# F-Test / F-Distribution Calculator API

> For the complete documentation index, see [llms.txt](/llms.txt).

Compare two variances with an F test, or turn an F statistic into a p-value and critical values.

Use this endpoint to add the tool to your app, site, workflow, or agent without rebuilding formulas, validation, examples, and docs.

- Slug: `f-test-f-distribution-calculator`
- Category: `math`
- Version: `2026-04-22`
- Credits per successful call: 1
- Starts on: free
- Max payload: 65536 bytes
- Privacy mode: `hash_only`
- Available on: free, starter, pro, business, scale
- Browser tool: https://miniwebtool.com/f-test-f-distribution-calculator/

## Endpoint

`POST https://api.miniwebtool.com/v1/tools/f-test-f-distribution-calculator/run`

## Request body

| Field | Type | Required | Description |
| --- | --- | --- | --- |
| `mode` | `str` | no | variances | samples | statistic Choices: variances, samples, statistic |
| `sd_1` | `float` | no | sample 1 standard deviation (variances mode) |
| `sd_2` | `float` | no | sample 2 standard deviation (variances mode) |
| `n_1` | `int` | no | sample 1 size (variances mode) |
| `n_2` | `int` | no | sample 2 size (variances mode) |
| `sample_1` | `str` | no | comma-separated data (samples mode) |
| `sample_2` | `str` | no | comma-separated data (samples mode) |
| `f_value` | `float` | no | F statistic (statistic mode) |
| `df_1` | `int` | no | numerator degrees of freedom (statistic mode) |
| `df_2` | `int` | no | denominator degrees of freedom (statistic mode) |
| `alpha` | `float` | no | significance level |
| `tail` | `str` | no | two | right Choices: two, right |

## Example request

```json
{
  "mode": "variances",
  "sd_1": 12.5,
  "sd_2": 8.4,
  "n_1": 25,
  "n_2": 20,
  "alpha": 0.05,
  "tail": "two"
}
```

## cURL

```bash
curl -X POST https://api.miniwebtool.com/v1/tools/f-test-f-distribution-calculator/run \
  -H 'Authorization: Bearer mwt_live_YOUR_KEY' \
  -H 'Content-Type: application/json' \
  -d '{"mode":"variances","sd_1":12.5,"sd_2":8.4,"n_1":25,"n_2":20,"alpha":0.05,"tail":"two"}'
```

## Response envelope

```json
{
  "request_id": "01K...",
  "tool": "f-test-f-distribution-calculator",
  "tool_version": "2026-04-22",
  "credits_used": 1,
  "result": {}
}
```

## Errors

Errors are RFC 7807 `application/problem+json`. Branch on `code`, not `title`.

## MCP

Agents can discover and call this tool through `https://api.miniwebtool.com/mcp` or `https://api.miniwebtool.com/v1/mcp` using MCP `tools/list` and `tools/call`.

## Frequently asked

### What does the F-Test / F-Distribution Calculator API do?

Compare two variances with an F test, or turn an F statistic into a p-value and critical values. Use it to add this utility without rebuilding formulas, validation, examples, and documentation.

### How much does one call cost?

1 credit per successful call. Failed calls do not bill.

### What parameters are required?

Required fields: (none). Full schema at `https://api.miniwebtool.com/v1/openapi.json`.

### Is this deterministic?

Yes. Same input, same output. Tool version: 2026-04-22.