# Confidence Interval Calculator API

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

Confidence interval for a population mean from raw data or summary statistics, using the t-distribution or the normal distribution.

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

- Slug: `confidence-interval-calculator`
- Category: `math`
- Version: `2026-04-22`
- Credits per successful call: 1
- Starts on: free
- Max payload: 262144 bytes
- Privacy mode: `hash_only`
- Available on: free, starter, pro, business, scale
- Browser tool: https://miniwebtool.com/confidence-interval-calculator/

## Endpoint

`POST https://api.miniwebtool.com/v1/tools/confidence-interval-calculator/run`

## Request body

| Field | Type | Required | Description |
| --- | --- | --- | --- |
| `mode` | `str` | no | raw | summary Choices: raw, summary |
| `data` | `str` | no | sample values for raw mode |
| `sample_size` | `int | None` | no | n, required for summary mode |
| `sample_mean` | `float | None` | no | sample mean, required for summary mode |
| `sample_std` | `float | None` | no | sample standard deviation, required for summary mode |
| `population_std_known` | `str` | no | no | yes Choices: no, yes |
| `confidence` | `str` | no | 0.95 | 0.90 | 0.99 | 0.98 | 0.80 Choices: 0.95, 0.90, 0.99, 0.98, 0.80 |
| `precision` | `int` | no | decimal places, 2-10 |

## Example request

```json
{
  "mode": "raw",
  "data": "12.1, 13.4, 11.8, 12.9, 13.1, 12.4, 12.8, 13.6, 12.2, 12.7",
  "confidence": "0.95"
}
```

## cURL

```bash
curl -X POST https://api.miniwebtool.com/v1/tools/confidence-interval-calculator/run \
  -H 'Authorization: Bearer mwt_live_YOUR_KEY' \
  -H 'Content-Type: application/json' \
  -d '{"mode":"raw","data":"12.1, 13.4, 11.8, 12.9, 13.1, 12.4, 12.8, 13.6, 12.2, 12.7","confidence":"0.95"}'
```

## Response envelope

```json
{
  "request_id": "01K...",
  "tool": "confidence-interval-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 Confidence Interval Calculator API do?

Confidence interval for a population mean from raw data or summary statistics, using the t-distribution or the normal distribution. 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.