What is the formula for resistors in parallel?

The standard reciprocal formula is 1/Rt = 1/R1 + 1/R2 + … + 1/Rn, so Rt = 1 ÷ (sum of all individual reciprocals). Equivalently, total conductance Gt = G1 + G2 + … + Gn, since conductance G = 1/R; the equivalent resistance is then 1/Gt.

Why is the total always less than the smallest resistor?

Each additional path gives current another route, reducing overall opposition. Mathematically, adding any positive term to the sum of reciprocals increases that sum, so 1 ÷ (larger sum) decreases — always below the smallest R.

Can I mix Ω, kΩ and MΩ in the same calculation?

Yes. Each row has its own unit selector. The calculator converts every value to ohms internally before applying the reciprocal formula, so mixing units is safe and accurate.

How does the conductance table help?

Conductance (G = 1/R, measured in siemens, S) adds directly in parallel. The table shows what fraction of the total conductance each resistor contributes — the higher its percentage, the more current that branch carries at a given voltage.

What is the solve-for-missing-resistor feature?

Rearranging the reciprocal formula gives 1/Rx = 1/Rt_target − Σ(1/Ri). Enter a target total resistance and the calculator finds the single extra resistor Rx you need to add to your existing network to reach that target. This is useful when you know the desired impedance and need to find a standard resistor value to add.

What happens with two equal resistors in parallel?

Two equal resistors of value R give R/2. Three equal resistors give R/3. In general, n equal resistors in parallel give R/n — a useful quick check when prototyping or using matched resistor arrays.

Is any data uploaded or stored?

No. Every calculation runs entirely in your browser with no network requests. Nothing is ever sent to a server.

Resistor Parallel Calculator

Parallel resistors are a fundamental building block of electronic circuits — appearing in current dividers, pull-up/pull-down networks, biasing stages, impedance matching pads and R-2R DAC ladders. When resistors are wired in parallel they share the same voltage across their terminals while current splits between the branches. The combined (equivalent) resistance is therefore lower than any single branch — and this calculator shows you exactly how much lower, including a full conductance breakdown and a solve-for-missing-R mode for working backwards from a target impedance.

The parallel resistance formula

The core identity comes from applying Kirchhoff’s current law: the total current entering the node equals the sum of branch currents.

I_total = V/R1 + V/R2 + … + V/Rn
        = V · (1/R1 + 1/R2 + … + 1/Rn)

Dividing both sides by V and comparing to Ohm’s law (I = V / Rt) gives:

1/Rt = 1/R1 + 1/R2 + … + 1/Rn

Or equivalently in terms of conductance G = 1/R (siemens, S):

Gt = G1 + G2 + … + Gn      ← conductances add directly in parallel
Rt = 1 / Gt

This calculator computes each branch conductance, sums them, and inverts the total. The working step is shown in full so you can follow every step.

Worked example

Three resistors — 100 Ω, 220 Ω and 470 Ω — wired in parallel:

Step	Calculation
G1 = 1/100 Ω	0.010 000 S
G2 = 1/220 Ω	0.004 545 S
G3 = 1/470 Ω	0.002 128 S
Gt = G1+G2+G3	0.016 673 S
Rt = 1/Gt	59.98 Ω

The result is well below 100 Ω, the smallest resistor — as expected. The 100 Ω branch carries 59.98 % of the total conductance and therefore ~60 % of the current; the 470 Ω branch carries only ~12.8 %.

A few quick reference combinations:

Resistors	Equivalent
100 Ω + 100 Ω	50 Ω
100 Ω + 220 Ω + 470 Ω	59.98 Ω
1 kΩ + 1 kΩ + 1 kΩ	333.33 Ω
10 kΩ + 47 kΩ	8.246 kΩ
1 MΩ + 1 MΩ	500 kΩ

Solve for a missing resistor

A common design task is the reverse problem: you have a network already delivering some resistance and you need to add one more parallel branch to hit a lower target. Re-arranging the formula:

1/Rx = 1/Rt_target − (1/R1 + 1/R2 + … + 1/Rn)
Rx   = 1 / (1/Rt_target − known_conductance_sum)

Enter the desired total in the “Solve for missing resistor” section and the calculator does this algebra for you, showing the required resistor value. If the target is greater than or equal to the current parallel combination the result is physically impossible (you cannot add a parallel resistor and increase total resistance) and the tool explains why.

Practical notes on choosing resistor values

When the calculated Rx does not correspond to a standard E-series value (E12, E24, E96), the usual approach is to pick the nearest standard value above Rx (which gives a result slightly below target) or the nearest below (slightly above target), then verify with the calculator. For precision circuits the E96 series offers 1 % tolerance values spaced roughly 2.5 % apart, giving enough resolution that the closest E96 value is almost always within 1–2 % of the ideal.

Every calculation here runs entirely in your browser — your component values are never sent anywhere.