Current Divider Calculator for Parallel Branches

Current Divider Rule

A current divider is the mirror image of a voltage divider, and the mirroring is where people trip. In a voltage divider the resistors share the voltage and the current is common; in a current divider they share the voltage and the CURRENT is divided. Which means the fraction has the other resistance on top — and that only works for two branches.

One voltage, many currents

Every branch runs between the same two nodes, so every branch has the same voltage across it. That is the only physical fact needed, and everything follows from it. First, what the whole group looks like:

The total current through that combination produces the shared voltage, and then each branch is simply Ohm’s law again:

That is the whole thing, and it is worth doing it this way every time: find the parallel resistance, find the voltage, then divide. Three short steps that cannot be got backwards.

The two-resistor shortcut, and its trap

For exactly two branches the general rule simplifies to the form most people remember:

Two warnings about it. The first is that the resistance on top belongs to the other branch, which is genuinely counter-intuitive until you see why: a branch takes more current when its own resistance is small, so its own resistance has to be in the denominator. The second is that this form does not generalise. With three branches there is no "the other resistance", and substituting the sum of the other two gives the wrong answer — a mistake common enough to be worth stating plainly.

In conductances it is just proportion

The cleanest way to see the rule is to work in conductance, the reciprocal of resistance. Then the split is a plain proportion, exactly like a voltage divider:

This is the form the calculator uses, and it is the one to think in. Conductance is how readily a branch passes current, so "current divides in proportion to conductance" is almost a tautology — and it makes the strange-looking two-resistor formula obvious rather than something to memorise.

Worked example

The 100 Ω branch takes 68.75 % of the current because it is the easier path. It also dissipates 473 mW against the 220 Ω branch’s 215 mW — more than twice as much. That is not a coincidence: since current goes as 1/R and power goes as I²R, power also goes as 1/R. The smallest resistor in a parallel group always takes the most current AND runs the hottest.

Why the Smallest Resistor Runs Hottest

Worth deriving, because the conclusion is stronger than most people expect and it decides which part in a parallel group fails first.

All branches share one voltage V, so each dissipates V²/R. Power is therefore inversely proportional to resistance, exactly as current is:

So halving a branch’s resistance doubles its current and doubles its dissipation. In a group of unequal resistors the smallest one takes the most current, gets the hottest, and is the one to size the power rating around — not the average, and certainly not the total divided by the number of branches.

The practical version: when paralleling resistors to share power, use identical values. Equal resistances share equally, which is the only arrangement where the total divided by the count is the right answer for each part.

Current Sharing Between Real Parallel Parts

The formula assumes you know each resistance. In practice you know each nominal resistance, and the difference matters more than it does for a voltage divider.

Resistors in parallel to share power

Four 1 Ω resistors in parallel look like a 0.25 Ω part with four times the power rating. With 5 % tolerance they do not share evenly: the lowest-value one can be 10 % below the highest and takes correspondingly more current and heat. Derate for that rather than assuming a perfect quarter each.

LEDs in parallel — the classic mistake

LEDs are not resistors. Their current depends exponentially on forward voltage, so two LEDs in parallel on one resistor do not share — the one with the slightly lower forward voltage takes most of the current, gets hotter, drops its forward voltage further, and takes more still. The fix is a resistor per string, which is exactly a current divider with the ballast resistors dominating.

Ballast resistors and why they work

Adding a resistor in series with each parallel branch makes the sharing depend on the resistors rather than on the parts. The larger the ballast relative to the variation you are trying to swamp, the more even the sharing — at the cost of the voltage it drops. This is why parallel MOSFETs get gate resistors and parallel batteries get link resistors.

The thermal runaway case

Sharing is stable when a branch getting hotter makes it take LESS current, and unstable when the opposite is true. Metal resistors have a positive temperature coefficient, so they self-balance. Semiconductors, and NTC thermistors, do not — which is the mechanism behind current hogging in parallel bipolar transistors.

Shunts: The Most Common Current Divider

The oldest practical use of a current divider is extending the range of a moving coil meter. It generalises to every measurement where most of the current has to bypass the sensing element.

A meter with internal resistance Rm reading full scale at Im, extended to read n times that, needs a shunt carrying the other (n − 1) share:

The same arithmetic appears wherever a low-value sense resistor sits in parallel with something: a current-sense amplifier reading a milliohm shunt, a battery monitor, a clamp meter’s calibration resistor. And it comes with the same caution every time — the resistance of the wiring and the joints is in series with the shunt, so a four-wire connection is what makes a low-value shunt accurate.

What This Calculator Assumes

• All branches connect between the same two nodes. If there is any resistance in the wiring between the branch connection points, the branches do not share exactly one voltage and the split changes.
• Ideal resistive branches. A branch containing a diode, an LED or a transistor does not have a single resistance, so the split it produces is not the one calculated here.
• DC or low frequency. At higher frequencies the inductance of each branch and the loop it forms start to matter, and current takes the lowest-impedance path rather than the lowest-resistance one.
• A current source drives the group. If the source is a voltage source with its own internal resistance, changing one branch changes the total current too.
• Nominal resistances. Tolerance means real sharing is less even than calculated, and the smallest branch is the one that suffers for it.

Common mistakes

• Putting the branch’s own resistance on top of the two-resistor formula. It is the OTHER resistance: I1 = I × R2 / (R1 + R2), because a low resistance takes more current.
• Using the two-resistor shortcut with three or more branches. Substituting the sum of the others is wrong — go through the parallel resistance and the shared voltage instead.
• Assuming parallel resistors share equally when they are not equal values. Share goes as 1/R, and so does dissipation.
• Sizing the power rating from the average branch. The smallest resistance takes the most current and the most heat, and it is the one that fails.
• Paralleling LEDs on one resistor and expecting them to share. They do not — the lowest-forward-voltage one takes most of the current. Use a resistor per string.
• Forgetting the wiring. A milliohm shunt with milliohms of connection resistance is a divider with an uncalibrated extra branch; use four-wire sensing.

Frequently asked questions

What is the current divider rule?

The current through one of several parallel branches is the total current times the parallel resistance of the whole group divided by that branch’s own resistance: Ik = Itotal × Rp / Rk. Equivalently, each branch takes a share proportional to its conductance.

How does current split between two parallel resistors?

In inverse proportion to their resistances. For two branches, I1 = I × R2 / (R1 + R2) — note the other resistance on top. A 100 Ω branch in parallel with a 220 Ω branch takes 68.75 % of the current.

Why does the smaller resistor get more current?

Because both branches have the same voltage across them, and Ohm’s law then gives a larger current through the smaller resistance. The same reasoning means it also dissipates more power, since power at a fixed voltage is V²/R.

How do I calculate current in three parallel branches?

Find the parallel resistance from 1/Rp = 1/R1 + 1/R2 + 1/R3, multiply it by the total current to get the shared voltage, then divide that voltage by each resistance. The two-resistor shortcut does not extend to three.

Do parallel resistors share power equally?

Only if they are equal values. Dissipation goes as 1/R, so the smallest resistance takes the largest share of the heat. Even with identical nominal values, tolerance means the real sharing is uneven — derate accordingly.

Why can’t I put LEDs in parallel on one resistor?

Because an LED’s current depends exponentially on its forward voltage, so the LED with the slightly lower forward voltage takes most of the current, heats up, drops its forward voltage further and takes more still. Give each string its own resistor.

What is a shunt resistor and how do I size it?

A low-value resistor in parallel with a measuring element, carrying most of the current so the element sees a known fraction. To multiply a meter’s range by n, the shunt is Rm/(n − 1). Because the value is small, the resistance of the connections matters — use four-wire sensing.