Parallel Resistor Calculator

Background.

Resistors in parallel do not add — they combine as reciprocals, and the result is always smaller than the smallest resistor in the network. That single fact catches people out more often than any other piece of introductory circuit arithmetic, because the intuition that adding more of something gives you more of it is exactly backwards here. Every branch you add gives the current another route to take, so the network gets easier to push current through, not harder. This calculator does the reciprocal arithmetic for up to twenty branches, then answers the two questions that usually follow it: how much current goes down each branch, and what one extra resistor would take the whole thing to the value you actually want.

Enter the branches separated by commas — engineering shorthand such as 4.7k and 1M is understood — along with the total current arriving at the junction and the equivalent resistance you are aiming for. A zero-ohm branch is refused rather than computed, because it is not a resistor: it is a wire across the network, the equivalent resistance really would be zero, and every other branch would carry no current at all. That is a fault to report, not a number to print.

The rule comes straight from Kirchhoff's current law. Every branch of a parallel network is connected across the same two nodes, so every branch has the identical voltage across it. Each therefore carries a current of V divided by its own resistance, and the currents have to sum to the total arriving at the junction. Divide through by the shared voltage and the voltages cancel, leaving the reciprocals adding: one over R_parallel equals one over R1 plus one over R2, and so on. OpenStax prints exactly that as Equation 10.3 in University Physics Volume 2, together with the consequence — the equivalent resistance is less than the smallest of the individual resistances.

For exactly two resistors the reciprocal form simplifies to the product-over-sum shortcut everyone memorises: R1 times R2, divided by R1 plus R2. It is worth knowing because it is quick in your head for common pairs, and worth remembering that it works for two branches only. Three resistors do not obey any product-over-sum arrangement, and the reciprocal form is the one to use.

The current-split result is where a parallel network stops being an arithmetic exercise and starts mattering. Since voltage is common, current divides in inverse proportion to resistance: a 100 Ω branch beside a 1 kΩ branch carries ten times the current and takes 90.9 % of the total. Power follows the current, so the smallest resistor in a parallel network gets the hottest — the precise reverse of a series chain, where the largest resistor dominates. If you are paralleling resistors to spread heat, this is the number that decides whether it worked: two well-matched parts share the load evenly, whereas a badly matched pair leaves one of them doing nearly all the work and running to its limit while the other stays cool.

The last output answers a practical bench question that comes up constantly. You have a network at 103 Ω and you need 60 Ω. What do you solder across it? The answer is one over the target minus one over the present value, all inverted — and the calculator does it, with the strict condition that the target has to be lower than what you already have. Adding a parallel branch can only lower resistance. If you need to go up, you need a series resistor instead, and this page will tell you so rather than returning a physically meaningless negative value.

Two scope limits, stated here rather than buried in an FAQ. This is a DC and low-frequency model: it ignores stray inductance and capacitance, which matter once a paralleled network is carrying fast edges. And it assumes ideal resistors of exactly the values you type. Real parts carry a tolerance, and in a parallel network that tolerance behaves the same way it does in a series chain — the percentage window of the combination equals the percentage window of the parts when they all share one tolerance, because the (1 ± t) factor comes straight back out of the reciprocal sum.

What is parallel resistor calculator?

A parallel connection is one in which two or more components are joined across the same pair of nodes, so that each sits directly across the same voltage. That shared voltage is the defining property, and it is the mirror image of the series case, where the shared quantity is current.

Because each branch sees the same voltage V, Ohm's law gives its current as I_i = V / R_i. Kirchhoff's current law says the currents leaving a node must equal the current entering it, so I_total = V/R1 + V/R2 + … + V/Rn = V x (1/R1 + 1/R2 + … + 1/Rn). Comparing that with I_total = V / R_P identifies the equivalent resistance as the reciprocal of the sum of reciprocals.

It is often clearer in terms of conductance. Conductance G is one over resistance, measured in siemens, and it says how easily current flows rather than how hard it is. In those terms the parallel rule is simply G_P = G1 + G2 + … + Gn: conductances add in parallel exactly as resistances add in series. Two branches of 1 kΩ each have a conductance of 1 mS; together they conduct 2 mS, which is 500 Ω.

Parallel connection is used to get a value below anything you have in stock, to share current and therefore heat across several physically small parts, to raise the total power rating of a resistive load, and — in the two-resistor case — as the output impedance of a voltage divider, which is why the Thevenin resistance of a divider is R1 in parallel with R2. It is not a way to raise a voltage rating: every branch sees the full applied voltage, so paralleling gains you nothing there.

How to use this calculator.

