Parallel Resistor Calculator

A parallel resistor calculator finds the single equivalent resistance that a group of resistors presents to the rest of the circuit. Parallel branches add reciprocals, so the total always falls below the smallest part: 100 Ω, 220 Ω and 330 Ω wired in parallel measure 56.897 Ω, while the same three parts wired in series measure 650 Ω.

This page covers both wiring styles because the arithmetic is the mirror image of the same idea, and because most real boards mix them. Enter up to ten values, pick parallel or series, add a supply voltage if you want the current and heat in each branch, and switch on the missing-resistor option when you know the total you want and need the one part that gets you there.

How resistors in parallel combine

When resistors sit side by side between the same two nodes, every one of them carries its own current and all of those currents come back together. More paths means less opposition, so the network conducts better than any single branch. Expressed as a formula:

Add the reciprocals, then take the reciprocal of the answer. For exactly two resistors that reduces to the familiar product-over-sum shortcut:

Series is the easy direction. Resistors in a single chain all carry the same current and their voltage drops stack, so the values simply add:

The reciprocal of a resistance is its conductance, measured in siemens. Seen that way the parallel rule stops looking strange: parallel branches add conductance the same way series resistors add resistance. That is exactly what this calculator sums internally before inverting the result.

Worked example: 100 Ω, 220 Ω and 330 Ω on a 12 V supply

Take the three resistors the calculator loads by default. First the reciprocals:

• 1 ÷ 100 = 0.0100000 S
• 1 ÷ 220 = 0.0045455 S
• 1 ÷ 330 = 0.0030303 S

Those add to 0.0175758 S, and the reciprocal of that sum is 56.897 Ω. Notice the answer sits below 100 Ω, the smallest part, exactly as the rule promises. Wired in series instead, the same three parts total 100 + 220 + 330 = 650 Ω, comfortably above the largest.

Now put 12 V across the parallel group. Each branch sees the full 12 V, so Ohm's law gives each current directly, and P = V² ÷ R gives each dissipation:

Two things stand out. The branch currents add up to the total, which is a useful check on any parallel calculation. And the 100 Ω resistor takes more than half the current and burns 1.440 W on its own, so a quarter-watt part in that position would fail within seconds. In a parallel bank, the smallest resistor is always the one to size first.

The same parts in series, for comparison

Rewire those three resistors end to end on the same 12 V supply and the picture flips. The total is 650 Ω, so the chain draws only 12 ÷ 650 = 18.462 mA, and that one current runs through all three. The voltage now splits in proportion to resistance: 1.846 V across the 100 Ω, 4.062 V across the 220 Ω and 6.092 V across the 330 Ω, adding back to 12 V. Dissipation follows P = I² × R, giving 34.083 mW, 74.982 mW and 112.473 mW for a total of just 221.538 mW. The same three components draw eleven times less power in series than in parallel, and now the largest resistor is the hot one instead of the smallest.

Two-resistor parallel combinations

Most bench work is two parts at a time, so this grid is worth keeping close. Each cell is the product-over-sum result for the row value in parallel with the column value, in ohms. Multiply every number by 1,000 to read it as kilohms.

The diagonal is the equal-pair case, always exactly half the value. Read across any row and you can see how quickly a large partner stops mattering: a 100 Ω resistor drops to 50.00 Ω next to another 100 Ω, but only to 90.91 Ω next to a 1,000 Ω.

Identical resistors: parallel versus series

Stacking copies of one value is the most common trick in the book, whether you are hunting a value you do not stock or spreading heat across packages. Using 1,000 Ω parts:

The power column is the practical payoff: identical resistors share the load evenly, so four 1/4 W parts in parallel handle a full watt at a quarter of the original resistance, and four in series handle the same watt at four times the resistance. This is how a bench dummy load or a high-wattage bleeder is usually built.

Solving for a missing resistor

The most useful mode on this page runs the formula backwards. You know what total you want and what you already have soldered in, and you need the one part that closes the gap. In parallel:

The table below starts from a single 100 Ω resistor and lists the second resistor needed to pull the pair down to each target. Every value comes straight from that rearrangement.

Two of those targets land exactly on a stock part, which is a nice reminder that a 150 Ω across a 100 Ω gives a clean 60 Ω. In series the same idea is plain subtraction: Rx = Rtarget − sum(Ri), so a 650 Ω chain that already holds 100 Ω and 220 Ω needs a 330 Ω to finish. If the calculator tells you the target is not reachable, the direction is wrong: a parallel target must sit below the equivalent resistance of the resistors already listed, and a series target must sit above their sum.

How to use this calculator

1. Pick the wiring: parallel for branches between the same two nodes, series for a single chain.
2. Choose the unit: ohms, kilohms or megohms. All values on the page use the same scale, so convert before you mix.
3. Type the values: start with the three defaults, edit them, add rows up to ten, or remove any row you do not need. Blank and zero rows are simply ignored.
4. Add a supply voltage if you want current and power. Each branch then shows its own current in parallel, or its own voltage drop in series.
5. Switch on missing-resistor solving when you know the total you want, and type that target. The calculator returns the exact Rx and the nearest E12 stock part.
6. Read the pairing table at the bottom to see what one more standard resistor would do to your first value in either wiring.

