Current Divider Calculator

Current entering a parallel pair splits in inverse proportion to the branches’ resistances — the easier path takes the larger share. Enter the total current and the two branch resistances, and this calculator returns each branch’s current.

The Crosswise Rule

Two branches in parallel share one voltage, so their currents stand in inverse ratio to their resistances; dividing the total accordingly gives I₁ = I_total × R₂ ÷ (R₁ + R₂) — branch 1's current computed from branch 2's resistance, the crosswise twist that makes the rule memorable once its reason is seen: the common voltage is I_total × (the parallel combination), and dividing that voltage by R₁ brings the other branch's resistance into the numerator. The current divider is the voltage divider's dual (series resistors share voltage in direct proportion), and the pair of rules, with Ohm's law, reduces most two-resistor networks on sight. The calculator handles the canonical two-branch case, prints both shares, and carries in its note the practitioner's audit — the shares must sum to the total — because a division rule whose answer self-checks is a rule that stays honest in the field. There is a laboratory corollary worth the bench space: two meters measuring the same circuit in parallel divide the circuit's current between themselves, each reading low by the other's presence — the observer effect in its most elementary electrical dress, and the reason a careful current measurement asks what the meter's own resistance did to the division it reported.

Worked Example: Ten Amps Between 100 and 200 Ohms

The defaults: I_total = 10 A, R₁ = 100 Ω, R₂ = 200 Ω. Branch 1 takes 10 × 200 ÷ 300 = 6.67 A; branch 2 takes 10 × 100 ÷ 300 = 3.33 A — the lower resistance carrying exactly double the current, as the 1:2 resistance ratio inverted promises, and the shares summing to the entered 10.00 A. The common voltage, for the reader checking the long way, is 666.7 V — high for the numbers chosen, but the arithmetic is the point: both branches at that voltage draw precisely the shares shown (667 ÷ 100 and 667 ÷ 200). Swap the resistances and the shares swap with them; make them equal and any total splits evenly, the trivial case that sanity-checks every nontrivial one.

Shunts: The Divider That Measures

The rule's industrial embodiment is the current shunt: to measure 100 A with a 5 A meter movement, place a precision low resistance in parallel with the meter such that the divider sends exactly 5% through the movement and 95% through the shunt — the crosswise formula run as a design (R_shunt = R_meter × I_meter ÷ (I_total − I_meter), the same division rearranged). Multirange ammeters are a rotary switch of such shunts; the clamp meter's magnetic cousin aside, nearly every large DC current measured on earth passes through a divider of this page's exact form, its ratio certified at the standards laboratory. The calculator designs them as readily as it analyses homework: enter the total and the branch you wish the meter to be, and the other branch's share — hence its required resistance at the common voltage — is one rearrangement away.

Paralleled Supplies and the Hogging Problem

Put two power supplies, two battery strings, or two alternators in parallel and the divider rule becomes a management problem: the branch with slightly lower internal resistance (or slightly higher set voltage) hogs the current, heats, ages, and hogs more — positive feedback the crosswise formula predicts coldly (a 5% resistance edge becomes a far larger current edge when the load resistance is small). Engineers fight it with deliberate sharing resistance, droop control, or active current-share buses, each a device for making the branches' effective resistances honestly equal. The calculator's two fields, run with the internal resistances as the branches, show the imbalance's seed in numbers small enough to respect before it is soldered.

The River Delta Reads the Same Rule

Nature divides currents by conductance everywhere: a river splitting around an island apportions its flow by the channels' ease (their hydraulic conductance), blood divides at a bifurcation by the vessels' radii to the fourth power (Poiseuille's conductance — why a slightly wider branch vessel steals flow so dramatically), and heat spreading through parallel paths takes the low-resistance route in the same proportions. The electrical divider is the circuit dialect of a transport universal. The calculator's crosswise form, learned on resistors, transfers intact to every one of those systems with their conductances substituted — the mark of a rule that has caught something real about how the world shares a flow among competing paths.

Related Tools

More from the Physics Calculators hub: the Capacitors in Series Calculator — the same crosswise spirit in capacitive dress — and the Wheatstone Bridge Calculator, itself two dividers compared at a null.

