What is the total of parallel resistors?
Type each resistor in its own row, in Ω, kΩ or MΩ. The parallel resistor calculator shows their total resistance; or pick “Resistor to add” to find the resistor that brings the total down to a target.
- Total resistance (Ω)
- 59.976798
With every resistor in parallel, the total resistance is 59.976798 Ω.
- Total conductance (S)
- 0.016673
- Total current (A)
- 0.200077
- Total power (W)
- 2.400928
Total resistance (Ω): 59.976798. With every resistor in parallel, the total resistance is 59.976798 Ω.
How to calculate
Computes the total resistance of resistors in parallel, 1 ÷ (1/R₁ + 1/R₂ + …), or the resistor to add in parallel to reach a target, with the total current and power at a voltage.
Example with the default inputs (Find Total resistance, Resistors in parallel [Resistance 100 Ω; Resistance 220 Ω; Resistance 470 Ω], Voltage (optional) 12 V): With every resistor in parallel, the total resistance is 59.976798 Ω.
Method: Total = 1 ÷ (1/R₁ + 1/R₂ + … + 1/Rₙ); resistor to add = 1 ÷ (1/target − (1/R₁ + … + 1/Rₙ)); current = V ÷ total; power = V² ÷ total.
- The resistors are ideal and all connected between the same two points.
- The voltage is DC, or the RMS value of AC across resistors (no reactance).
- Each resistance is from 1 µΩ to 1 TΩ.
Worked examples
Each example is checked against the calculator on every build.
- Find Total resistance, Resistors in parallel 100; 220; 470 gives Total resistance (Ω) 59.976798, Total conductance (S) 0.016673.Source: OpenStax, University Physics Volume 2, §10.2 Resistors in Series and Parallel, https://openstax.org/books/university-physics-volume-2/pages/10-2-resistors-in-series-and-parallel
- Find Total resistance, Resistors in parallel 1000; 1000, Voltage (optional) 12 V gives Total resistance (Ω) 500, Total current (A) 0.024, Total power (W) 0.288.
- Find Total resistance, Resistors in parallel 10; 20; 30 gives Total resistance (Ω) 5.454545.
- Find Resistor to add, Resistors in parallel 150, Target total 100 Ω gives Resistor to add (Ω) 300.
- Find Total resistance, Resistors in parallel 4.5; 4.5 gives Total resistance (Ω) 2.25.
How it works
- Total resistance: R = 1 ÷ (1/R₁ + 1/R₂ + … + 1/Rₙ), for 1 to 20 resistors.
- Total conductance: G = 1/R₁ + 1/R₂ + … + 1/Rₙ, in siemens.
- Resistor to add (with “Resistor to add”): R = 1 ÷ (1/target − (1/R₁ + … + 1/Rₙ)). The page shows the resistor to add first; the total, with it added, equals the target.
- With a voltage V (12 V by default; clear the box to leave these out): total current = V × G, total power = V² × G.
Resistances can be typed in mΩ, Ω, kΩ or MΩ, and voltages in mV, V or kV; results are in Ω, S, A and W.
Exact arithmetic. Each value is read as the exact decimal you typed, in the unit you typed it in (the page stores it in ohms or volts and reads it back as the decimal with the fewest significant digits, in one of the box's units, that gives the same stored number; on a tie, the unit listed first in the box's unit menu wins). Every step is a fraction, so 4.5 Ω ∥ 4.5 Ω is exactly 2.25 Ω.
Rounding. Results show with at most 6 decimals (6 significant figures below 0.0001), rounded half up from the exact value, with trailing zeros left off. A result shown with 15 or more significant digits (a very large value with its decimals) can differ from the exact value in its last shown digit, because the page keeps results as 64-bit floating-point numbers, which hold about 16 significant digits.
No answer. With “Resistor to add”, a target equal to or above the total of the resistors you have has no answer, because a resistor in parallel only lowers the total: "Adding a resistor in parallel only lowers the total, so the target must be below X Ω.", where X is that total.
Assumptions
- Ideal resistors, all between the same two points.
- DC, or AC RMS values across pure resistance.
- Each resistance from 1 µΩ to 1 TΩ; the voltage from 0 to 1,000 kV.
Worked examples by hand
100 Ω, 220 Ω and 470 Ω. 1/100 + 1/220 + 1/470 = 431/25,850 = 0.016673 S, so the total is 25,850 ÷ 431 = 59.976798 Ω.
Two 1 kΩ resistors at 12 V. 1 ÷ (2/1,000) = 500 Ω; current 12 ÷ 500 = 0.024 A; power 144 ÷ 500 = 0.288 W.
10 Ω, 20 Ω and 30 Ω. 6/60 + 3/60 + 2/60 = 11/60, so the total is 60/11 = 5.454545 Ω.
The resistor to put across 150 Ω for 100 Ω. 1/100 − 1/150 = 1/300, so add 300 Ω.
4.5 Ω and 4.5 Ω. 2/4.5 = 4/9 S, so the total is 2.25 Ω.
Other questions people ask
How do I calculate resistors in parallel?
Add up the reciprocals and take the reciprocal of the sum: 1/R = 1/R₁ + 1/R₂ + … For 100 Ω, 220 Ω and 470 Ω: 1/100 + 1/220 + 1/470 = 0.016673, so R = 1 ÷ 0.016673 = 59.98 Ω.
What is the formula for two resistors in parallel?
For two resistors, R = (R₁ × R₂) ÷ (R₁ + R₂), the product over the sum. For 100 Ω and 220 Ω: 22,000 ÷ 320 = 68.75 Ω. For more than two, use the sum of reciprocals.
Why is the total less than the smallest resistor?
Each resistor in parallel is one more path for the current, so the circuit passes more current at the same voltage and the total resistance falls. The total is always below the smallest resistor. Two equal resistors give half of one: 1 kΩ ∥ 1 kΩ = 500 Ω.
How do I find the resistor to add in parallel?
Subtract the conductance you have from the conductance you want: R = 1 ÷ (1/target − 1/R₁ − …). To bring 150 Ω down to 100 Ω, add 1 ÷ (1/100 − 1/150) = 300 Ω. The target must be below the total you already have.
What current flows through resistors in parallel?
Every resistor has the same voltage across it, so the total current is V ÷ total resistance, and each resistor takes V ÷ its own resistance. Two 1 kΩ resistors at 12 V draw 12 ÷ 500 = 0.024 A (24 mA) together, 12 mA each, and turn 12² ÷ 500 = 0.288 W into heat.
What is conductance?
Conductance is 1 ÷ resistance, measured in siemens (S). In parallel, conductances simply add, which is why the formula adds reciprocals.