56.8966
Ω
0.056897
kΩ
0.210909
A
0.12
A
0.054545
A
0.036364
A
2.5309
W
56.8966
Ω
0.056897
kΩ
0.210909
A
0.12
A
0.054545
A
0.036364
A
2.5309
W
The Resistors in Parallel Calculator determines the equivalent resistance of resistors connected side by side, sharing the same two nodes. For parallel resistors, the reciprocal of the total resistance equals the sum of the reciprocals:
$$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots + \frac{1}{R_n}$$
Or equivalently for three resistors:
$$R_T = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}}$$
A key property of parallel resistance is that the total is always less than the smallest individual resistor. Adding more parallel paths always reduces the equivalent resistance because you are providing additional paths for current to flow.
In a parallel circuit, the voltage across all branches is identical (equal to the supply voltage), while the current divides among branches inversely proportional to their resistance. The branch with the lowest resistance carries the most current:
$$I_k = \frac{V}{R_k}$$
The total current is the sum of all branch currents, consistent with Kirchhoff's Current Law (KCL). This current division principle is used to design current splitters, bias networks, and load-sharing circuits.
For the special case of two resistors in parallel, the formula simplifies to the "product over sum" rule:
$$R_T = \frac{R_1 \times R_2}{R_1 + R_2}$$
Parallel resistor networks are ubiquitous in electronics: household wiring uses parallel connections so each outlet receives full voltage, transistor bias circuits use parallel resistor pairs, and precision resistor networks combine multiple values to achieve tight tolerances.
This calculator handles three parallel resistors and optionally computes branch currents and total power when a supply voltage is provided. For fewer resistors, note that setting a resistor to an extremely high value (e.g., 999999999 Ω) effectively removes it from the calculation.
Enter up to three parallel resistor values. The calculator computes 1/R_T = 1/R₁ + 1/R₂ + 1/R₃ and inverts to find the total equivalent resistance. If a supply voltage is provided, it also calculates individual branch currents (I_k = V/R_k), total current, and total power dissipation (P = V²/R_T).
The total parallel resistance is always less than the smallest individual resistor. If the result seems too low, verify that you intended parallel (not series) connection. The lowest-value resistor carries the most current and dissipates the most power — ensure it is adequately rated.
Inputs
Results
Two 1 kΩ resistors in parallel: R_T = 1000/2 = 500 Ω (half of each). Current splits equally: 10 mA each, 20 mA total. This is a quick way to halve resistance.
Inputs
Results
R_T = 1/(1/100 + 1/220 + 1/330) ≈ 56.9 Ω — less than the smallest (100 Ω). R₁ carries the most current (120 mA) because it has the lowest resistance.
Each parallel branch provides an additional path for current. More paths mean less total opposition to flow. Mathematically, adding any positive term to 1/R₁ in the sum 1/R_T = 1/R₁ + 1/R₂ + ... makes 1/R_T larger, so R_T must be smaller than R₁.
For exactly two resistors in parallel: R_T = (R₁ × R₂)/(R₁ + R₂). This shortcut avoids dealing with reciprocals. For example, 100 Ω and 200 Ω in parallel: R_T = (100 × 200)/(100 + 200) = 20000/300 = 66.67 Ω.
For N identical resistors of value R: R_T = R/N. Two 100 Ω resistors in parallel give 50 Ω, three give 33.3 Ω, ten give 10 Ω. This is an easy way to achieve precise low-value resistances from higher-value standard components.
Current divides inversely proportional to resistance. The branch current is I_k = V/R_k. The lowest resistance branch carries the most current. All branch currents sum to the total current (Kirchhoff's Current Law).
Unlike series circuits, the remaining parallel branches continue to function. The total resistance increases (less parallel paths), and the remaining branches carry more total current. This is why household wiring uses parallel connections — one failed device doesn't affect others.
For more than three resistors, calculate the parallel combination of three, then combine that result in parallel with additional resistors. Alternatively, sum all the reciprocals: 1/R_T = 1/R₁ + 1/R₂ + ... + 1/Rₙ and invert.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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