# Series and parallel resistor calculator

> Series and parallel resistor calculator: total resistance of any number of resistors, plus capacitors or inductors in series or parallel.

操作できるページ：https://www.calcopenly.com/ja/science/series-parallel-calculator
分野：科学の計算機

Resistors add in series, R = R₁ + R₂ + …, while in parallel their reciprocals add, 1/R = 1/R₁ + 1/R₂ + … . Inductors follow the same two rules when their magnetic fields do not interact. Capacitors do the opposite: they add in parallel and combine by reciprocals in series. Enter any number of values in one unit; 4.7k is read as 4,700.

The default, 100 Ω, 220 Ω and 470 Ω in parallel, gives 59.98 Ω, below the smallest part as every parallel network must be; the same three in series give 790 Ω. Combining parts is how a value outside the E-series is built, such as 500 Ω from two 1 kΩ resistors in parallel.

The parts are treated as ideal: no lead or contact resistance, no capacitor leakage and no mutual inductance between coils.

## 入力

- **Components** (選択肢：Resistors, Capacitors, Inductors)
- **Connected in** (選択肢：Series, Parallel)
- **Values**: Separate with commas or spaces; 4.7k works for kilo
- **単位** (選択肢：mΩ, Ω, kΩ, MΩ)
- **単位** (選択肢：pF, nF, µF, mF, F)
- **単位** (選択肢：nH, µH, mH, H)

## 結果

- Equivalent value — 主な結果
- In base units
- Number of components

## 計算式

$$
\text{Series: } R = \sum R_i,\ L = \sum L_i,\ \tfrac1C = \sum \tfrac1{C_i}\qquad \text{Parallel: } \tfrac1R = \sum \tfrac1{R_i},\ \tfrac1L = \sum \tfrac1{L_i},\ C = \sum C_i
$$

## 計算例

### 100, 220, 470 Ω in series

- Components: Resistors
- Connected in: Series
- Values: 100, 220, 470
- 単位: Ω
- **Equivalent value: 790 Ω**
- 照合元：Python 3.8 decimal: 100 + 220 + 470

### 100, 220, 470 Ω in parallel

- Components: Resistors
- Connected in: Parallel
- Values: 100, 220, 470
- 単位: Ω
- **Equivalent value: 59.9768 Ω**
- 照合元：Python 3.8 fractions: 1/(1/100 + 1/220 + 1/470) = 25850/431 = 59.976798…

### Two equal 1 kΩ in parallel

- Components: Resistors
- Connected in: Parallel
- Values: 1k 1k
- 単位: Ω
- **Equivalent value: 500 Ω**
- 照合元：R/n for n equal resistors (OpenStax UP2 §10.2)

### Three 100 nF in parallel

- Components: Capacitors
- Connected in: Parallel
- Values: 100 100 100
- 単位: nF
- **Equivalent value: 300 nF**
- 照合元：Sum: 300 nF

### 10 µF and 22 µF in series

- Components: Capacitors
- Connected in: Series
- Values: 10, 22
- 単位: µF
- **Equivalent value: 6.875 µF**
- **In base units: 6.875 × 10⁻⁶ F**
- 照合元：Python 3.8 fractions: 1/(1/10 + 1/22) = 6.875 µF

### 10 mH and 4.7 mH in series

- Components: Inductors
- Connected in: Series
- Values: 10, 4.7
- 単位: mH
- **Equivalent value: 14.7 mH**
- **In base units: 1.47 × 10⁻² H**
- 照合元：Sum: 14.7 mH (no mutual coupling)

## よくある質問

### How do you calculate resistors in parallel?

Add the reciprocals and invert: 1/R = 1/R₁ + 1/R₂ + … . For two resistors this reduces to product over sum, R = R₁R₂/(R₁ + R₂), so 100 Ω and 220 Ω in parallel give 22,000/320 = 68.75 Ω. The total is always smaller than the smallest resistor, because each extra path carries more current.

### What is the resistance of equal resistors in parallel?

Divide one resistor's value by the number of resistors: n equal resistors R in parallel give R/n. Two 1 kΩ resistors give 500 Ω and four 100 Ω resistors give 25 Ω. They share the current equally, so the power ratings add too: four ¼ W resistors in parallel can dissipate 1 W between them.

### How do you add capacitors in series and in parallel?

In parallel, capacitances add directly: three 100 nF capacitors give 300 nF. In series, the reciprocals add, 1/C = 1/C₁ + 1/C₂, so 10 µF and 22 µF give 6.875 µF, less than the smaller part. Series capacitors carry the same charge, so the smaller capacitor takes the larger share of the voltage.

### Do inductors add like resistors?

Yes, when their magnetic fields do not couple: L = L₁ + L₂ in series and 1/L = 1/L₁ + 1/L₂ in parallel, so 10 mH and 4.7 mH in series give 14.7 mH. Coils that share flux add or subtract a mutual-inductance term of 2M in series, depending on winding direction, which this calculator does not model.

### 「Series and parallel resistor calculator」の精度はどのくらいですか？

精度は入力値と計算方法の前提に依存します。十進演算には有効数字50桁を使いますが、推定、数値計算手法、元データの精度はそれより低い場合があります。表示の丸め処理でこれらの制約がなくなるわけではありません。 独立した出典の解答と照合した計算例：7。 例えば、「100, 220, 470 Ω in series」はPython 3.8 decimal: 100 + 220 + 470と照合しています。

### この計算方法の出典は何ですか？

OpenStax University Physics Volume 2, §10.2 Resistors in series and parallel; §8.2 Capacitors in series and in parallel; HyperPhysics — Inductors in series and parallel (no mutual inductance).

## 出典

- [OpenStax University Physics Volume 2, §10.2 Resistors in series and parallel; §8.2 Capacitors in series and in parallel](https://openstax.org/books/university-physics-volume-2/pages/10-2-resistors-in-series-and-parallel)
- [HyperPhysics — Inductors in series and parallel (no mutual inductance)](http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indcom.html)