stated power rating gives enough headroom for temperature rise and long-term reliability.

1. Enter at least two resistor values in ohms (R1 and R2 are required; R3 and R4 are optional).
2. Optionally enter the supply voltage if you also want currents.
3. Press Calculate to get the equivalent parallel resistance.
4. If you added a voltage, read the total current and the current through each branch.
5. Compare the result against the quick-reference table above to confirm it looks reasonable.

Why is the total resistance lower than the smallest resistor?

Each new parallel branch gives current an extra path, so the overall opposition to current drops. The equivalent resistance can never exceed the smallest single resistor, and it approaches zero if a branch is a dead short.

What happens if one branch is a short circuit (0 Ω)?

A zero-ohm branch makes the total resistance zero, so all the current rushes through it and none through the others. That is why a solder bridge or a blown component across a parallel net can overheat and damage the supply.

Can I mix different resistor values?

Yes. The reciprocal formula handles any positive values, whether they are equal or wildly different. Very unequal branches simply carry very unequal currents.

How is this different from series resistance?

In series, resistances add (R_total = R₁ + R₂ + …) and the current is the same everywhere. In parallel, conductances add and the voltage is the same everywhere but the current splits.

Does the calculator account for resistor tolerance?

No. It uses the exact values you type. Real parts vary by their tolerance band, so treat the result as the nominal value and allow a small margin in critical designs.

Parallel resistors are a neat way to hit a value you do not have in your kit: two 100 Ω resistors in parallel give 50 Ω, and a 100 Ω next to a 220 Ω gives about 69 Ω. It also lets you share power — two ¼ W resistors in parallel behave like a ½ W part.

If you are building an LED array, wire the LEDs in parallel each with its own current-limiting resistor (see our LED resistor calculator); do not share one resistor across parallel LEDs or they will not share current evenly.

For very large numbers of identical resistors, just divide one resistor''s value by the count — ten 1 kΩ resistors in parallel are a clean 100 Ω.

When a branch current matters for safety, size each resistor for at least twice the power it will actually dissipate, exactly as you would for a single LED resistor.

One field caveat worth knowing: if you measure a resistor in circuit with a multimeter, any parallel paths already on the board pull the reading below the resistor''s marked value. A 100 Ω part that reads 54 Ω on the bench is usually fine — it is just sharing the measurement with a neighbouring branch, not faulty.