Series-parallel resistor network calculator
A 100 Ω resistor, a 220 Ω and 330 Ω parallel pair and a 1 kΩ resistor in series come to 1232 Ω. Describe series and parallel groups nested inside one another and get one equivalent resistance. Free in your browser.
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- Your data stays on your device
Run — free
Worked example
- Network
- [series: 100, [parallel: 220, 330], 1k]
- Equivalent ohms
- 1,232
- Normalized expression
- [series: 100, [parallel: 220, 330], 1000]
- Resistor count
- 4
- Series groups
- 1
This series-parallel resistor network calculator reduces a mixed resistor circuit to one equivalent resistance. Enter the topology as a bracket expression, nesting parallel branches inside series paths or series paths inside parallel branches as required. Values can be written in ohms, kilo-ohms, or mega-ohms. The result includes the equivalent resistance in ohms, a normalized version of the expression, and counts that make it easier to check whether the entire network was interpreted as intended.
Describe the topology with nested groups
A mixed resistor network cannot be represented safely by a flat list because connection order matters. Use a group beginning with [series: when current follows one path through every listed item, and use [parallel: when the listed items form alternative branches between the same two nodes. Separate items with commas and close every group with a square bracket.
A resistor can appear directly as a positive number, while another complete group can occupy the same position as a resistor. For example, [series: 100, [parallel: 220, 330], 1k] describes a 100-ohm resistor, a parallel pair, and a 1-kilo-ohm resistor connected in series. Nesting can continue in either direction, so a branch of a parallel group may itself contain several series resistors.
The calculator requires at least two items in every group because a one-item series or parallel wrapper adds no electrical information and often signals an incomplete expression. Whitespace and capitalization of the group names do not affect the calculation, but commas, colons, and brackets remain part of the grammar and help expose topology mistakes rather than guessing what was intended.
How equivalent resistance is reduced
The calculator evaluates the innermost groups first and works outward until only one resistance remains. For a series group, it adds every member because the same current passes through each resistor and the voltage drops accumulate. For a parallel group, it adds conductances, which are the reciprocals of resistance, and then takes the reciprocal of that total.
This general reciprocal method works for two or more branches and avoids relying on the special product-over-sum shortcut that applies only to two resistors. Every literal is converted to ohms before arithmetic begins: a suffix such as kΩ or kohm multiplies by one thousand, while MΩ or Mohm multiplies by one million. The normalized expression returned in the result shows those converted values and preserves the parsed grouping, providing a useful review step when unit prefixes are mixed.
Values must be finite and greater than zero. A zero-ohm ideal short would require special topology rules and can hide division-by-zero errors, so it is rejected rather than silently approximated.
Check the model before using the result
Equivalent resistance is meaningful only when the bracket expression matches the real circuit nodes. Components drawn near one another are not necessarily in parallel, and resistors are in series only when their shared node has no other current path. Trace the circuit from one terminal to the other, identify the smallest unambiguous series or parallel subnetwork, encode that subnetwork, and then replace it conceptually with its group before moving outward.
The returned resistor count and series and parallel group counts provide quick checks against the schematic. If the expression contains fewer physical resistors than the drawing, a branch may have been omitted; if the group counts seem surprising, review the bracket boundaries. This calculator is intended for networks that can be reduced entirely by successive series and parallel combinations.
Bridge networks, such as a balanced or unbalanced Wheatstone bridge with a cross-connection, are not always reducible through these two operations and require nodal analysis or another circuit method. Also remember that the result is nominal: real components have tolerance, temperature coefficients, and frequency-dependent behavior. Use the equivalent value for design calculations, sanity checks, documentation, or education, then apply component tolerances and power ratings separately where the engineering decision depends on worst-case behavior.
What you can do with it
Reduce a resistor ladder section
Encode reducible ladder stages as nested series and parallel groups and obtain the resistance seen from the selected terminals.
Verify a hand calculation
Compare a manually reduced circuit with a normalized expression, equivalent resistance, and component counts.
Document a design alternative
Record the exact topology and compare combinations of available resistor values without an ambiguous flat formula.
FAQ
What bracket syntax should I use?
Use [series: item, item] or [parallel: item, item]. Each item can be a positive resistance or another complete bracket group.
Which resistance units are accepted?
Bare numbers are ohms. You may also use Ω or ohm, kΩ or kohm, and MΩ or Mohm suffixes. All values are converted to ohms in the result.
Can it calculate a Wheatstone bridge?
Only if the particular circuit can first be reduced into genuine series and parallel groups. A general bridge with a cross-connection needs nodal or mesh analysis.
Why are zero and negative resistance rejected?
This capability models ordinary positive resistors. Zero creates an ideal short requiring separate topology handling, while negative resistance is outside the supported passive-network model.
How are three or more parallel branches combined?
The calculator adds the conductances, the reciprocals of each resistance, and then takes the reciprocal of that total. This works for any number of branches, unlike the product-over-sum shortcut, which only applies to two resistors.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/elec/resistors-mixed \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"network":"[series: 100, [parallel: 220, 330], 1k]"}'const res = await fetch("https://api.kit.forhosting.com/elec/resistors-mixed", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"network": "[series: 100, [parallel: 220, 330], 1k]"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/resistors-mixed",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"network": "[series: 100, [parallel: 220, 330], 1k]"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/resistors-mixed", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"network":"[series: 100, [parallel: 220, 330], 1k]"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"network":"[series: 100, [parallel: 220, 330], 1k]"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/resistors-mixed", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"network": "[series: 100, [parallel: 220, 330], 1k]"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.resistors_mixed",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_chars | 10000 |
max_items | 1000 |
max_depth | 64 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How equivalent resistance is reduced
The calculation is deterministic, uses no external data, and applies stable numeric rounding to keep repeated API and browser results consistent.
Technical questions
How much does an API calculation cost?
Each API request costs $0.002. The same deterministic calculation can also run free in the browser.