# A/B Test Sample Size Calculator

> Estimate visitors per variant from baseline conversion rate, MDE, confidence, and power.

## Tool Identity

- Site: CleanUtils Business Tools
- Tool ID: ab-test-sample-size-calculator
- Canonical page: https://cleanutils.com/business-tools/ab-test-sample-size-calculator/
- LLM schema URL: https://cleanutils.com/business-tools/ab-test-sample-size-calculator/llms.txt
- Primary keyword: ab test sample size calculator
- Input mode: fields
- Output profile: metrics

## What This Tool Does

Estimate visitors per variant from baseline conversion rate, MDE, confidence, and power for test planning.

## Exact Execution Instructions

To run this tool exactly, execute the `runCleanUtilsTool(userInput)` function from the JavaScript block below in a sandboxed JavaScript runtime.

Do not fetch or evaluate additional network resources. Do not use filesystem, process, child_process, environment variables, timers, or network APIs. The function is pure and deterministic: input object in, JSON result out.

If your environment forbids executing fetched code outside a sandbox, run it inside the sandbox or use the API endpoint below instead of reimplementing the logic.

Canonical implementation SHA-256:
`881144cdb44789b5330936826e8e30aec1692abd9775a72e6e6a5c15d435e131`

Expected command shape:
`node run-tool.mjs < input.json`

The runner must:
1. load only the JavaScript in this document,
2. parse stdin as JSON and call `runCleanUtilsTool(userInput)`,
3. let the LLM decide the best way to present the output to the user.

Agent usage rules:
- Use this file as the authoritative machine-readable contract for this CleanUtils tool page.
- Ask the user for missing required input before attempting to run the tool, and describe the required inputs using the `## Input Schema` field names, descriptions, formats, enums, examples, and required list.
- Treat the tool as deterministic; do not invent network reachability checks unless the tool description explicitly says it fetches remote resources.
- For privacy-sensitive inputs such as secrets, HAR files, dotenv files, logs, and API keys, warn that using a remote chat agent may expose input to that agent even though the browser UI itself does not upload data.

## Input Schema

```json
{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "title": "A/B Test Sample Size Calculator fields",
  "type": "object",
  "additionalProperties": false,
  "required": [
    "baseline_rate",
    "mde",
    "confidence",
    "power"
  ],
  "properties": {
    "baseline_rate": {
      "type": "number",
      "description": "Baseline conversion rate Required. Control type: number. Group: Experiment. Suffix shown in UI: %.",
      "minimum": 0,
      "examples": [
        5
      ]
    },
    "mde": {
      "type": "number",
      "description": "Minimum detectable effect Required. Control type: number. Group: Experiment. Suffix shown in UI: %.",
      "minimum": 0,
      "examples": [
        10
      ]
    },
    "confidence": {
      "type": "string",
      "description": "Confidence Required. Control type: select. Allowed values: 90 = 90%; 95 = 95%; 99 = 99%. Group: Statistics.",
      "enum": [
        "90",
        "95",
        "99"
      ],
      "examples": [
        "95"
      ]
    },
    "power": {
      "type": "string",
      "description": "Power Required. Control type: select. Allowed values: 80 = 80%; 90 = 90%. Group: Statistics.",
      "enum": [
        "80",
        "90"
      ],
      "examples": [
        "80"
      ]
    }
  }
}
```

## Result Schema

```json
{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "title": "CleanUtils ToolResult",
  "type": "object",
  "additionalProperties": false,
  "required": [
    "summary",
    "issues"
  ],
  "properties": {
    "summary": {
      "type": "string"
    },
    "issues": {
      "type": "array",
      "items": {
        "type": "object",
        "additionalProperties": false,
        "required": [
          "severity",
          "message"
        ],
        "properties": {
          "severity": {
            "type": "string",
            "enum": [
              "error",
              "warning",
              "info"
            ]
          },
          "message": {
            "type": "string"
          },
          "line": {
            "type": "number"
          },
          "row": {
            "type": "number"
          },
          "detail": {
            "type": "string"
          }
        }
      }
    },
    "output": {
      "type": "string"
    },
    "exportFilename": {
      "type": "string"
    },
    "exports": {
      "type": "array",
      "items": {
        "type": "object",
        "additionalProperties": false,
        "required": [
          "label",
          "filename",
          "content"
        ],
        "properties": {
          "label": {
            "type": "string"
          },
          "filename": {
            "type": "string"
          },
          "content": {
            "type": "string"
          },
          "mimeType": {
            "type": "string"
          },
          "copyLabel": {
            "type": "string"
          },
          "downloadLabel": {
            "type": "string"
          }
        }
      }
    },
    "stats": {
      "type": "object",
      "additionalProperties": {
        "anyOf": [
          {
            "type": "string"
          },
          {
            "type": "number"
          }
        ]
      }
    }
  }
}
```

