Parallel Resistor Calculator

How to use the Parallel Resistor Calculator

What this calculator does

This calculator reduces a set of ideal positive resistors connected in parallel to one equivalent resistance, or rearranges the same relationship to find one missing branch resistor needed to hit a chosen equivalent resistance. It models the standard steady-state resistor network relationship: every branch has the same voltage across it, and the reciprocal resistances add. It does not model resistor tolerance, temperature coefficient, wiring resistance, parasitic effects, power rating, or non-ohmic components. For the circuit rule behind the calculation, see the OpenStax treatment of resistors in series and parallel.

When to use it

Use the calculator when you are combining available resistor values to approximate a target, checking the effective load seen by a source, verifying a classroom or lab calculation, or solving backward for the additional parallel branch that would bring an existing network to a lower equivalent resistance. Because this tool works only with positive finite resistance values, it is best suited to ordinary ideal-resistor calculations rather than intentional short circuits or open-circuit limits.

How to calculate

1. The calculator opens with a ready-to-use demonstration: Resistor 1 (R1) = 100 Ω and Resistor 2 (R2) = 220 Ω. The result and a validated example workbook are available immediately.
2. Under Calculate, keep Equivalent resistance when you know the branch resistances. Replace the sample values with your own positive decimal values. Use Add resistor to extend the network to as many as ten branches.
3. Choose Missing resistor when you know the desired total. Enter Desired equivalent resistance and the known branch resistances. In this mode, up to nine known branches are accepted because the calculated missing branch is the tenth possible resistor.
4. Read the large primary result, then use Total conductance, Smallest branch, Equivalent / smallest, and the branch table to check whether the network behaves as expected.
5. Select Download Excel to export the current validated state as a real .xlsx workbook. Reset clears the demonstration and all added rows; export is then disabled until a complete valid state is entered again.

Input guide

Calculate is a required mode selector with two options. Equivalent resistance expects at least one branch value and returns the network equivalent. Missing resistor instead solves for a positive finite branch that would produce your target total. Switching modes changes the required inputs but never changes the underlying reciprocal formula.

Resistor 1 (R1) through Resistor 10 (R10) are resistance values in ohms. Enter ordinary decimal notation such as 100, 47.5, or 0.25. Values must be greater than zero and no larger than 10¹⁵ Ω. Comma decimals, thousands separators, scientific notation, typed unit symbols, negative numbers, and zero are rejected rather than silently reinterpreted. Higher branch resistance contributes less conductance; lower branch resistance contributes more and therefore pulls the equivalent resistance downward. A common mistake is to add parallel resistances directly as if they were in series.

Desired equivalent resistance appears only in Missing resistor mode. It is required there, uses the same positive-decimal ohm format, and must be lower than the equivalent resistance of the known branches. That restriction is physical: adding a positive resistor in parallel can only lower the equivalent resistance. For example, if the known branches are 100 Ω and 150 Ω, their equivalent is 60 Ω, so a 50 Ω target is feasible; a 70 Ω target is not.

Output guide

Equivalent resistance is the primary result in the standard mode and is an exact identity for the entered ideal resistor values, subject only to display rounding. It can never exceed the smallest positive branch resistance. Missing resistor value is the primary result in the inverse mode and gives the additional positive branch required to reach the target. Branches counts the active branches in the completed network, including the solved missing branch when applicable. Unit confirms that all resistance values are shown in ohms.

Total conductance is the sum of the branch conductances in siemens, where conductance is 1/R. Smallest branch is the lowest resistance in the completed network. Equivalent / smallest expresses the equivalent resistance as a percentage of that smallest branch; it is at or below 100% for a valid parallel network. In the Branch breakdown table, Branch identifies each resistor, Resistance (Ω) repeats its canonical resistance, Conductance (S) shows its reciprocal, and Conductance share reports that branch's fraction of total conductance. The shares sum to 100% apart from display rounding.

Worked example

The startup example uses 100 Ω and 220 Ω. Their conductances are 1/100 = 0.01 S and 1/220 ≈ 0.00454545 S. Adding them gives 0.01454545 S. Taking the reciprocal gives 1/0.01454545 = 68.75 Ω, which is the first-open primary result. The 100 Ω branch contributes 68.75% of the total conductance and the 220 Ω branch contributes 31.25%. The equivalent is 68.75% of the smallest branch value, so the secondary ratio is also 68.75%.

Learn more

The ohm is the SI unit of electrical resistance, with 1 Ω = 1 V/A; the NIST overview of SI electrical units provides the unit context. OpenStax also explains why parallel branches share the same potential difference while their currents divide according to resistance, which is the physical basis for the reciprocal formula used here.