A current divider splits a total current between parallel branches in inverse proportion to their resistance: Iₙ = Itotal × Rp ÷ Rₙ. For two resistors that becomes I₁ = I × R₂ ÷ (R₁ + R₂). The smaller resistor always carries more current.
Enter the total current and the branch resistances to get each branch current, the equivalent resistance and the shared voltage. This is a learning and design aid for resistor circuits; for building or mains wiring, follow your electrical code and consult a qualified electrician.
How to use this calculator
- Enter the total current flowing into the parallel group, in amps. Use decimals for milliamps (50 mA = 0.05 A).
- List the branch resistances in ohms, separated by commas or spaces — two or as many as you like.
- Read the current through each resistor, starting with R1.
- Check the equivalent resistance and the voltage across the branches, which is the same for every branch.
- Use Share to save or send the result.
How it's calculated
The calculator first finds the equivalent parallel resistance, then the shared voltage, then each branch current:
1/R_p = 1/R₁ + 1/R₂ + … + 1/Rₙ(OpenStax College Physics 2e §21.1)V = I_total × R_p— each resistor in parallel has the same full voltage applied to it.Iₙ = V / Rₙ = I_total × R_p / Rₙ(Ohm's law)
Here Itotal is the current entering the parallel group, Rₙ is the resistance of branch n, Rp is the equivalent resistance and V is the voltage across the group. For exactly two resistors, Rp = R₁R₂ ÷ (R₁ + R₂), which simplifies to the familiar form in MIT OpenCourseWare 6.061: I₂ = I × R₁ ÷ (R₁ + R₂). Notice the other resistor goes on top.
Worked examples
10 A through 2 Ω and 3 Ω
Rp = 2 × 3 ÷ 5 = 1.2 Ω, so V = 10 × 1.2 = 12 V. I₁ = 12 ÷ 2 = 6 A and I₂ = 12 ÷ 3 = 4 A. Check: 6 + 4 = 10 A.
22 A through 200, 300 and 100 Ω
Rp = 54.55 Ω and V = 1,200 V. The branches carry 6, 4, 12 A — the 100 Ω branch takes half the total. This matches the Oregon State ENGR 102 example.
OpenStax Example 21.2: 12 V across 1, 6 and 13 Ω
Rp = 0.804 Ω, so the source supplies 14.92 A. Dividing that current gives 12, 2, 0.92 A, the same values OpenStax reports, and power P = I²R in each branch of 144, 24, 11.1 W.
50 mA shared by 100 Ω and 1 kΩ
The 100 Ω branch takes 45.45 mA and the 1 kΩ branch 4.55 mA. When one resistor is ten times the other, it carries one-eleventh of the total.
Two-resistor split by ratio
How 1 A divides between R₁ and a larger R₂. Multiply by your actual current.
| R₂ ÷ R₁ | Current in R₁ | Current in R₂ | R₁ share |
|---|---|---|---|
| 1 | 0.5 A | 0.5 A | 50% |
| 2 | 0.6667 A | 0.3333 A | 66.7% |
| 3 | 0.75 A | 0.25 A | 75% |
| 4 | 0.8 A | 0.2 A | 80% |
| 5 | 0.8333 A | 0.1667 A | 83.3% |
| 9 | 0.9 A | 0.1 A | 90% |
| 10 | 0.9091 A | 0.0909 A | 90.9% |
| 100 | 0.9901 A | 0.0099 A | 99% |
Where current dividers are used
The classic example is the ammeter shunt. OpenStax College Physics 2e §21.4 describes turning a sensitive galvanometer into an ammeter by placing a small shunt resistance in parallel with it, so most of the current bypasses the meter. In their example, a 25 Ω galvanometer that reads full scale at 50 μA is paired with a 0.00125 Ω shunt for a 1.0 A range. Running 1 A through that pair in this calculator puts 50 μA through the meter and 0.99995 A through the shunt — the divider rule at work. The same idea shows up whenever parallel paths share a supply, from paralleled resistors that spread heat to LED strings on separate branches.
