How to use the resistor network calculator
- Type the network in the Network box. Use + for resistors in series, || for parallel and brackets to group.
- Write values in ohms, or with k, M or G, such as 4.7k or 2.2M.
- Optionally enter a voltage across the whole network to get the voltage, current and power in every resistor.
- Read the equivalent resistance and the table that labels each resistor R1, R2 and so on in the order they appear.
Formula
Series: R = R1 + R2 + ... + Rn
Parallel: 1 / R = 1 / R1 + 1 / R2 + ... + 1 / Rn
|| binds tighter than +, so 220 || 330 + 100 means (220 || 330) + 100
Total current I = V / R; in series every resistor carries I; in parallel every branch has the full voltage V
Power in a resistor = V x I; the powers add up to V^2 / R
The page reduces the expression from the inside out, then passes the voltage and current back down the tree to reach each resistor.
One bracket, then 12 volts
100 + (220 || 330): the parallel pair is 220 x 330 / 550 = 132 ohm, and adding the 100 ohm in series gives 232 ohm. The structure reads R1 + (R2 || R3).
For 1k + (2.2k || (4.7k + 1k)) the inner series is 5.7 kilohm, the parallel with 2.2 kilohm is 1.58734 kilohm, and the total is 2.58734 kilohm. At 12 V the total current is 4.63796 mA and the total power is 55.6556 mW. R2 sees 7.3620 V and carries 3.3464 mA.
Reading the expression
A resistor network is a tree. Groups joined by + are in series, groups joined by || are in parallel, and brackets let you put a series group inside a parallel one or the other way around. Because parallel binds tighter than series, 100 + 220 || 330 needs no brackets, but adding them makes the intent obvious and costs nothing.
Values can end in k for kilohms, M for megohms or G for gigohms, so 4.7k is 4,700 ohms. The page accepts up to 40 resistors with brackets nested up to 12 levels deep.
Checking a design
Seeing the voltage and power in each resistor lets you check ratings before building a circuit, since a resistor that dissipates more than its rating will overheat. The total power equals the supply voltage squared divided by the equivalent resistance, which the page checks by adding the individual values.
Related tools: the Ohm's law calculator for single resistors, the voltage divider calculator for two-resistor dividers, the resistor pair combination finder for choosing standard values, the resistor color code calculator and the LED resistor calculator.
Assumptions and limits
- Resistors are ideal: exact values, no tolerance, no temperature change and no wire resistance.
- The voltage is a steady DC value across the whole network.
- Every resistor must be greater than 0 ohms. Wires and shorts are not modeled.
- Resistors are labeled in the order they appear in the expression, from left to right.
Frequently asked questions
What does || mean?
It marks two or more resistors connected in parallel, side by side across the same two points. The pair 220 || 330 has an equivalent resistance of 132 ohms, less than either resistor alone.
Why is the parallel result always smaller than the smallest resistor?
Each parallel branch gives current another path, so together they pass more current than any one alone for the same voltage. More current at the same voltage means less resistance.
Can I include a zero-ohm link or a wire?
No. A zero-ohm element would short out its group and leave the voltage split with no meaning, so every resistor must be above 0. Use a very small value such as 0.01 if you need to model a low-resistance link.
Does the order of resistors in series matter?
Not for the total resistance or the current. Each resistor in series carries the same current, so the voltage across each depends only on its own value.