# Mentzer index

Mentzer index

Status: WEDGE
Price: $0.005 USDC
`GET /api/calc/mentzer`
HTML: https://magentlab.com/docs/mentzer
Markdown: https://magentlab.com/docs/mentzer.md

Not a medical device. Not a diagnosis, dose, or listing recommendation.

## What it computes

Compute the Mentzer 1973 index as mean corpuscular volume in fL divided by red-cell count in millions per µL, with the letter’s <13 / >13 / =13 bands.

## When to use

When an agent needs the published MCV/RBC quotient and must not invent a later Mentzer cutoff or a diagnosis of thalassemia or iron deficiency.

## When not to use

- Not a medical device. Not a diagnosis of thalassemia or iron deficiency.
- Mentzer 1973 is the MCV/RBC ratio only. A quotient of 13 is indeterminate; magent does not assign a disease.
- Does not apply later Mentzer cutoffs that are not in the 1973 Lancet letter.

## Formula

```
mentzer_index = mcv_fl / rbc_million_ul
```

## Citation

[Differentiation of iron deficiency from thalassaemia trait](https://doi.org/10.1016/s0140-6736(73)91446-3)
Mentzer WC Jr
Lancet. 1973 Apr 21;1(7808):882
DOI: [10.1016/s0140-6736(73)91446-3](https://doi.org/10.1016/s0140-6736(73)91446-3)

## Worked example

### MCV 70 fL, RBC 5.6 million/µL

Given: `mcv_fl=70, rbc_million_ul=5.6`

1. mentzer_index = 70 / 5.6 = 12.5
2. 12.5 < 13 → thalassemia_trait (favors β-thalassaemia trait; not a diagnosis)


### MCV 65 fL, RBC 5.0 million/µL

Given: `mcv_fl=65, rbc_million_ul=5.0`

1. mentzer_index = 65 / 5.0 = 13.0
2. 13.0 = 13 → indeterminate (neither side of the letter)


### MCV 80 fL, RBC 5.0 million/µL

Given: `mcv_fl=80, rbc_million_ul=5.0`

1. mentzer_index = 80 / 5.0 = 16.0
2. 16.0 > 13 → iron_deficiency (favors iron deficiency; not a diagnosis)


## Also searched as

- Mentzer index
- MCV RBC ratio
- MCV divided by RBC
- thalassemia trait vs iron deficiency
- beta thalassemia Mentzer
- Mentzer 1973

## Parameters

- `mcv_fl` (number, required): Mean corpuscular volume in fL (50-120).
- `rbc_million_ul` (number, required): Red-cell count in millions per µL (1.0-8.0). Required.

## Bulk (POST)

POST the same path with a JSON items array. The first item is the GET unit; each additional item is $0.002. Invalid items return HTTP 400 before settlement.

Method: `POST /api/calc/mentzer`
Max items: 25
Price: unit_amount + extra_item_amount * (n - 1) (unit 5000 atomic, extra 2000 atomic)
Status: PREVIEW

- 1 to 25 items. Each item uses the same keys as the GET query parameters.
- POST of 1 item costs the same as GET. Lists longer than 25: chunk into multiple POSTs. Extra items still execute; do not pad dummy rows.
- The first invalid item fails the whole request (index in the 400 JSON). You are not charged.
- HTTP 200 is {count, path, items}. Each items[i] is the GET 200 body for that row.
- Catalog misses (empty matches, found=false) stay paid 200s inside that slot.
- x402 resource URL is this path plus n and body_sha256. Browsers that prefer text/html get the same paywall as GET; Pay retries POST with the same items.

Example request:

```json
{
  "items": [
    {
      "mcv_fl": "70",
      "rbc_million_ul": "5.6"
    },
    {
      "mcv_fl": "70",
      "rbc_million_ul": "5.6"
    }
  ]
}
```

Human paywall (two-item fixture): https://api.magentlab.com/paywall/bulk/mentzer

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/mentzer",
  "items": [
    {
      "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
      "citation": {
        "authors": "Mentzer WC Jr",
        "doi": "10.1016/s0140-6736(73)91446-3",
        "id": "mentzer-1973",
        "pmid": "4123424",
        "source": "Lancet. 1973 Apr 21;1(7808):882",
        "title": "Differentiation of iron deficiency from thalassaemia trait"
      },
      "formula": "mentzer",
      "formula_expression": "mentzer_index = mcv_fl / rbc_million_ul",
      "mcv_fl": 70.0,
      "mentzer_band": "thalassemia_trait",
      "mentzer_index": 12.5,
      "rbc_million_ul": 5.6
    },
    {
      "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
      "citation": {
        "authors": "Mentzer WC Jr",
        "doi": "10.1016/s0140-6736(73)91446-3",
        "id": "mentzer-1973",
        "pmid": "4123424",
        "source": "Lancet. 1973 Apr 21;1(7808):882",
        "title": "Differentiation of iron deficiency from thalassaemia trait"
      },
      "formula": "mentzer",
      "formula_expression": "mentzer_index = mcv_fl / rbc_million_ul",
      "mcv_fl": 70.0,
      "mentzer_band": "thalassemia_trait",
      "mentzer_index": 12.5,
      "rbc_million_ul": 5.6
    }
  ]
}
```

## Response fields

- `formula` (string): mentzer
- `formula_expression` (string): Exact expression used
- `mcv_fl` (number): Mean corpuscular volume used, fL
- `rbc_million_ul` (number): Red-cell count used, millions per µL
- `mentzer_index` (number): MCV divided by RBC count, 1 decimal
- `mentzer_band` (string): Mentzer 1973 letter band: thalassemia_trait (index < 13), iron_deficiency (index > 13), or indeterminate (index = 13). Favors a side of the differential; not a diagnosis.
- `citation` (object): Mentzer 1973 Lancet letter citation
- `disclaimer` (string): Not-a-device notice

## Example JSON

Frozen fixture. Not a live lookup.

