Why is parallel resistance always less than the smallest resistor?

For positive resistors, each parallel branch adds a positive reciprocal to the sum, so equivalent resistance falls below the smallest branch value. This says nothing about a fixed zero limit for arbitrary added values.

Can I calculate parallel resistance for more than 10 resistors?

While this calculator supports up to 10 resistors for practical purposes, the formula works for any number of resistors. For more than 10, you can calculate in groups of 10 and then combine the results.

What happens if I connect resistors of very different values in parallel?

The total resistance will be very close to the value of the smallest resistor. For example, if you have a 10Ω resistor in parallel with a 1000Ω resistor, the total will be approximately 9.9Ω – the larger resistor has minimal effect on the total.

How do I calculate parallel resistance for just two resistors?

For two resistors, you can use the simplified formula: R_total = (R1 × R2) / (R1 + R2). This is often called the 'product over sum' formula and is easier to calculate than the reciprocal formula.

Parallel Resistance Calculator – Calculate Total Resistance

Find equivalent resistance for parallel resistors

Method and source check

Last checked: Sep 30, 2026

Automated source and implementation review, including worked examples and documented numerical limits. This review does not provide professional advice or specialist approval.

Method

For two to ten ideal positive resistors, sum 1/R for each parallel branch and invert the sum to get equivalent resistance.

R_eq = 1 / Σ(1/R_i)

Variables and units

R_i: each resistance in Ω
R_eq: equivalent resistance in Ω

Worked example

100Ω in parallel with 100Ω gives 50Ω.

Limitations

The calculation retains floating-point precision, and the UI displays up to six significant digits; the tested 0.00005 Ω resistance remains visible.

Ideal positive-resistor arithmetic only; component tolerance, heating, and physical installation are outside this calculation.
The form schema rejects derived overflow and unsupported numerical combinations before showing results; the calculation helper expects schema-validated input.
100Ω || 100Ω → 50Ω
10Ω || 1000Ω → about 9.90099Ω
0.0001Ω || 0.0001Ω → 0.00005Ω
Two 1e-320 Ω resistors are rejected on a resistor input because their reciprocal sum overflows.

Sources

Resistors in Series and Parallel — OpenStax, Rice University(opens in a new tab)

Table of Contents

How to Use

Enter at least two positive resistance values in ohms.
Add more resistor fields if needed, up to ten total.
Read the equivalent resistance and review the entered values.

Enter at least two positive resistance values in ohms

Add more resistor fields if needed, up to ten total. When resistors are connected in parallel, they share the same voltage across them but divide the current. The total resistance of parallel resistors is always less than the smallest individual resistor value.

The formula for calculating total resistance in parallel is: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn, where R1, R2, ..., Rn are the individual resistor values.

Method source: OpenStax, Rice University. https://openstax.org/books/university-physics-volume-2/pages/10-2-resistors-in-series-and-parallel

Parallel vs Series Resistors

Property	Series	Parallel
Total Resistance	R_total = R1 + R2 + ... + Rn	1/R_total = 1/R1 + 1/R2 + ... + 1/Rn
Current	Same through all resistors	Divides among resistors
Voltage	Divides among resistors	Same across all resistors
Result	Total R is greater than largest R	Total R is less than smallest R

Worked example

Two 100 Ω resistors in parallel have equivalent resistance 1 ÷ (1/100 + 1/100) = 50 Ω. Each added positive branch lowers the equivalent resistance.

Calculation Tips

For equal positive resistors, N identical branches of resistance R have equivalent resistance R/N. Each added positive branch lowers the total, but a general sequence of different values need not approach zero.

Frequently Asked Questions

Why is parallel resistance always less than the smallest resistor?: For positive resistors, each parallel branch adds a positive reciprocal to the sum, so equivalent resistance falls below the smallest branch value. This says nothing about a fixed zero limit for arbitrary added values.
Can I calculate parallel resistance for more than 10 resistors?: While this calculator supports up to 10 resistors for practical purposes, the formula works for any number of resistors. For more than 10, you can calculate in groups of 10 and then combine the results.
What happens if I connect resistors of very different values in parallel?: The total resistance will be very close to the value of the smallest resistor. For example, if you have a 10Ω resistor in parallel with a 1000Ω resistor, the total will be approximately 9.9Ω – the larger resistor has minimal effect on the total.
How do I calculate parallel resistance for just two resistors?: For two resistors, you can use the simplified formula: R_total = (R1 × R2) / (R1 + R2). This is often called the 'product over sum' formula and is easier to calculate than the reciprocal formula.

Related Calculators

Science

Parallel Resistance Calculator – Calculate Total Resistance

Method

Variables and units

Worked example

Limitations

Sources

How to Use

Enter at least two positive resistance values in ohms

Parallel vs Series Resistors

Worked example

Calculation Tips

Frequently Asked Questions

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