Parallel resistance calculator
Two 10 Ω resistors in parallel give 5 Ω, and three 100 Ω resistors give about 33.3 Ω. Enter the value of each branch to get the single equivalent resistance, rounded to the decimals you choose. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Resistors
- 10, 10
- Quantity
- 2 ohm
- Equivalent
- 5
- Reciprocal sum
- 0.2
- Precision
- 10
This parallel resistance calculator returns the single equivalent resistance of two or more resistors connected in parallel. The governing identity is one over Req equals the sum of one over each branch resistance, so Req equals one divided by the sum of the individual conductances. Parallel paths lower the total resistance: two equal resistors of value R combine to R over two, and n equal resistors of value R combine to R over n. Classic checks you may already know include ten ohms in parallel with ten ohms giving five ohms, one hundred ohms with one hundred ohms and one hundred ohms giving about thirty-three point three ohms, and a lone resistor leaving Req equal to that single value. The engine uses only finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
Parallel resistance explained, and how to read the result
Resistors in parallel share the same voltage across every branch while the total current splits among the paths. The combined effect is a lower equivalent resistance than the smallest branch, because more paths increase overall conductance. Algebraically the rule is one over Req equals the sum of one over each Ri, which is exactly the sum of conductances Gi equals one over Ri.
A single positive resistor is valid and simply echoes that value as the equivalent, which matches the limit case of the same formula. Negative resistance is also rejected because this tool models ordinary ohmic branches only. There is no series mode, no reactive impedance, and no Monte Carlo sampling: the engine either evaluates the closed form inside the supported numeric range or rejects the input.
Where parallel Req checks fit in study, design, and software
Students meet parallel resistance when a circuit unit introduces branch currents, when a lab asks for the ohmmeter reading across a parallel network, or when a contest problem gives several ohm values and asks for the single equivalent without a full SPICE run. Teachers can pre-generate answer keys for modest resistor sets without trusting opaque calculator apps that silently mix kilo-ohms with ohms or switch notation without saying so.
Developers call the same contract from scripts to seed deterministic test vectors for breadboard planners, to normalize user-entered load networks before a bill-of-materials sketch, or to satisfy programming-challenge statements that demand Req rather than a hand-waved estimate. Field technicians and makers use it for quick checks on LED current-limit networks, pull-up combinations, and sensor dividers when only discrete resistor values are known.
What you can do with it
Homework and lab checks
Compute Req for parallel resistor networks before grading worksheets or DC lab write-ups.
Design and education software
Normalize user-entered branch resistances into a single Req for planners, tutors, and interactive circuit lessons.
FAQ
What does the parallel resistance calculator cost?
It is free in your browser on this page.
What formula is used for Req?
Two equal resistors of value R give R/2.
What happens if a resistance is zero?
A zero ohm branch is an ideal short and makes the 1/R term in the parallel formula undefined in this tool.
Does this tool also compute series resistance?
No. It only evaluates the parallel combination. Series equivalent resistance is the ordinary sum of the branch values.
Why are results rounded to a precision?
Default precision is 10 decimal places; you can set precision from 0 to 15.
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-parallel \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"resistors":[10,10]}'const res = await fetch("https://api.kit.forhosting.com/elec/resistors-parallel", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"resistors": [
10,
10
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/resistors-parallel",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"resistors": [
10,
10
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/resistors-parallel", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"resistors":[10,10]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"resistors":[10,10]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/resistors-parallel", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"resistors": [
10,
10
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.resistors_parallel",
"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_n | 1000 |
max_abs_ohm | 1000000000000000 |
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
Any zero resistance is rejected with invalid_input, because a zero ohm branch is an ideal short and makes the reciprocal term undefined in the standard parallel formula used here.
What parallel resistance means and what the response contains
This calculator accepts a list of positive resistance values and returns the normalized resistor array, the count of branches, the equivalent resistance rounded to the requested precision, the reciprocal sum used as an intermediate, a short formula reminder, the method tag parallel_conductance, the precision used, and a unit hint of ohm for SI-consistent inputs. Zero resistance is never accepted: an ideal short would force the parallel combination toward zero ohms and would require a reciprocal of zero in the summation, so the request fails with invalid_input and a message that names the zero problem.
How resistor lists are read and how Req stays reproducible
A comma or whitespace separated string is also accepted and split into the same numeric list. Each entry must be a positive finite decimal within the documented magnitude ceiling; embedded spaces inside a token, hex prefixes, and non-numeric junk are rejected with a clear message so a bad cell does not become a wrong equivalent. Zero and near-zero values fail explicitly because the parallel formula divides by each Ri. The preferred field is resistors, an array of finite numbers in ohms or any consistent unit, but aliases values, R, resistances, ohms, and list are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Empty arrays fail with invalid_input, and lists longer than the declared maximum count are rejected before any arithmetic runs. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for the resistor list, the equivalent, and the reciprocal sum, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing conductance sums yourself.
Where parallel Req checks fit in study, design, and software
Product and education tools use the endpoint when a learner types a list of branch resistances and the UI must show the parallel equivalent and the reciprocal sum. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with power or series helpers when you need related electrical steps, and with other math endpoints when you are building a small lab of free, deterministic circuit calculators for study and software tests.
Integration use cases
Deterministic test fixtures
Generate reproducible parallel equivalents for unit tests, breadboard demos, and CI assertions on 1/Req = Σ(1/Ri).