```json
{
  "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
  "citation": {
    "authors": "Mentzer WC Jr",
    "doi": "10.1016/s0140-6736(73)91446-3",
    "id": "mentzer-1973",
    "pmid": "4123424",
    "source": "Lancet. 1973 Apr 21;1(7808):882",
    "title": "Differentiation of iron deficiency from thalassaemia trait"
  },
  "formula": "mentzer",
  "formula_expression": "mentzer_index = mcv_fl / rbc_million_ul",
  "mcv_fl": 70.0,
  "mentzer_band": "thalassemia_trait",
  "mentzer_index": 12.5,
  "rbc_million_ul": 5.6
}
```

## Errors

- HTTP 400 `invalid_mcv`: mcv_fl must be a number from 50 to 120. Returned before settlement; you are not charged.
- HTTP 400 `invalid_rbc_million_ul`: rbc_million_ul must be a number from 1.0 to 8.0. Returned before settlement; you are not charged.
- HTTP 400 `invalid_items`: POST body must be a JSON object with only an items array Returned before settlement; you are not charged.
- HTTP 400 `invalid_item_count`: items must be an array of 1 to 25 objects Returned before settlement; you are not charged.
- HTTP 400 `invalid_item`: each items entry must be a JSON object Returned before settlement; you are not charged.

Shared HTTP 402 and 503: https://magentlab.com/docs/payments

## Related tools

- [ANC](https://magentlab.com/docs/anc) — Compute absolute neutrophil count from WBC and neutrophil plus band percents, plus a Bodey 1966 granulocyte band.
- [Reticulocyte index](https://magentlab.com/docs/reticulocyte-index) — Compute corrected reticulocyte count, a Hillman 1969 maturation-shift reticulocyte index, and optional absolute reticulocyte count from percent reticulocytes, hematocrit, and RBC.

## Payment

Unpaid requests return HTTP 402 even if query parameters or POST items are missing or invalid, so CDP and agents can index the path. After a PAYMENT-SIGNATURE, invalid params return HTTP 400 JSON before settlement. magent does not charge. Fix the params, then request a new 402 quote for that complete URL. Catalog misses (empty matches, found=false) are valid paid 200s.

- GET the tool with Accept: application/json (do not send Accept: text/html unless you want the human paywall).
- HTTP 402 means you have not paid. Decode the base64 PAYMENT-REQUIRED header. HTTP 503 is not a new quote.
- Sign accepts[0] (exact, EIP-3009) with validBefore = now + maxTimeoutSeconds (600 seconds), or accepts[1] (batch-settlement deposit/voucher) on product GET. Ping and POST {items} stay exact. Magent retries transient facilitator 429/5xx before answering.
- Retry the same URL with PAYMENT-SIGNATURE (base64 JSON echoing accepted, payload, and extensions when present).
- Success is HTTP 200 JSON plus PAYMENT-RESPONSE. exact settles before the tool. batch-settlement verifies (and deposit-settles) before the tool and commits the charge after HTTP 2xx. HTTP 503: retry the same PAYMENT-SIGNATURE. Mint a new exact nonce only after a new HTTP 402.

- offered `exact` on eip155:8453: Fixed-price USDC on Base. The buyer authorizes the advertised amount (EIP-3009). magent settles before the tool runs (paymentFlow upfront). extra.assetTransferMethod=eip3009 extra.paymentFlow=upfront.
- offered `batch-settlement` on eip155:8453: Payment-channel vouchers claimed later in batches. Exact stays accepts[0]. Same-path POST {items} is still exact. extra.assetTransferMethod=eip3009 extra.paymentFlow=authorization.

- not offered `upto`: Not offered. Usage-based: buyer authorizes a ceiling, seller settles the actual amount after work. Reserved for a future metered tool. Not for current calculators or code search.

Same-path POST {items} is still scheme exact: one EIP-3009 authorization for GET unit plus $0.002 per extra item. That is not x402 batch-settlement (payment channels / vouchers).

Shared HTTP 402 and 503 table: https://magentlab.com/docs/payments

Stdio MCP (one process per host): https://magentlab.com/docs/mcp

## Guarantees

- HTTP 402 is unpaid, including a missing query. After PAYMENT-SIGNATURE, invalid parameters return HTTP 400 before settlement. You are not charged.
- exact: settlement finishes before the tool (paymentFlow upfront). batch-settlement: verify/deposit before the tool; chargedCumulativeAmount commits after HTTP 2xx. Uncertain or failed settlement fails closed (HTTP 503). Retry the same PAYMENT-SIGNATURE.
- HTTP 402 is unpaid only. Do not sign a second authorization because of a 503.
- Execution is timeout-bounded and concurrency-capped.
- Calculator inputs are stored encrypted for allowlisted operators (Magent Console). They are not in public logs, SSH lookups, catalog, or rollups. Request logs store path without query.