Relative standard deviation
A standard deviation of 2.5 on a mean of 50 is an RSD of 5 %. Enter the two summaries you already hold and get the spread as a percentage of the mean, ready for a precision table or batch review. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Std
- 2.5
- Mean
- 50
- Rsd
- 5
- Rsd percent
- 5
- Cv
- 0.05
Analysts in chemistry, quality control, and assay validation search for this percentage because HPLC software, USP monographs, and method-transfer reports print %RSD, not a unitless coefficient of variation. This calculator accepts the two numbers you already have — a finite standard deviation σ and a non-zero finite mean μ — and returns RSD% = (σ / μ) × 100. It does not re-estimate σ from a raw observation list; if you only have the original measurements, compute the mean and standard deviation first, or use a descriptive-statistics landing built for that list.
What relative standard deviation measures
The relative standard deviation, often written %RSD or RSD%, is the standard deviation expressed as a percentage of the mean. The identity is RSD percent equals sigma divided by mu, then multiplied by one hundred. That single extra division is what turns an absolute spread, which carries the same unit as the data, into a scale-free percentage that you can compare across assays, batches, and instruments.
A six-injection HPLC precision study with a mean peak area of ten thousand and a standard deviation of one hundred has an RSD of one percent; a dissolution result with a mean of fifty milligrams and a standard deviation of two and a half milligrams has an RSD of five percent. Both numbers are the ones that method-validation reports, ICH Q2 style precision tables, and many laboratory information systems already print. This calculator is built for the moment you already hold those two summaries.
You do not paste the raw injection list here. A zero standard deviation with a non-zero mean is accepted and yields an RSD of zero percent, which is the honest statement that every observation equalled the mean. Negative means are accepted; the formula uses the signed mean, so the percentage inherits that sign.
If a local SOP reports the absolute mean in the denominator, take the absolute value of the returned RSD. Pages that compute a coefficient of variation from a raw numeric list, or that return only sigma, answer different queries and must keep their own landings.
Where %RSD is used, precision, and nearby tools
Analytical chemistry is the home of the phrase relative standard deviation. System-suitability tests for chromatography often cap injection precision at a few percent RSD; assay repeatability, intermediate precision, and method-transfer reports quote the same percentage so a reviewer can compare laboratories that work on different absolute scales. Quality-control dashboards convert a batch mean and a batch sigma into %RSD before they decide whether a process is tight enough to release.
Teaching labs ask students to compute %RSD from a given mean and standard deviation so the percentage, not the raw spread, is what appears in the notebook. This capability stays on that two-number path on purpose. It does not parse a CSV of peak areas, choose population versus sample divisors, or fit a distribution.
If you need σ estimated from a raw list, use a standard-deviation or coefficient-of-variation landing; those are different search intents and must not cannibalize this page. Results are rounded to twelve decimal places for stable goldens and cross-engine parity; ordinary laboratory values such as 2.5 over 50, 1.5 over 100, or a zero standard deviation stay exact under that policy. The browser tool is free on the visitor’s device.
What you can do with it
HPLC and assay precision checks
Convert an already-computed injection standard deviation and mean into the %RSD that system-suitability and ICH-style precision tables require.
Homework and method-validation worksheets
Students and reviewers plug σ and μ from a problem statement or a certificate of analysis and confirm the percentage without re-keying the raw list.
FAQ
What happens if the mean is zero?
Relative standard deviation is undefined when the mean is zero because the formula divides by μ. Validation failures are not charged.
Can the standard deviation be zero?
Yes. A zero standard deviation with a non-zero mean means every observation equalled the mean, so RSD% is 0. A negative standard deviation is rejected.
How do I calculate %RSD?
Divide the standard deviation by the mean and multiply by 100. A standard deviation of 2.5 with a mean of 50 gives 0.05, which is an RSD of 5 %.
Can I paste my raw measurements instead?
No. This calculator starts from a standard deviation and a mean that are already computed. If you only have the original readings, work out their mean and standard deviation first, then enter those two numbers here.
What happens if the mean is negative?
It is accepted and the percentage keeps the sign of the mean, so the RSD comes out negative. If your procedure divides by the absolute mean, simply take the absolute value of the result.
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/stat/relative-standard-deviation \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"std":2.5,"mean":50}'const res = await fetch("https://api.kit.forhosting.com/stat/relative-standard-deviation", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"std": 2.5,
"mean": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/stat/relative-standard-deviation",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"std": 2.5,
"mean": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/stat/relative-standard-deviation", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"std":2.5,"mean":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"std":2.5,"mean":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/stat/relative-standard-deviation", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"std": 2.5,
"mean": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "stat.relative_standard_deviation",
"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_abs | 1000000000000 |
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
The relative standard deviation (RSD) expresses spread as a percentage of the mean: divide the standard deviation by the mean and multiply by one hundred. A zero mean is rejected with invalid_input because division by zero would make the percentage undefined. Successful API calls cost $0.002; failed validation is not charged.
What relative standard deviation measures
You type or POST the standard deviation and the mean, and you receive the percentage. The mean must be a non-zero finite number: when mu is exactly zero the ratio is undefined, and the endpoint answers with invalid_input rather than Infinity.
How to call the calculator and read the result
Send two required finite numbers: std for the already-computed standard deviation and mean for the arithmetic mean. Digit strings that parse to finite numbers are allowed so a pasted worksheet value does not need a second conversion. A negative standard deviation is rejected because σ cannot be negative by definition. A mean of exactly zero is rejected with a message that relative standard deviation is undefined when the mean is zero. Aliases sd, standard_deviation, sigma, and s are accepted for the first field; mu, average, and xbar are accepted for the second, so classroom wording and laboratory JSON both work without a rename step. Missing fields, empty strings, the bare tokens plus or minus or a lone decimal point, non-numeric text, NaN, Infinity, objects, and values whose absolute size exceeds one trillion are rejected with invalid_input naming the problem field, and those failures are not billed. On success the JSON echoes std and mean after stable twelve-decimal rounding, reports rsd and the synonymous rsd_percent as (σ / μ) × 100, reports cv as the unitless ratio σ / μ, and restates the identity in the formula field so a client can display it next to the number. Example: std = 2.5 and mean = 50 yield rsd_percent = 5 and cv = 0.05, because two and a half is five percent of fifty. The pair std = 1.5 and mean = 100 yields one and a half percent. Pricing for a successful item is a flat $0.002.
Where %RSD is used, precision, and nearby tools
API requests use prepaid KIT balance at $0.002 per successful item; invalid input does not consume balance.
Integration use cases
Scripts and CI numeric fixtures
Pipelines freeze JSON goldens for %RSD so a refactor cannot change the (σ / μ) × 100 contract or silently accept a zero mean.
Technical questions
How do I calculate relative standard deviation from standard deviation and mean?
RSD% = (σ / μ) × 100. POST the finite standard deviation as std and the non-zero mean as mean (or use the free browser form). The response returns rsd, rsd_percent, and the unitless ratio cv.
Is relative standard deviation the same as the coefficient of variation?
They share the ratio σ / μ. This calculator reports that ratio as cv and the percentage form as rsd_percent. It takes σ and μ as inputs; it does not estimate them from a raw list.
Is the relative standard deviation calculator free?
The in-browser runner uses the same library as the API and costs nothing. API requests use prepaid KIT balance at $0.002 per successful item; invalid input is not billed.