# Parallel Resistance Calculator

Contents

## SI Prefixes

You should know these. If you don’t, you need to learn them.

Prefix Symbol Value
pico– p 10−12 = 0.000 000 000 001
nano– n 10−9 = 0.000 000 001
micro– µ 10−6 = 0.000 001
milli– m 10−3 = 0.001
kilo– k 103 = 1 000
mega– M 106 = 1 000 000
giga– G 109 = 1 000 000 000
tera– T 1012 = 1 000 000 000 000

## Resistors in Series

The formula for calculating the total resistance for resistors in series is fairly straightforward.

Rtotal = R1 + R2 + R3 + … + Rn

For example, if you have three resistors with values 330 Ω, 47 kΩ, and 1 kΩ, you can calculate Rtotal like this:

Rtotal = 330 Ω + 47000 Ω + 1000 Ω = 48330 Ω or 48.33 kΩ

## Resistors in Parallel

The formula for calculating the total resistance for resistors in parallel is a little more complicated.

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

Step 1: We need to clear all the fractions by multiplying by the lowest common denominator, which is (Rtotal × R1 × R2). Multiplying both sides by the lowest common denominator, we get

(Rtotal × R1 × R2) × (1 / Rtotal) = (1 / R1 + 1 / R2) × (Rtotal × R1 × R2)

Step 2: Using the distributive property (I bet you wish you had paid attention in math class), we get

(Rtotal × R1 × R2) / Rtotal = (Rtotal × R1 × R2) / R1 + (Rtotal × R1 × R2) / R2

Step 3: Simplifying the equation, we get

(Rtotal × R1 × R2) / Rtotal = (Rtotal × R1 × R2) / R1 + (Rtotal × R1 × R2) / R2

Which is the same as

R1 × R2 = Rtotal × R2 + Rtotal × R1

Step 4: Collecting all the R1 terms on the left side of the equal sign we get

R1 × R2 − Rtotal × R1 = Rtotal × R2

Which is the same as

R1 × (R2 − Rtotal) = Rtotal × R2

Step 5: Dividing both sides by (R2 − Rtotal) we get

R1 = (R2 × Rtotal) / (R2 − Rtotal)

Using the same method we get

R2 = (R1 × Rtotal) / (R1 − Rtotal)

Step 6: Back at step 3 we had

R1 × R2 = Rtotal × R2 + Rtotal × R1

Using the distributive property, we get

R1 × R2 = Rtotal × (R2 + R1)

Step 7: Divide both sides by (R2 + R1) and we get

(R1 × R2) / (R2 + R1) = Rtotal

Which is the same as

Rtotal = (R1 × R2) / (R1 + R2)

So when we have a circuit with two resistors in parallel, our three formulas for calculating the values of R1, R2, or Rtotal when we have two of the three values are

Rtotal = (R1 × R2) / (R1 + R2)

R1 = (R2 × Rtotal) / (R2 − Rtotal)

R2 = (R1 × Rtotal) / (R1 − Rtotal)

That is a lot of work to do by hand. Fortunately, we have the computer do the work for us. In the next section we have a parallel resistance calculator for circuits with two parallel resistors.

## Parallel Resistance Calculator for Two Resistors

To use the calculator, enter a resistor value in two of the three boxes. The third value of the parallel circuit will be calculated.

For example, you could enter values for R1 and R2 and have Rtotal calculated. Or you could enter Rtotal and R1 and have R2 calculated. Or you could enter Rtotal and R2 and have R1 calculated.

The drop-down list allows you to set the unit of measurement for R1, R2, and Rtotal. You can choose µΩ (microohm), mΩ (milliohm), Ω (ohm), kΩ (kiloohm), or MΩ (megaohm).

 Resistor R1 µΩ (microohm)mΩ (milliohm)Ω (ohm)kΩ (kiloohm)MΩ (megaohm) Resistor R2 µΩ (microohm)mΩ (milliohm)Ω (ohm)kΩ (kiloohm)MΩ (megaohm) Parallel Resistance Rtotal µΩ (microohm)mΩ (milliohm)Ω (ohm)kΩ (kiloohm)MΩ (megaohm)

Coming soon…