Current divider vs voltage divider
In series, the same current flows through every resistor and the voltage divides; the larger resistor gets the larger share of the voltage. In parallel it's the reverse: every branch sees the same voltage and the current divides, with the smaller resistor taking the larger share. If you remember one thing, remember that current prefers the path of lower resistance but still flows through every branch.
Common mistakes
- Putting the wrong resistor on top. In the two-resistor formula, the current in R₁ uses R₂ in the numerator. Getting this backwards gives the larger current to the larger resistor.
- Adding resistances as if in series. Parallel resistance is the reciprocal of the sum of reciprocals, not the sum.
- Mixing units. Keep all resistances in ohms (1 kΩ = 1,000 Ω) and current in amps.
- Forgetting power ratings. The branch with the most current may also dissipate the most power. Check P = I²R against each resistor's wattage rating.
- Assuming an ideal source. The divider rule assumes the total current is known. If you know the source voltage instead, the current is V ÷ Rp (plus any source resistance in series).
When this calculator doesn't apply
This calculator only handles plain resistance. Circuits with capacitors or inductors on AC, and non-linear parts such as diodes and LEDs, need a different analysis — the simple ratio above won't give the right branch currents.
Related calculators
For household circuits, conductor size depends on current, length and code rules — see the wire size calculator. For battery capacity in watt-hours, use the mAh to Wh converter.
Frequently asked questions
What is the current divider formula?
For two resistors in parallel, I₁ = I × R₂ / (R₁ + R₂) and I₂ = I × R₁ / (R₁ + R₂). For any number of resistors, Iₙ = I × R_p / Rₙ, where 1/R_p = 1/R₁ + 1/R₂ + …
How is 10 A split between 2 Ω and 3 Ω?
6, 4 A — the smaller resistor takes the larger share of the current.
How is 22 A split between 200, 300 and 100 Ω?
6, 4, 12 A. The equivalent resistance is 54.545 Ω.
Does more current flow through the smaller resistor?
Yes. Every parallel branch has the same voltage, so by Ohm's law (I = V/R) the branch with the lowest resistance carries the most current. Current divides in inverse proportion to resistance.
What is the current divider rule with conductance?
Using conductance G = 1/R, each branch gets Iₙ = I × Gₙ / (G₁ + G₂ + …). Current divides in direct proportion to conductance, which is often easier with three or more branches.
What happens if two parallel resistors are equal?
The current splits evenly. 10 A through two 5 Ω resistors gives 5, 5 A, and the equivalent resistance is 2.5 Ω — half of one resistor.
Is the equivalent resistance always smaller than the smallest resistor?
Yes. OpenStax notes that total parallel resistance is less than the smallest individual resistance. For 1, 6 and 13 Ω it is 0.804 Ω.
What is the difference between a current divider and a voltage divider?
A current divider is resistors in parallel: they share the same voltage and split the current. A voltage divider is resistors in series: they carry the same current and split the voltage, with the larger resistor taking the larger share.
How do I check a current divider answer?
Add the branch currents. By Kirchhoff's junction rule the currents leaving a junction must equal the current entering it, so the branch currents must add up to the total.
How much power does each branch use?
Use P = I²R for each branch. In OpenStax's 12 V example with 1, 6 and 13 Ω, the branches dissipate 144, 24, 11.1 W.
Sources & method
- OpenStax College Physics 2e, §21.1 — resistors in series and parallel
- OpenStax College Physics 2e, §20.4 — electric power and energy (P = IV = I²R = V²/R)
- OpenStax College Physics 2e, §21.4 — DC voltmeters and ammeters (shunt resistor)
- OpenStax College Physics 2e, §21.3 — Kirchhoff's rules (junction rule)
- OpenStax University Physics Vol. 2, §10.2 — resistors in series and parallel
- MIT OpenCourseWare 6.061, Chapter 1 — current divider (Eq. 5)
- Oregon State University ENGR 102 — voltage and current dividers
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