Parallel Resistor Calculator: Formula and Examples

A parallel resistor calculator finds the equivalent resistance of two or more resistors connected across the same two nodes. Enter each resistance in ohms to get their combined resistance; the example below uses a two-resistor calculator specification, while the formulas also explain how to handle larger groups.

Formula

For resistors connected in parallel, add their conductances, where conductance is the reciprocal of resistance. The equivalent resistance is the reciprocal of that sum:

1 / R_eq = 1 / R₁ + 1 / R₂ + … + 1 / R_n

Equivalently, R_eq = 1 / (1 / R₁ + 1 / R₂ + … + 1 / R_n).

• R_eq is the equivalent resistance in ohms (Ω).
• R₁, R₂, …, R_n are the individual resistor values in ohms.
• Conductance is measured in siemens (S), equal to 1/Ω. The calculator’s second output is the sum of the conductances for its two inputs.

For exactly two resistors, the same result can be calculated with the product-over-sum shortcut: R_eq = (R₁ × R₂) / (R₁ + R₂). The reciprocal formula works for any number of resistors; the shortcut applies only to a pair.

Worked Example

Using the calculator’s default values, R₁ = 100 Ω and R₂ = 100 Ω:

1. Find each reciprocal: 1/100 = 0.01 S and 1/100 = 0.01 S.
2. Add the conductances: 0.01 + 0.01 = 0.02 S.
3. Take the reciprocal: R_eq = 1/0.02 = 50 Ω.

The equivalent resistance is 50.00 Ω, and the total conductance is 0.0200 S. Two equal resistors in parallel have half the resistance of either one, which provides a useful check.

How Parallel Resistance Works

Resistors are in parallel when both ends of each resistor connect to the same two electrical nodes. Each branch therefore has the same voltage across it. Current divides among the branches according to their resistances: for a given voltage, a lower-resistance branch carries more current.

The total current is the sum of the branch currents. From Ohm’s law, each branch current is voltage divided by its resistance. Adding those currents leads directly to the conductance formula above. This is why parallel resistances do not add like series resistances do.

For positive resistor values, adding a parallel branch always reduces the equivalent resistance. The result must be less than the smallest individual resistance. If a calculation gives a larger result, check whether the circuit is actually in parallel and whether the arithmetic or units are correct.

How to Use the Calculator

• Enter the resistance of each of the two parallel branches in ohms. Use the resistor’s nominal value or a measured value, depending on what you need to estimate.
• For more than two branches, calculate the result for two at a time, then combine that equivalent with the next resistor. Alternatively, sum all the reciprocals and take one reciprocal.
• Read the equivalent resistance as the value a single ideal resistor would need to have to produce the same voltage-current relationship at the circuit’s terminals.

Keep units consistent. If your values are in kilo-ohms, convert them to ohms before entering them (1 kΩ = 1,000 Ω), or calculate entirely in kilo-ohms and convert the final result. The equations work in any consistent resistance unit, but mixing ohms and kilo-ohms in one sum gives an invalid answer.

Examples and Practical Checks

For 100 Ω and 200 Ω in parallel, the product-over-sum formula gives (100 × 200) / (100 + 200) = 20,000/300 ≈ 66.67 Ω. That is below 100 Ω, the smaller branch resistance. If a 300 Ω resistor is added as a third parallel branch, the total becomes 1/(1/100 + 1/200 + 1/300) ≈ 54.55 Ω.

For N identical resistors, each with resistance R, the equivalent resistance is R/N. Four identical 1 kΩ resistors in parallel therefore give 250 Ω ideally. Actual components have tolerances, so a physical measurement may differ from the ideal calculation.

Resistance and conductance are reciprocals, but their numerical values use different units. Do not add resistance values and then take a reciprocal; add the reciprocal values (conductances) first. Also avoid rounding each reciprocal too early, especially when values differ greatly. Keep extra digits through the calculation and round the final answer to a precision that makes sense for the input values.

Assumptions and Limitations

This calculation assumes ordinary, positive, fixed resistances and an ideal parallel connection. It does not account for resistor tolerance, temperature changes, wiring resistance, contact resistance, or components whose resistance changes with voltage, current, or frequency. For precision work, use the actual component specifications and consider the operating conditions.

An open branch has effectively infinite resistance and contributes zero conductance, so it does not change the result. A short circuit has resistance close to zero and can make the ideal equivalent approach zero; in a real circuit, current may then be limited by the source and wiring rather than by the parallel resistors. Do not treat this calculator as a substitute for checking power ratings or the circuit’s current requirements.

Frequently Asked Questions

How do you calculate two resistors in parallel?
Use R_eq = (R₁ × R₂)/(R₁ + R₂), or take the reciprocal of the sum of their reciprocals. Both methods give the same result for positive resistance values.

Why is parallel resistance lower?
Each added branch provides another path for current. The conductances add, so total conductance rises and its reciprocal—the equivalent resistance—falls.

Can I use this formula for three or more resistors?
Yes. Add 1/R for every parallel resistor, then take the reciprocal of the total. The product-over-sum shortcut is only for two resistors at a time.

What happens when the resistors are equal?
The equivalent resistance is the resistance of one resistor divided by the number of parallel resistors. For example, three equal 90 Ω resistors have an ideal equivalent resistance of 30 Ω.

Can I mix ohms and kilo-ohms?
Not in the same calculation unless you convert them to a common unit first. One kilo-ohm equals 1,000 ohms; consistent units ensure the reciprocal sum is meaningful.

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in r1 | Resistor 1 | ohm | 100 | 0
in r2 | Resistor 2 | ohm | 100 | 0
out req | Equivalent resistance | ohm | 1 / (1 / r1 + 1 / r2) | 2
out conductance | Total conductance | siemens | 1 / r1 + 1 / r2 | 4