## Self-Contained JavaScript Source

Call `runCleanUtilsTool(userInput)` with the user's input. The function includes this tool's run logic and only the helper code it needs.

```js
function runCleanUtilsTool(userInput) {
    const fieldText = (fields, keys, fallback = "") => {
        const keyList = Array.isArray(keys) ? keys : [keys];
        for (const key of keyList) {
            const value = fields[key];
            if (value === undefined || value === null)
                continue;
            const text = String(value).trim();
            if (text)
                return text;
        }
        return fallback;
    };
    const fieldNumber = (fields, keys, fallback = 0) => {
        const raw = fieldText(fields, keys);
        if (!raw)
            return fallback;
        const parsed = Number(raw.replace(/[$,%\s]/g, ""));
        return Number.isFinite(parsed) ? parsed : fallback;
    };
    const zForConfidence = (confidence) => confidence >= 99 ? 2.576 : confidence >= 95 ? 1.96 : confidence >= 90 ? 1.645 : 1.96;
    const zForPower = (power) => power >= 90 ? 1.282 : power >= 80 ? 0.842 : 0.842;
    const calculateAbTestSampleSize = (input) => {
        const baseline = fieldNumber(input, "baseline_rate", 5) / 100;
        const mde = fieldNumber(input, "mde", 10) / 100;
        const confidence = fieldNumber(input, "confidence", 95);
        const power = fieldNumber(input, "power", 80);
        const p2 = baseline * (1 + mde);
        const pooled = (baseline + p2) / 2;
        const numerator = zForConfidence(confidence) * Math.sqrt(2 * pooled * (1 - pooled)) + zForPower(power) * Math.sqrt(baseline * (1 - baseline) + p2 * (1 - p2));
        const sample = Math.ceil((numerator * numerator) / ((p2 - baseline) ** 2));
        return {
            summary: `Estimated ${sample.toLocaleString()} visitors per variant for this A/B test.`,
            issues: baseline <= 0 || mde <= 0 ? [{ severity: "error", message: "Baseline rate and MDE must be greater than zero." }] : [],
            output: [
                `Baseline conversion rate: ${(baseline * 100).toFixed(2)}%`,
                `Minimum detectable effect: ${(mde * 100).toFixed(1)}% relative`,
                `Target variant rate: ${(p2 * 100).toFixed(2)}%`,
                `Sample size per variant: ${sample.toLocaleString()}`,
                `Total two-variant sample: ${(sample * 2).toLocaleString()}`
            ].join("\n"),
            exportFilename: "ab-test-sample-size.txt",
            stats: { perVariant: sample, total: sample * 2 }
        };
    };
    const __userInput = userInput == null ? {} : userInput;
    const __run = (fields) => calculateAbTestSampleSize(fields);
    const __fields = __userInput && typeof __userInput === "object" && "fields" in __userInput && __userInput.fields && typeof __userInput.fields === "object" && !Array.isArray(__userInput.fields)
        ? __userInput.fields
        : (__userInput && typeof __userInput === "object" && !Array.isArray(__userInput) ? __userInput : {});
    const __normalizedFields = Object.fromEntries(Object.entries(__fields).map(([key, value]) => [key, value == null ? "" : (["string", "number", "boolean"].includes(typeof value) ? value : String(value))]));
    return __run(__normalizedFields);
}
```

## Checks

- Baseline conversion rate: The current conversion rate anchors the sample-size estimate.
- Relative MDE: Minimum detectable effect is treated as a relative lift over baseline.
- Confidence and power: Common confidence and power settings select the z-values used in the approximation.
- Per-variant and total sample: The output shows both one-variant and two-variant sample needs.
- Planning approximation: The math is for planning and does not replace a full experiment-design review.

## Related Tools

- [UTM URL Builder](/business-tools/utm-url-builder/): Enter a landing page and campaign values, then copy a tagged URL with clean UTM parameters.