Parallel Resistance

1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn

Quick answer

This calculator solves 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn for 1/Rtotal. With Resistor Values 0.47 kΩ, 1.03 kΩ, 2.21 kΩ, the result is 281.6.

Calculator

Result
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Formula

1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn

Description

Parallel resistors share the same voltage across them, and the total resistance is found by the reciprocal of the sum of reciprocals. The result is always less than the smallest individual resistor because each additional path provides more ways for current to flow. For two resistors the shortcut formula Rtotal = (R1 × R2) / (R1 + R2) is often used. Two equal resistors in parallel yield exactly half of one resistor's value.

Variables

  • Rtotal — Total equivalent resistance (Ω)
  • R1, R2, ... Rn — Individual resistor values (Ω)

Practical Notes

Parallel combinations are used to create lower resistance values, increase power handling capacity, and reduce the effective tolerance of a resistor network. In PCB design, parallel resistors are also used as termination networks for high-speed signal lines.

Symbols and units

Symbol Meaning Default unit Accepted units
values Resistor Values Ω mΩ, Ω, kΩ, MΩ

Step by step

  1. 1. What you know: Resistor Values 0.47 kΩ, 1.03 kΩ, 2.21 kΩ
  2. 2. The relation: 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn
  3. 3. Substitute: values = 0.47 kΩ, 1.03 kΩ, 2.21 kΩ
  4. 4. Result: 1/Rtotal = 281.6

Totals for common combinations

Components Values Total
2 0.47 kΩ + 0.47 kΩ 0.235 kΩ
2 0.47 kΩ + 1.03 kΩ 0.3227 kΩ
2 0.47 kΩ + 4.7 kΩ 0.4273 kΩ
3 0.47 kΩ + 0.47 kΩ + 0.47 kΩ 156.7 Ω
3 0.47 kΩ + 1.03 kΩ + 2.21 kΩ 0.2816 kΩ
4 0.47 kΩ + 0.47 kΩ + 0.47 kΩ + 0.47 kΩ 117.5 Ω
4 0.47 kΩ + 1.03 kΩ + 2.21 kΩ + 4.7 kΩ 0.2657 kΩ
5 0.47 kΩ + 0.47 kΩ + 0.47 kΩ + 0.47 kΩ + 0.47 kΩ 94 Ω

Worked examples

Minimum range

Given: Resistor Values 0.47 kΩ, 1.03 kΩ, 2.21 kΩ

Result: 1/Rtotal = 281.6

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Frequently asked questions

How do you calculate Parallel Resistance?

Use 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn. With Resistor Values 0.47 kΩ, 1.03 kΩ, 2.21 kΩ, 1/Rtotal works out to 281.6.

What is the formula for Parallel Resistance?

The formula is 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn. Parallel resistors share the same voltage across them, and the total resistance is found by the reciprocal of the sum of reciprocals.

Related Concepts

All Resistors formulas →
Series Resistance Parallel Resistance LED Resistor Resistor Power Derating Resistive Attenuator Resistor Tolerance Range Resistor Thermal Noise (Johnson–Nyquist) Potentiometer Output

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