How to calculate resistors in parallel
Resistors are in parallel when each one connects across the same two points, so every resistor has the same voltage across it. This calculator works out the total (equivalent) resistance of any number of parallel resistors and, for the source voltage you enter, the current and power in each of them. The circuit drawing follows every value you type: each resistor shows its colour bands, current, power and share of the current; past eight resistors the drawing shows the first few and the last two, with a ⋯ branch standing for the rest.
How to use the parallel resistor calculator
- Enter the source voltage. It is the same across every resistor. Leave it at 0 V if you only need the total resistance.
- Choose how many resistors with the + and − buttons or by typing the number: 2, 10, 100, anything up to 500.
- Type each resistance. Write values the way they appear on parts and schematics: 4700, 4.7k,
4k7,470R, 2.2M or2M2. A lower-case m means milli and a capital M means mega. - Read the results under the drawing: total resistance, total current, total power and total conductance. Click a resistor in the drawing to edit it.
- Open the Results table for each resistor's conductance, current, share of the current, power and a suggested power rating, or use Copy results to paste them into notes or a spreadsheet.
The parallel resistance formula
In a parallel circuit the voltage is shared and the currents add up. Each resistor passes I = V/R, so the source supplies V/R1 + V/R2 + … + V/Rn. Dividing that by V gives the formula for the equivalent resistance:
1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4
Your 4 resistors 1/Req = 1/1 kΩ + 1/2.2 kΩ + 1/4.7 kΩ + 1/10 kΩ = 1.767 mS, so Req = 565.8 Ω.
The reciprocal of a resistance, 1/R, is its conductance, measured in siemens (S). In parallel, conductances simply add, and the total resistance is the reciprocal of the total conductance.
Two resistors: product over sum
Req = (R1 × R2) / (R1 + R2)
For 4.7 kΩ and 10 kΩ: (4.7 × 10) / (4.7 + 10) kΩ = 3.197 kΩ. For three or more resistors, combine two at a time or use the full formula above.
Your R1 and R2 (1 kΩ × 2.2 kΩ) / (1 kΩ + 2.2 kΩ) = 687.5 Ω; adding the other 2 brings it down to 565.8 Ω.
Equal resistors
Req = R / n
Two 10 kΩ resistors give 5 kΩ, and ten 470 Ω resistors give 47 Ω. Equal resistors also share the power equally, so ten ¼ W resistors in parallel can together handle about 2.5 W.
Current and power in each resistor
Every branch has the full source voltage across it, so its current and power depend only on its own resistance:
Ik = V / Rk Pk = V² / Rk
The smallest resistor carries the largest current and gets the hottest. Its share of the total current is its conductance divided by the total conductance; this is the current divider rule, Ik = Itotal × Req / Rk.
Your circuit, step by step
This section follows the values panel: 4 resistors across 12 V.
- Find each conductance, G = 1/R: G1 = 1/1 kΩ = 1 mS; G2 = 1/2.2 kΩ = 455 µS; G3 = 1/4.7 kΩ = 213 µS; G4 = 1/10 kΩ = 100 µS.
- Add them: G = 1 mS + 455 µS + 213 µS + 100 µS = 1.767 mS.
- Take the reciprocal: Req = 1 / 1.767 mS = 565.8 Ω, which is 57% of the smallest resistor (R1).
- Total current: I = V / Req = 12 V / 565.8 Ω = 21.21 mA, and the source delivers P = V × I = 254.5 mW.
- Each resistor has the full 12 V across it, so I = V / R and P = V² / R:
| Resistor | Current I = V / R | Power P = V² / R | Share |
|---|---|---|---|
| R1 = 1 kΩ | 12 mA | 144 mW | 57% |
| R2 = 2.2 kΩ | 5.45 mA | 65.5 mW | 26% |
| R3 = 4.7 kΩ | 2.55 mA | 30.6 mW | 12% |
| R4 = 10 kΩ | 1.2 mA | 14.4 mW | 5.7% |
| Total: 565.8 Ω | 21.2 mA | 254 mW | 100% |
Worked example: 4.7 kΩ, 10 kΩ and 22 kΩ at 12 V
Add the conductances: 1/4.7 kΩ + 1/10 kΩ + 1/22 kΩ = 358.2 µS. The total resistance is the reciprocal, Req = 2.792 kΩ, less than the smallest resistor as always. The source then supplies 12 V / 2.792 kΩ = 4.3 mA, and the circuit uses 51.6 mW in total.
| Resistor | Conductance | Current | Share | Power |
|---|---|---|---|---|
| R1 = 4.7 kΩ | 213 µS | 2.55 mA | 59% | 30.6 mW |
| R2 = 10 kΩ | 100 µS | 1.2 mA | 28% | 14.4 mW |
| R3 = 22 kΩ | 45.5 µS | 545 µA | 13% | 6.55 mW |
| Total: 2.792 kΩ | 358 µS | 4.3 mA | 100% | 51.6 mW |
The branch currents add up to the source current, which is a quick way to check any parallel calculation.
Good to know
- The total is always below the smallest resistor. Adding any resistor in parallel, however large, lowers the total a little more.
- A much smaller resistor dominates. 100 Ω in parallel with 1 MΩ is still about 99.99 Ω.
- A 0 Ω branch is a short circuit. It would take all the current, which is why the calculator needs values above 0 Ω.
- Tolerance carries through. Real resistors are within 5% (four bands) or 1% (five bands) of their marked value, so the measured total varies by about the same amount.
- Mind the power rating. Choose resistors rated for at least about twice the power they dissipate; the Results table suggests a standard rating for each one.
Resistor colour codes in the drawing
Each resistor in the drawing carries the colour bands its value would have. Values with two significant digits, such as 4.7 kΩ (yellow, violet, red), get four bands: two digits, a multiplier and a gold 5% tolerance band, on a beige body. Values that need three digits, such as 4.12 kΩ, get five bands with a brown 1% tolerance band, on a blue body like metal-film resistors. Values needing more digits, or below 0.1 Ω, are drawn plain grey because no standard colour code shows them.
Questions
Is the total resistance in parallel always smaller?
Yes. The total conductance is the sum of every branch's conductance, so it is larger than any single branch's, and the total resistance is therefore smaller than the smallest resistor.
Does the voltage change the total resistance?
No. For ordinary resistors the equivalent resistance depends only on the resistances. The voltage sets how much current flows and how much power each resistor turns into heat.
How do I make a value I don't have?
Put standard values in parallel: two 10 kΩ make 5 kΩ, 1 kΩ with 1 kΩ makes 500 Ω, and 220 Ω with 330 Ω makes 132 Ω. Type the combination here to check it before you solder.
What is the difference between series and parallel?
In series the same current flows through every resistor and the resistances add (Req = R1 + R2 + …). In parallel every resistor has the same voltage and the conductances add, which always gives less than the smallest resistor.