Parallel Resistance Calculator

Equivalent Resistance of Parallel Resistors

Parallel Resistance Formula

Formula

\[ \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots + \frac{1}{R_n} \] \[ R_{\text{eq}} = \left( \sum_{i=1}^{n} \frac{1}{R_i} \right)^{-1} \] \[ R_{\text{eq}} = \frac{R_1 \cdot R_2}{R_1 + R_2} \quad \text{(two resistors only)} \]

Where:

\(R_{\text{eq}}\) — equivalent (total) resistance of the parallel network (Ω)
\(R_1, R_2, \ldots, R_n\) — individual resistor values (Ω)
\(n\) — number of resistors connected in parallel

The general rule is that conductances add: the reciprocal of the equivalent resistance equals the sum of the reciprocals of all individual resistances. For two resistors, this simplifies to the well-known "product over sum" formula.

Parallel Resistance – Calculation Example

Example: three resistors of 10 Ω, 22 Ω, and 33 Ω are connected in parallel (the calculator's default values).

\[ \frac{1}{R_{\text{eq}}} = \frac{1}{10} + \frac{1}{22} + \frac{1}{33} = 0.1 + 0.04545 + 0.03030 = 0.17576 \]

\[ R_{\text{eq}} = \frac{1}{0.17576} \approx 5.6897~\Omega \]

Result: the equivalent resistance is approximately 5.69 Ω — lower than the smallest individual resistor, as always happens in a parallel circuit.

How to Use the Parallel Resistance Calculator

Locate the Resistance values input field.
Type the resistance of each resistor in ohms, separated by commas — for example 10, 22, 33. You can enter any number of values.
The Equivalent Resistance result updates automatically as you type.
To add or remove resistors, simply edit the list — add a new value after a comma or delete one. Invalid or non-positive entries are ignored.

What Is Parallel Resistance?

When resistors are connected in parallel, they share the same two nodes, so each resistor experiences the same voltage. Instead of adding resistances (as in a series circuit), the current has multiple paths to flow through, which reduces the overall opposition to current. That is why the equivalent resistance of a parallel network is always smaller than the smallest resistor in the group.

Another way to understand the formula is through conductance \(G = 1/R\), measured in siemens. In a parallel circuit, conductances simply add up: \(G_{\text{eq}} = G_1 + G_2 + \ldots + G_n\). Taking the reciprocal gives the equivalent resistance. This is the same logic used in the Parallel Inductance Calculator, while series circuits follow the opposite rule — see the Series Inductance Calculator for comparison.

Parallel resistance matters in practice because it lets you create resistance values that are not available as standard components. For example, two 10 Ω resistors in parallel give 5 Ω, and combining values from the E12 or E24 series can approximate almost any target. Parallel connection also increases the total power-handling capability: since the current divides among the resistors, each one dissipates only a fraction of the total power, allowing several small resistors to do the job of one large one.

Common applications include current-sharing networks, shunt resistors for current measurement, bleeder resistors in power supplies, safe discharging of capacitors, and fine-tuning bias networks. When sizing a series resistor for a voltage-reference circuit, you can combine this tool with the Zener Diode Resistor Calculator.

Assumptions, Limitations and Practical Tips

Smallest resistor dominates: with very unequal values, the equivalent resistance is only slightly below the smallest resistor. A 100 Ω resistor in parallel with 10 kΩ gives about 99 Ω.
Equal resistors shortcut: for \(n\) identical resistors \(R\) in parallel, the equivalent resistance is simply \(R/n\).
Ideal components assumed: the calculation ignores lead resistance, tolerance, and temperature coefficients. Real resistor tolerances (±1%, ±5%) can noticeably shift the result when precision matters.
Units must be consistent: enter all values in the same unit (ohms). Convert kΩ and MΩ to ohms first — e.g., 4.7 kΩ is 4700 Ω.
Power rating: check that each resistor's power dissipation stays within its rating; in a parallel network the smallest resistor carries the largest share of the current.
Conductors count too: parallel wires and PCB traces also follow this rule; for related transmission-line calculations see the Parallel Wire Impedance Calculator and the Wire Gauge Calculator.

Frequently Asked Questions

How do I calculate parallel resistance by hand without the calculator?

Take the reciprocal of each resistance, add them all together, then take the reciprocal of the sum. For example, with 4 Ω and 12 Ω: \(1/4 + 1/12 = 0.25 + 0.0833 = 0.3333\), and \(1/0.3333 = 3\) Ω. For exactly two resistors you can also use the shortcut \(R_{\text{eq}} = (R_1 \cdot R_2)/(R_1 + R_2)\) — multiply the values, then divide by their sum.

Why is the total resistance always smaller than the smallest resistor?

In a parallel circuit each resistor adds a new path for current, so the total current for a given voltage is larger than through any single resistor alone. More current at the same voltage means lower overall resistance, by Ohm's law. Adding more parallel resistors can only decrease the equivalent resistance — never increase it. This is the opposite of a series circuit, where resistances add up.

How do I enter values in kΩ, MΩ, or mΩ?

The calculator expects all values in ohms, so convert first: 1 kΩ = 1000 Ω, 1 MΩ = 1,000,000 Ω, and 1 mΩ = 0.001 Ω. For example, to combine 4.7 kΩ with 330 Ω, enter 4700, 330 — not 4.7k, 330. Mixing units (e.g., typing 4.7 when you mean 4700 Ω) is the most common source of wildly wrong results, so double-check your input.

Is there a shortcut for several equal resistors in parallel?

Yes. For \(n\) identical resistors of value \(R\) in parallel, the equivalent resistance is simply \(R/n\). Two 100 Ω resistors give 50 Ω, four 100 Ω resistors give 25 Ω, and ten 10 kΩ resistors give 1 kΩ. This is handy for building non-standard values from parts you have on hand, and it also spreads the power dissipation evenly across all resistors.

What is the difference between parallel and series resistance?

In a series connection the resistances simply add: \(R_{\text{eq}} = R_1 + R_2 + \ldots\), and the total is larger than any single resistor, with the same current flowing through each. In parallel the reciprocals add, the total is smaller than the smallest resistor, and the same voltage appears across each one. A frequent mistake is applying the sum formula to a parallel circuit or vice versa — always check how the components are actually wired.

How do I account for resistor tolerance in the result?

The calculator assumes exact values, but real resistors have tolerances of ±1% or ±5%. To estimate the worst case, run the calculation once with all values at their minimum and once at their maximum tolerance limits. The spread can be surprisingly wide: with two 100 Ω ±5% resistors in parallel, the result can range from about 47.5 Ω to 52.5 Ω. For precision dividers or references, use ±1% or tighter parts.

How does power dissipation work with parallel resistors?

Each parallel resistor dissipates power according to \(P = V^2/R\), where V is the shared voltage. The smallest resistance draws the most current and dissipates the most power, so check its rating first. Paralleling resistors also increases total power capacity: two 0.25 W resistors of the same value can safely dissipate about 0.5 W combined. Always leave a margin — running a resistor at its full rated dissipation makes it run very hot.