# Z-score calculator

- Human page: https://happytails.ai/en/calculators/z-score-calculator/
- Markdown: https://happytails.ai/en/calculators/z-score-calculator.md
- Structured JSON: https://happytails.ai/agents/en/calculators/z-score-calculator/index.json
- Visibility: public

## Tool capabilities

| Property | Value |
| --- | --- |
| Tool ID | `z-score-calculator` |
| Category | calculators |
| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |
| Browser execution | Automatic updates after valid input or file selection. |
| Browser processing | Browser; see tool notes for network behavior. |
| HTTP API | Not callable through HTTP. |
| Browser-agent interface | run_current_tool |

### Implementation notes

Z-score = (observed value - mean) / standard deviation. Supply the mean and standard deviation for the same dataset. A z-score measures distance in standard deviations; it does not establish a probability or assume a normal distribution. Values are limited to magnitude 1 trillion.

### Inputs and settings

No free-text input is required. Use the file inputs and/or settings below.

| Setting | Meaning | Control type | Default | Constraints |
| --- | --- | --- | --- | --- |
| `value` | Observed value | number | 115 | step=any |
| `mean` | Mean | number | 100 | step=any |
| `deviation` | Standard deviation | number | 15 | min=0 step=any |

### Browser-agent workflow

1. Open the human page in a browser that supports WebMCP.
2. Discover the interface exposed by that page; use its actual schema.
3. Select files on the page first when the tool requires files.
4. Call `run_current_tool` with valid input and settings.
5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.

Calls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.

### Planning specification

The formula is (value minus mean) divided by standard deviation. Standard deviation must be positive. Inputs are limited to magnitude 1 trillion. The result describes standardized distance, not a probability; no normal-distribution assumption is applied.

This describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.

### Complete machine-readable capability record

```json
{
  "id": "z-score-calculator",
  "category": "calculators",
  "built": true,
  "requirements": "The formula is (value minus mean) divided by standard deviation. Standard deviation must be positive. Inputs are limited to magnitude 1 trillion. The result describes standardized distance, not a probability; no normal-distribution assumption is applied.",
  "implementation": {
    "fields": [
      {
        "key": "value",
        "label": "Observed value",
        "value": 115,
        "type": "number",
        "step": "any"
      },
      {
        "key": "mean",
        "label": "Mean",
        "value": 100,
        "type": "number",
        "step": "any"
      },
      {
        "key": "deviation",
        "label": "Standard deviation",
        "value": 15,
        "type": "number",
        "step": "any",
        "min": 0
      }
    ],
    "input": false,
    "live": true,
    "presentation": "metrics",
    "note": "Z-score = (observed value - mean) / standard deviation. Supply the mean and standard deviation for the same dataset. A z-score measures distance in standard deviations; it does not establish a probability or assume a normal distribution. Values are limited to magnitude 1 trillion.",
    "experience": {
      "automatic": true,
      "single": false,
      "inputMaxLength": 1000000,
      "inputMode": "text",
      "label": "Your text",
      "placeholder": "Type or paste your input…",
      "help": "Change the input or settings to update your result. Results update as you type. Up to 1,000,000 characters.",
      "action": null
    },
    "mode": "automatic",
    "interactive": false
  },
  "execution": "Browser interface",
  "api": null,
  "browser_agent": {
    "supported": true,
    "name": "run_current_tool",
    "discovery": "WebMCP on the human page in a supporting browser",
    "verification": "See audit/API-AUDIT.md; availability is not verification"
  }
}
```

## Page guide

See how many standard deviations a value sits above or below the mean.

How can we improve this tool?

Report a problem or share an idea.

Please leave out private information. Your message and the tool name go to our team via PostHog.

### How to use Z-score calculator

1. Enter the observed value, the dataset mean and its standard deviation. A positive score is above the mean, a negative score is below it and zero is exactly at the mean.
2. An observed value of 115, a mean of 100 and a standard deviation of 15 give a z-score of 1. The observation is one standard deviation above the mean.

## Useful next steps

- [Average](https://happytails.ai/en/calculators/average/) ([Markdown](https://happytails.ai/en/calculators/average.md))

- [Standard deviation](https://happytails.ai/en/calculators/standard-deviation/) ([Markdown](https://happytails.ai/en/calculators/standard-deviation.md))

- [Weighted average calculator](https://happytails.ai/en/calculators/weighted-average/) ([Markdown](https://happytails.ai/en/calculators/weighted-average.md))

## Compare a value with its dataset

Enter the observed value, the dataset mean and its standard deviation. A positive score is above the mean, a negative score is below it and zero is exactly at the mean.

### Try a small example

An observed value of 115, a mean of 100 and a standard deviation of 15 give a z-score of 1. The observation is one standard deviation above the mean.

### What to know

The formula is (value minus mean) divided by standard deviation. Standard deviation must be positive. Inputs are limited to magnitude 1 trillion. The result describes standardized distance, not a probability; no normal-distribution assumption is applied.