F Critical Value Calculator
With 5 and 10 degrees of freedom and a 0.05 level, you get the F value that leaves 5 % of the distribution in the upper tail. An observed F above it falls in the rejection region, with no printed table needed. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Numerator df
- 5
- Denominator df
- 10
- Significance level
- 0.05
- Critical value
- 3.3258345304
- Tail
- upper
The F critical value calculator returns the cutoff used for an upper-tail F test when you provide numerator degrees of freedom, denominator degrees of freedom, and a significance level. It evaluates the F distribution deterministically and reports the critical value together with the inputs and tail convention, making the result easy to verify, record, or use in a statistical workflow without consulting a printed table.
Enter the degrees of freedom in the correct order
An F distribution is identified by two degrees-of-freedom values, and their order matters. The numerator degrees of freedom describe the variation represented above the fraction bar in the F statistic, while the denominator degrees of freedom describe the variation below it. In an analysis of variance, these values commonly come from the between-group and within-group components.
In a variance-ratio test, they correspond to the samples whose variances appear in the numerator and denominator. Enter each as a whole number of at least one. Reversing them generally produces a different cutoff because the F distribution is asymmetric.
The calculator echoes both values in the result so that a saved answer remains auditable. Confirm the formula used by your test before entering the values, especially when software documentation labels them only as df1 and df2.
Interpret significance as an upper-tail probability
The significance level is the probability left to the right of the returned critical value. For example, a conventional alpha input asks for the point whose upper-tail area equals that alpha. A calculated F statistic greater than the cutoff therefore falls in the rejection region for a standard right-tailed test.
The level must be a finite number strictly between zero and one; percentages should first be expressed as proportions. Smaller significance levels move the cutoff farther into the right tail, while larger levels bring it closer to the main mass of the distribution. Keep the level chosen before viewing results when following a formal hypothesis-testing plan, and report it alongside both degrees of freedom and the observed F statistic.
Use the result in tests, reports, and automated checks
A bounded bisection search makes the calculation deterministic, while a continued-fraction evaluation supplies the cumulative probability. This method avoids a network lookup and gives more flexibility than a printed table, whose rows and columns may cover only a few common degrees of freedom and significance levels. Compare your observed F statistic with the returned upper-tail cutoff using the same numerator and denominator ordering.
Exceeding the cutoff indicates rejection under the usual right-tailed rule; it does not measure effect size, practical importance, or the probability that the null hypothesis is true. Retain the complete output when building an audit trail because it records the inputs and tail convention next to the answer. Results use standard floating-point arithmetic, so applications that require certified numerical tolerances should define their rounding and verification policy explicitly.
What you can do with it
Check an ANOVA cutoff
Find the upper-tail F threshold associated with the model and residual degrees of freedom before comparing an observed test statistic.
Automate variance-test decisions
Generate a reproducible cutoff inside a reporting or quality-control workflow without maintaining a static F table.
Verify statistical software output
Recalculate a reported critical value from df1, df2, and alpha to confirm the tail convention and parameter order.
FAQ
What tail does this calculator use?
It returns an upper-tail critical value: the probability above the cutoff equals the supplied significance level.
Should I enter five percent as 5 or 0.05?
Enter significance as a proportion, so five percent is 0.05. The value must be strictly between zero and one.
Does reversing numerator and denominator degrees of freedom matter?
Yes. The F distribution is asymmetric, so swapping df1 and df2 usually changes the critical value.
How do I use the F critical value in my test?
Compare your observed F statistic with the cutoff, keeping the same order of numerator and denominator. If your F is larger, it falls in the rejection region of a standard right-tailed test.
Can I get a lower-tail or two-sided F critical value?
No. The result is always the upper-tail cutoff. A lower-tail or two-sided variance test needs additional reasoning and cannot be obtained by simply relabeling the same number.
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/f-critical-value \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"numerator_df":5,"denominator_df":10,"significance_level":0.05}'const res = await fetch("https://api.kit.forhosting.com/stat/f-critical-value", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"numerator_df": 5,
"denominator_df": 10,
"significance_level": 0.05
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/stat/f-critical-value",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"numerator_df": 5,
"denominator_df": 10,
"significance_level": 0.05
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/stat/f-critical-value", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"numerator_df":5,"denominator_df":10,"significance_level":0.05}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"numerator_df":5,"denominator_df":10,"significance_level":0.05}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/stat/f-critical-value", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"numerator_df": 5,
"denominator_df": 10,
"significance_level": 0.05
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "stat.f_critical_value",
"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.
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
Enter the degrees of freedom in the correct order
If either value is zero, negative, fractional, missing, or otherwise invalid, the request is rejected rather than silently rounded. That strict behavior helps prevent a plausible-looking critical value from being attached to the wrong sampling distribution.
Interpret significance as an upper-tail probability
The endpoint treats significance_level and its alpha alias identically, but the canonical result always names significance_level and explicitly reports the tail as upper. This convention matters because a lower-tail or two-sided variance test requires additional reasoning and cannot be obtained merely by relabeling the same number.
Use the result in tests, reports, and automated checks
The returned critical_value is computed by inverting the regularized incomplete beta representation of the F cumulative distribution. The browser calculation is free, while an API request uses the published $0.002 base price.
Technical questions
Can degrees of freedom be zero or fractional?
No. Both degrees-of-freedom inputs must be whole numbers of at least one; invalid values produce an invalid_input error.
How much does an API calculation cost?
Each API request uses the $0.002 base price. The same deterministic calculation can run free in the browser.