# Nadler blood volume

Nadler blood volume

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

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

## What it computes

Compute Nadler 1962 predicted blood volume in liters and milliliters from height, weight, and sex.

## When to use

When an agent needs published Nadler blood volume and must not invent liters, apply 70 mL/kg, or silently use Lemmens–Bernstein–Brodsky.

## When not to use

- Adults as published. Nadler 1962 did not take age; this tool does not take age.
- Not a transfusion order. magent does not choose a product, rate, or threshold.
- Nadler 1962 only. Not Lemmens–Bernstein–Brodsky and not a 70 mL/kg rule of thumb.

## Formula

```
BV_L = 0.3669 * H^3 + 0.03219 * W + 0.6041 (male); BV_L = 0.3561 * H^3 + 0.03308 * W + 0.1833 (female); H meters, W kg
```

## Citation

[Prediction of blood volume in normal human adults](https://pubmed.ncbi.nlm.nih.gov/21936146)
Nadler SB, Hidalgo JH, Bloch T
Surgery. 1962;51(2):224-232
DOI: none

## Worked example

### Male 170 cm, 70 kg

Given: `height_cm=170, sex=male, weight_kg=70`

1. H = 170 / 100 = 1.7 m; H^3 = 4.913
2. BV_L = 0.3669 * 4.913 + 0.03219 * 70 + 0.6041 = 4.660 L
3. blood_volume_ml = round(4.660 * 1000) = 4660 mL


## Also searched as

- Nadler blood volume
- estimated blood volume
- EBV Nadler
- predicted blood volume
- Nadler formula
- blood volume liters
- male female blood volume

## Parameters

- `height_cm` (number, optional): Height in centimeters. Provide height_cm or height_in.
- `height_in` (number, optional): Height in inches. Converted as cm = in * 2.54.
- `weight_kg` (number, optional): Weight in kilograms. Provide weight_kg or weight_lb.
- `weight_lb` (number, optional): Weight in pounds. Converted as kg = lb * 0.45359237.
- `sex` (string, required): Sex used by Nadler 1962 (separate male and female equations).

## 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/nadler`
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": [
    {
      "height_cm": "170",
      "sex": "male",
      "weight_kg": "70"
    },
    {
      "height_cm": "170",
      "sex": "male",
      "weight_kg": "70"
    }
  ]
}
```

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

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/nadler",
  "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": "Nadler SB, Hidalgo JH, Bloch T",
        "id": "nadler-1962",
        "pmid": "21936146",
        "source": "Surgery. 1962;51(2):224-232",
        "title": "Prediction of blood volume in normal human adults"
      },
      "formula": "nadler",
      "formula_expression": "BV_L = 0.3669 * H^3 + 0.03219 * W + 0.6041 (male); BV_L = 0.3561 * H^3 + 0.03308 * W + 0.1833 (female); H meters, W kg",
      "sex": "male",
      "weight_kg": 70.0,
      "height_cm": 170.0,
      "blood_volume_l": 4.66,
      "blood_volume_ml": 4660
    },
    {
      "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": "Nadler SB, Hidalgo JH, Bloch T",
        "id": "nadler-1962",
        "pmid": "21936146",
        "source": "Surgery. 1962;51(2):224-232",
        "title": "Prediction of blood volume in normal human adults"
      },
      "formula": "nadler",
      "formula_expression": "BV_L = 0.3669 * H^3 + 0.03219 * W + 0.6041 (male); BV_L = 0.3561 * H^3 + 0.03308 * W + 0.1833 (female); H meters, W kg",
      "sex": "male",
      "weight_kg": 70.0,
      "height_cm": 170.0,
      "blood_volume_l": 4.66,
      "blood_volume_ml": 4660
    }
  ]
}
```

## Response fields

- `formula` (string): nadler
- `formula_expression` (string): Exact male and female expressions
- `sex` (string): female or male
- `height_cm` (number): Normalized height in cm
- `weight_kg` (number): Normalized weight in kg
- `blood_volume_l` (number): Predicted blood volume in liters, 3 decimals
- `blood_volume_ml` (integer): Predicted blood volume in milliliters, integer
- `citation` (object): Nadler Surgery 1962 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": "Nadler SB, Hidalgo JH, Bloch T",
    "id": "nadler-1962",
    "pmid": "21936146",
    "source": "Surgery. 1962;51(2):224-232",
    "title": "Prediction of blood volume in normal human adults"
  },
  "formula": "nadler",
  "formula_expression": "BV_L = 0.3669 * H^3 + 0.03219 * W + 0.6041 (male); BV_L = 0.3561 * H^3 + 0.03308 * W + 0.1833 (female); H meters, W kg",
  "sex": "male",
  "weight_kg": 70.0,
  "height_cm": 170.0,
  "blood_volume_l": 4.66,
  "blood_volume_ml": 4660
}
```

## Errors

- HTTP 400 `invalid_height`: height_cm (50-250) or height_in (20-98) is required Returned before settlement; you are not charged.
- HTTP 400 `invalid_weight`: weight_kg (1-500) or weight_lb (2-1100) is required Returned before settlement; you are not charged.
- HTTP 400 `invalid_sex`: sex must be female or male 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

- [BMI](https://magentlab.com/docs/bmi) — Compute Keys/Quetelet body-mass index from height and weight, plus a WHO adult band.
- [Devine IBW](https://magentlab.com/docs/ibw) — Compute Devine ideal body weight and 0.4 adjusted body weight from height, sex, and actual weight.
- [Mosteller BSA](https://magentlab.com/docs/bsa) — Compute Mosteller body surface area in m^2 from height and weight.

## 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.