1. 01List the branches, separated by commas. These are the resistors that sit across the same two points in the circuit — if they do not share both connection points, they are not in parallel.
2. 02Use engineering shorthand if it is quicker: 4.7k, 10K, 1M and 2.2G are all read correctly. Write 0.001 rather than 1m; a lower-case m is refused rather than guessed at.
3. 03Enter the total current arriving at the junction, in amperes. If you know the voltage across the network instead, divide it by the equivalent resistance the calculator returns and re-enter — or just read the voltage output, which is the same relationship the other way round.
4. 04Check the equivalent resistance against the smallest branch. It must be smaller. If it is not, something in the list was mistyped, and the branch count output will usually show it.
5. 05Read the current split. The lowest-value branch carries the most current and dissipates the most heat, so it is the part whose power rating you size first — the opposite of a series chain.
6. 06If you are paralleling resistors to share power, look at how even the split is. An uneven split means one part is doing most of the work; match the values more closely, or size that part for its actual share rather than for an equal one.
7. 07Set the target to the equivalent resistance you want and read the extra branch needed. The target must be below the present equivalent — parallel branches can only lower resistance.
8. 08To go the other way and raise the resistance, use the series calculator instead. Series raises, parallel lowers; there is no way round that with passive resistors.

The formula.

The parallel rule follows from one constraint and one law. The constraint is that every branch spans the same two nodes, so the voltage V across each of them is identical. The law is Kirchhoff's current law: the current entering a node equals the sum of the currents leaving it.

Apply Ohm's law branch by branch: I₁ = V/R₁, I₂ = V/R₂, and so on. Sum them: I_total = V/R₁ + V/R₂ + … + V/Rₙ = V·(1/R₁ + 1/R₂ + … + 1/Rₙ). Since I_total = V/R_P by definition of the equivalent resistance, dividing by V gives 1/R_P = Σ 1/Rᵢ, which is OpenStax Equation 10.3. Inverting both sides gives R_P = (Σ 1/Rᵢ)⁻¹.

That the result is always below the smallest branch follows immediately: the sum of reciprocals is strictly larger than the largest single reciprocal, which is one over the smallest resistance, so its inverse is strictly smaller than that smallest resistance. For two branches the algebra collapses to the product-over-sum form R_P = R₁R₂/(R₁+R₂), which is exact for two and only two resistors.

The current split is the same relation read the other way. With V = I_total × R_P known, each branch carries Iᵢ = V/Rᵢ, and its share of the total is Iᵢ/I_total = R_P/Rᵢ. Because power is P = V²/R at a common voltage, power divides in the same ratio as current: the smallest resistor takes the largest share of both. This is the exact inverse of the series case and is the single most useful thing to carry away from this page.

The trim resistor comes from treating conductance as additive. To move from a present conductance G_P = 1/R_P to a target conductance 1/R_target, you need to add the difference: G_add = 1/R_target − 1/R_P, so R_add = 1/(1/R_target − 1/R_P). That difference is positive only when R_target is strictly below R_P, which is why a target at or above the present equivalent is refused. A negative resistance is not a component you can solder in.

Rounding happens once, at the end. Every intermediate reciprocal and sum is computed as exact decimal arithmetic at forty significant digits — which matters here more than in the series case, because reciprocals of decimal values are usually non-terminating — and the returned numbers are rounded to ten decimal places only as they cross the boundary out of the calculator. The refusal test on the target compares unrounded Decimals, so a target a hair below the equivalent is accepted and returns a very large but finite trim resistor rather than tipping over into infinity.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax (Rice University), "University Physics Volume 2", §10.2 "Resistors in Series and Parallel". Equation 10.3 states the parallel rule as RP = (1/R1 + 1/R2 + 1/R3 + ⋯ + 1/RN−1 + 1/RN)⁻¹ = (Σ 1/Ri)⁻¹, and the same section states that "this relationship results in an equivalent resistance RP that is less than the smallest of the individual resistances" and that power divides among parallel branches by conductance. Retrieved and read 2026-07-29.
2. [2]"Series and parallel circuits", reference article, retrieved and read 2026-07-29. Independent statement of the same rule: R = (1/R1 + 1/R2 + 1/R3 + ⋯ + 1/Rn)⁻¹, the product-over-sum form R = R1R2/(R1 + R2) for two branches, and the statement that total resistance "will always be less than the value of the smallest resistance". Agrees with OpenStax Equation 10.3 term for term.
3. [3]Vishay BCcomponents, "MRS16, MRS25 Professional Thin Film Leaded Resistors", document 28724, revision 07-Mar-16. Source of the power- and voltage-rating context used in the heat-sharing FAQ: rated dissipation P70 of 0.4 W (MRS16) and 0.6 W (MRS25) — rated at 70 °C ambient — maximum operating voltage 200 V and 350 V, peak permissible film temperature 155 °C. Retrieved and read 2026-07-29.
4. [4]Vishay, "D/CRCW e3 Standard Thick Film Chip Resistors", document 20035, revision 14-Apr-2026. Confirms the same rating basis on surface-mount parts and shows why paralleling does not raise a voltage rating: maximum operating voltage is a per-part limit that every branch of a parallel network sees in full, running from 75 V on an 0402 to 500 V on a 2512. Retrieved and read 2026-07-29.
5. [5]IEC 60063:2015, "Preferred number series for resistors and capacitors", third edition, 27 March 2015. Defines the E24 (±5 %) and E96 (±1 %) value sets referenced when judging whether a computed trim resistor is a value you can actually buy. Retrieved 2026-07-29 via the reference summary of the series values and their standard tolerances.