Parallel & Series Resistor Calculator
Total resistance in series and parallel, current sharing, the partner resistor for a target value, and E12/E24/E96 pairs for values not in the series.
Formulas
- Series: R = R1 + R2 + … + Rn (same current, voltage divides)
- Parallel: 1/R = 1/R1 + 1/R2 + … + 1/Rn (same voltage, current divides)
- Two in parallel: R = R1 × R2 ÷ (R1 + R2); n equal values: R ÷ n
- Current share in parallel: Ik ÷ I = R ÷ Rk (more through the smaller)
- Partner: parallel R2 = R1 × Rt ÷ (R1 − Rt); series R2 = Rt − R1
Common parallel values
| Parallel | Total |
|---|---|
| 10 kΩ ∥ 10 kΩ | 5 kΩ |
| 10 kΩ ∥ 4.7 kΩ | 3.197 kΩ |
| 1 kΩ ∥ 1 kΩ ∥ 1 kΩ | 333.3 Ω |
| 120 Ω ∥ 120 Ω | 60 Ω |
| 100 kΩ ∥ 10 kΩ | 9.091 kΩ |
6.04 kΩ from two E24 values
The top three ways to make 6.04 kΩ (an E96 value) from two E24 values, computed by this page.
| Combination | Value | Error |
|---|---|---|
| 6.2 kΩ ∥ 240 kΩ | 6.044 kΩ | +0.06 % |
| 9.1 kΩ ∥ 18 kΩ | 6.044 kΩ | +0.07 % |
| 6.2 kΩ ∥ 220 kΩ | 6.03 kΩ | -0.16 % |
How to read it
- A parallel total is always below the smallest resistor and a series total above the largest, so parallel is for going down and series for going up.
- In parallel a large resistor changes the total only a little: 1 MΩ across 10 kΩ gives about 9.90 kΩ (−1 %), useful for trimming.
- Each resistor takes its own share of power. In series (same current) the larger one dissipates more; in parallel (same voltage) the smaller one does (P = I²R, P = V²/R).
Where it is used
- When the value you need is not in the series (dividers, current sensing, ADC references), join two. For a divider where the ratio matters, the Voltage Divider Calculator's pairs fit directly.
- If a device's built-in 120 Ω RS-485 terminator and an external one are both on, you get 120 ∥ 120 = 60 Ω — the value to look for when terminations overlap.
- To share power in a shunt or current-limiting resistor, use n equal values in parallel: the total is R ÷ n and each takes 1/n of the power.
FAQ
What is the formula for two resistors in parallel?
R = R1 × R2 ÷ (R1 + R2). For 10 kΩ and 4.7 kΩ: 47,000,000 ÷ 14,700 ≈ 3.197 kΩ. For three or more, add the reciprocals and take the reciprocal.
What do two equal resistors in parallel give?
Half the value (10 kΩ ∥ 10 kΩ = 5 kΩ). n equal values give R ÷ n.
How do I make a value that is not a standard value?
Join two standard values in series or parallel. «Two standard values» above lists E12, E24 or E96 pairs by error. If one standard value is already close enough, that is simpler.
What do 4k7 and 2M2 mean?
The unit letter stands where the decimal point goes: 4k7 = 4.7 kΩ, 2M2 = 2.2 MΩ, 0R47 = 0.47 Ω. This calculator reads that notation too.
For pairs that set a divider ratio, use the Voltage Divider Calculator. For an LED current-limiting resistor, use the LED Resistor Calculator.
Basis
Series and parallel totals and the partner value are computed from circuit definitions (Ohm's and Kirchhoff's laws). E12, E24 and E96 values come from Vishay document 28372 (the IEC 60063 tables), shared with the Voltage Divider Calculator.