Parallel Resistor Calculator
Resistors wired in parallel share the same voltage but split the current, so the combined resistance is always smaller than the smallest branch. Enter your resistor values as a comma-separated list, pick a unit, and optionally add a supply voltage to also see total current and power. A reverse-solve mode finds the extra resistor needed to hit a target total.
Formula
Worked example
For 100 Ω, 220 Ω and 330 Ω: 1/R = 1/100 + 1/220 + 1/330 = 0.01 + 0.004545 + 0.003030 = 0.017576 S. Inverting gives R = 1 / 0.017576 ≈ 56.897 Ω, smaller than the 100 Ω branch. Across 12 V that combination draws I = 12 / 56.897 ≈ 0.2109 A and dissipates P = 12² / 56.897 ≈ 2.531 W.
How parallel resistance works
When resistors are connected in parallel they all bridge the same two nodes, so each one sees the identical voltage across it. Because every resistor offers an additional path for current, the total current leaving the source is the sum of the branch currents, and the circuit behaves as a single resistor whose conductance equals the sum of the individual conductances. Conductance is the reciprocal of resistance, which is why the formula adds 1/R₁ + 1/R₂ + … rather than the resistances themselves. Inverting that sum returns the equivalent resistance. A useful sanity check is that the total is always smaller than the smallest resistor in the group, since adding any extra path can only make it easier for current to flow.
Common cases and shortcuts
Two special cases come up constantly in electronics. For exactly two resistors, the formula simplifies to the product-over-sum rule R = (R₁ × R₂) / (R₁ + R₂), which is quick to do by hand. For n identical resistors each of value R, the total collapses to R / n, three 300 Ω resistors in parallel give exactly 100 Ω. Engineers use parallel combinations to reach a resistance value that is not available as a standard part, to share power dissipation across several components, or to lower the output impedance of a stage. Tolerance matters too: combining real resistors averages out some random variation, so a bank of parallel resistors can be more precise than any single one. Use the unit selector to enter kilohm or megohm values directly without converting by hand.
Reverse solving and adding current and power
Switch to reverse mode when you know the total resistance you want and the resistors you already have wired in parallel, and you need the one more resistor to add. The calculator subtracts the conductance you already have from the conductance the target requires, then inverts the difference to give the missing resistor. Because a parallel path can only lower resistance, the target must be smaller than what you already have, otherwise no positive resistor can reach it. Add an optional supply voltage in either mode and the calculator applies Ohm's law to report the total current the combination draws, I = V / R, and the total power it dissipates, P = V² / R. That is handy for checking that your resistors are rated for the heat, since power is shared across the bank in inverse proportion to each resistance.
Parallel resistance examples
| Resistors (Ω) | Total resistance (Ω) |
|---|---|
| 100, 100 | 50 |
| 100, 200 | 66.667 |
| 100, 220, 330 | 56.897 |
| 1000, 1000, 1000 | 333.333 |
| 470, 680 | 277.913 |
The equivalent resistance is always smaller than the smallest resistor in the group.
Frequently asked questions
Why is parallel resistance smaller than the smallest resistor?
Each resistor adds another path for current to flow between the same two points. More paths mean more total current for a given voltage, which is equivalent to a lower overall resistance. The combined value can never exceed the smallest individual branch.
What is the shortcut for two resistors in parallel?
Use the product-over-sum rule: R = (R₁ × R₂) / (R₁ + R₂). For 100 Ω and 200 Ω that is (100 × 200) / (100 + 200) = 20000 / 300 ≈ 66.67 Ω. It only works for exactly two resistors.
How do I combine many identical resistors in parallel?
Divide the resistor value by the number of resistors. Four 1000 Ω resistors in parallel give 1000 / 4 = 250 Ω. This is just the general reciprocal formula with every term equal.
How does the reverse (missing resistor) mode work?
Switch the mode to reverse, enter the total resistance you want and the resistors you already have in parallel. The calculator converts the target to a conductance, subtracts the conductance you already have, and inverts the remainder to give the resistor you still need to add. The target must be smaller than your current combination, because a parallel resistor can only lower the total.
Can this calculator give total current and power?
Yes. Enter a supply voltage and it applies Ohm's law to the equivalent resistance: total current is I = V / R and total power is P = V² / R. This is the current the source delivers and the heat dissipated across the whole parallel bank.