Everything recalculates as you type, so it is quick to sweep a value and watch where the equivalent resistance lands.

Who this calculator is for

• Hobbyists and makers building a value that is not in the parts drawer out of two that are.
• Students checking homework on network reduction, current dividers and power sharing.
• Electronics technicians reading an unfamiliar board and needing to know what a resistor bank presents to the supply.
• Anyone building a load bank or a bleeder resistor where the wattage matters more than the exact value.
• Automotive and LED tinkerers adding a load resistor across an existing circuit and needing to know the new total and its heat.

Key terms

• Equivalent resistance (Req): the single resistance that would behave identically to the whole network, seen from its two terminals.
• Conductance (G): the reciprocal of resistance, in siemens. Parallel branches add conductance.
• Current divider: the parallel counterpart of the voltage divider. Branch current is proportional to conductance, so the smallest resistor takes the largest share.
• E12 series: the standard 12-value-per-decade resistor ladder (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82) behind most 5% and 10% stock.
• Tolerance: how far a real part may sit from its printed value, commonly 5% or 1%.
• Power rating: the heat a resistor can shed continuously, typically 1/8 W, 1/4 W, 1/2 W or 1 W in through-hole parts.

What changes the result the most

• The smallest resistor in a parallel group dominates everything. It sets most of the equivalent value, carries most of the current and takes most of the heat.
• How many branches you add. Each new parallel branch lowers the total, but with rapidly diminishing returns once its value is far above the smallest.
• The wiring choice itself. Our three example parts read 56.897 Ω in parallel and 650 Ω in series, a factor of more than eleven from the same components.
• The supply voltage, which does not touch the resistance at all but scales current linearly and power with the square. Doubling 12 V to 24 V quadruples the 2.531 W total to 10.124 W.
• Unit slips. Mixing a kilohm value into an ohm field is off by a thousand and is the single most common wrong answer.

Tips from the bench

• Sanity-check the direction first. A parallel answer below the smallest part and a series answer above the largest are free checks that catch most arithmetic slips.
• Use equal pairs where you can. Two identical parts halve the resistance, double the power handling and keep the tolerance behavior simple.
• Reduce big networks in stages. Collapse each parallel cluster, then treat the results as a series chain, and run this calculator once per stage.
• Derate for heat. Pick parts rated for at least twice the calculated dissipation, and more if they sit in a sealed enclosure or against other hot components.
• Measure after you build. With the power off, an ohmmeter across the network should land within the combined tolerance of the calculated value. A wide miss usually means a solder bridge or an open joint.

Limitations and assumptions

• Ideal resistors only. Tolerance, temperature coefficient and aging are not modeled; two 5% 100 Ω parts nominally give 50.00 Ω but can legitimately measure anywhere from 47.50 Ω to 52.50 Ω.
• DC or purely resistive AC. Capacitance and inductance make the combination frequency dependent, which needs impedance math rather than plain resistance.
• No wiring resistance. Leads, traces, connectors and solder joints add their own milliohms, which matter once the network itself is only a few ohms.
• Simple topologies. Purely parallel and purely series groups are covered; bridge, delta and wye networks need a conversion step before you can reduce them.
• Steady state. Power figures assume continuous operation, not pulses, where a resistor can briefly absorb far more energy than its rating.

Sources

• National Institute of Standards and Technology (NIST) - Special Publication 811, Guide for the Use of the International System of Units (SI): the ohm, the siemens, the volt, the ampere and the watt, and the prefixes used on this page.
• International Electrotechnical Commission - IEC 60063, preferred number series for resistors and capacitors: the source of the E6, E12 and E24 ladders, including the twelve E12 values listed above.
• The parallel rule (1/Req = sum of 1/Ri), the series rule (Req = sum of Ri), Ohm's law (V = I x R) and the power equation (P = V² / R) are exact algebraic identities for ideal resistors, so every figure on this page is reproducible by hand and needs no external data table.

How it compares to related calculators

This page answers "what does this resistor network measure, and what does each part carry?" Sister tools take neighboring questions. Use the Ohm's Law Calculator when you have a single element and need to move between voltage, current, resistance and power. Use the Voltage Divider Calculator when two resistors in series are there to produce a specific output voltage rather than a specific resistance. Use the Resistor Color Code Calculator when you need to read the bands on a part before you can enter it here. For the drop along a run of wire rather than through components, the Voltage Drop Calculator is the right tool, and the Watts to Amps Calculator converts a power figure into the current a supply has to deliver. If the heat you calculate here runs continuously, the Electricity Cost Calculator turns those watts into dollars per month.