Frequently Asked Questions

Why is it the OTHER resistance in the numerator?

Because the shares are inverse: branch 1's greed is measured by how reluctant branch 2 is. Derive it once and the pattern is permanent — the common voltage is the total current times the parallel equivalent R₁R₂ ÷ (R₁ + R₂); branch 1's current is that voltage over R₁, and R₁ cancels one factor, leaving R₂ upstairs. Students who memorise without the derivation swap the branches under pressure; the calculator's printed shares, audited by their sum, protect the professional who has no time to re-derive — though this FAQ just did, in two lines, for the record.

What about three or more branches?

The rule generalises through conductances: each branch's share is its conductance (1 ÷ R) over the sum of all conductances, times the total — for two branches this collapses to the crosswise form the calculator implements. In practice the three-branch case is usually handled pairwise or by computing the common voltage first (V = I_total × R_parallel) and dividing per branch. The calculator stays with two branches, the form in which the rule is actually quoted and examined, and this FAQ leaves the conductance generalisation in the reader's hands with its derivation implied.

Does it work for AC?

With impedances in place of resistances, yes — the same crosswise division, now complex, so the shares differ in phase as well as size (a capacitive and an inductive branch can each carry more current than the total, their sum being a phasor cancellation — the parallel-resonance paradox that power engineers meet in tank circuits). The calculator's jurisdiction is the resistive DC case its labels state; the AC generalisation substitutes Z for R throughout and otherwise changes nothing structural, which is the deepest compliment circuit theory pays its DC originals.

What if one branch is a short circuit?

Then it takes everything: R₂ → 0 sends branch 1's share (set by R₂) to zero and branch 2's to the total — the formula's limit is the physics' verdict, a short in parallel with anything is the only path that matters. The calculator rejects a zero resistance input (division by zero in the parallel equivalent) and this FAQ reports the limit honestly: in real circuits the "short" has milliohms, the source has internal resistance, and the enormous resulting current is the fuse's biography. The idealisation boundary is stated so the reader computes the real case with the real milliohms entered.

How does it differ from the voltage divider?

Dually: the voltage divider splits a voltage among series resistors in direct proportion to their resistances; the current divider splits a current among parallel resistors in inverse proportion. Together they are the two reduction rules of resistive network analysis, and between them (plus series-parallel equivalents) most textbook networks collapse without Kirchhoff's full machinery. The hub gives the current rule its own page because its crosswise twist is the one practitioners fumble — the voltage rule being, by comparison, the intuitive direction.

What does the divider say about fuses and protection?

That parallel paths protect each other only when their sharing is honest: a fuse in one branch sees that branch's divided share, not the total — which is why paralleled fuses (used for large currents) are matched and mounted to share thermally as well as electrically, and why a failed-open branch silently transfers its share to its siblings, overloading them in cascade, the arithmetic of many a melted multi-string battery pack. The calculator's two-branch split is the protection engineer's first audit: enter the branches' resistances honestly (including the fuse's own) and the shares predict whose fuse ages fastest.

How do I use this to pick a bleeder or load resistor?

Size it by the share you intend it to steal: a bleeder across a supply is a deliberate second branch, and its current (hence its resistance at the rail voltage) is chosen as a stated fraction of the load's — the divider run with the bleeder as branch 2 tells you the load's remaining share and the total the supply must source. Safety bleeders on capacitor banks are sized the same way with a time-constant condition attached. The calculator's two fields are the bleeder designer's entire workspace, which is why the rule's crosswise form is worth automating rather than re-deriving per schematic.

Who systematised these rules?

The divider arithmetic descends from Ohm's law (1827) through Kirchhoff's circuit laws (1845), which supply the two conservation statements (voltages around a loop sum to zero; currents at a node sum to zero) from which both dividers are corollaries. The rules' compact forms are textbook distillations of the following century — the working shorthand of the telegraph and power industries. The calculator computes the shorthand; the laws beneath it are named here so the reader knows the shorthand's authority and its limits (linear, lumped, steady — the usual treaty).