# Sodium deficit

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

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

## What it computes

Estimate sodium (cation) deficit from weight, sex-specific TBW, and measured serum Na versus a chosen target.

## When to use

When an agent needs Adrogué–Madias deficit arithmetic and must not invent TBW or a replacement amount.

## When not to use

- Not a treatment order and not a sodium infusion protocol. The result is an estimate of cation deficit versus a target sodium, not a dosing or correction-rate order.
- Does not model ongoing losses, SIADH, or the safe rate of correction. Sex-only TBW fractions (0.6 male, 0.5 female); no extra elderly adjustment.

## Formula

```
TBW_L = 0.6 * weight_kg (male) or 0.5 * weight_kg (female); sodium_deficit_mmol = TBW_L * (desired_na_mmol_l - sodium_mmol_l)
```

## Citation

Hyponatremia
Adrogué HJ, Madias NE
N Engl J Med. 2000;342(21):1581-1589
DOI: [10.1056/NEJM200005253422107](https://doi.org/10.1056/NEJM200005253422107)

## Worked example

### 70 kg male, Na 120 to 140 mmol/L

Given: `desired_na_mmol_l=140, sex=male, sodium_mmol_l=120, weight_kg=70`

1. TBW = 0.6 × 70 = 42 L (male fraction from the teaching formula)
2. deficit = 42 × (140 − 120) = 840 mmol


## Parameters

- `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 for TBW: 0.6 × weight (male) or 0.5 × weight (female).
- `sodium_mmol_l` (number, required): Measured serum sodium in mmol/L. Range 90-135 (hyponatremia).
- `desired_na_mmol_l` (number, optional): Target serum sodium in mmol/L (120-150), must exceed measured Na. Omitted uses 140.

## Bulk (POST)

POST the same path with a JSON items array. Price is n times the GET unit. Invalid items return HTTP 400 before settlement.

Method: `POST /api/calc/sodium_deficit`
Max items: 25
Price: unit_amount * n (unit 5000 atomic)
Status: PREVIEW

- 1 to 25 items. Each item uses the same keys as the GET query parameters.
- 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": [
    {
      "desired_na_mmol_l": "140",
      "sex": "male",
      "sodium_mmol_l": "120",
      "weight_kg": "70"
    },
    {
      "desired_na_mmol_l": "140",
      "sex": "male",
      "sodium_mmol_l": "120",
      "weight_kg": "70"
    }
  ]
}
```

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

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/sodium_deficit",
  "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": "Adrogué HJ, Madias NE",
        "doi": "10.1056/NEJM200005253422107",
        "id": "adrogue-madias-hyponatremia-2000",
        "source": "N Engl J Med. 2000;342(21):1581-1589",
        "title": "Hyponatremia"
      },
      "formula": "adrogue_madias",
      "formula_expression": "TBW_L = 0.6 * weight_kg (male) or 0.5 * weight_kg (female); sodium_deficit_mmol = TBW_L * (desired_na_mmol_l - sodium_mmol_l)",
      "sex": "male",
      "weight_kg": 70.0,
      "sodium_mmol_l": 120.0,
      "desired_na_mmol_l": 140.0,
      "sodium_deficit_mmol": 840.0,
      "tbw_l": 42.0
    },
    {
      "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": "Adrogué HJ, Madias NE",
        "doi": "10.1056/NEJM200005253422107",
        "id": "adrogue-madias-hyponatremia-2000",
        "source": "N Engl J Med. 2000;342(21):1581-1589",
        "title": "Hyponatremia"
      },
      "formula": "adrogue_madias",
      "formula_expression": "TBW_L = 0.6 * weight_kg (male) or 0.5 * weight_kg (female); sodium_deficit_mmol = TBW_L * (desired_na_mmol_l - sodium_mmol_l)",
      "sex": "male",
      "weight_kg": 70.0,
      "sodium_mmol_l": 120.0,
      "desired_na_mmol_l": 140.0,
      "sodium_deficit_mmol": 840.0,
      "tbw_l": 42.0
    }
  ]
}
```

## Response fields

- `formula` (string): adrogue_madias
- `formula_expression` (string): Exact expression used
- `weight_kg` (number): Normalized weight in kg
- `sex` (string): male or female used for TBW fraction
- `tbw_l` (number): Total body water in L, 0.6 or 0.5 × weight_kg, 1 decimal
- `sodium_mmol_l` (number): Measured serum sodium used
- `desired_na_mmol_l` (number): Target serum sodium (140 when omitted)
- `sodium_deficit_mmol` (number): Estimated sodium (cation) deficit in mmol, 1 decimal
- `citation` (object): Adrogué and Madias NEJM 2000 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": "Adrogué HJ, Madias NE",
    "doi": "10.1056/NEJM200005253422107",
    "id": "adrogue-madias-hyponatremia-2000",
    "source": "N Engl J Med. 2000;342(21):1581-1589",
    "title": "Hyponatremia"
  },
  "formula": "adrogue_madias",
  "formula_expression": "TBW_L = 0.6 * weight_kg (male) or 0.5 * weight_kg (female); sodium_deficit_mmol = TBW_L * (desired_na_mmol_l - sodium_mmol_l)",
  "sex": "male",
  "weight_kg": 70.0,
  "sodium_mmol_l": 120.0,
  "desired_na_mmol_l": 140.0,
  "sodium_deficit_mmol": 840.0,
  "tbw_l": 42.0
}
```

## Errors

- 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_hyponatremia_sodium`: sodium_mmol_l must be a number from 90 to 135 (hyponatremia). Returned before settlement; you are not charged.
- HTTP 400 `invalid_desired_sodium`: desired_na_mmol_l must be a number from 120 to 150 greater than sodium_mmol_l. 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.
- HTTP 402 `payment_required`: Missing or invalid PAYMENT-SIGNATURE; decode the PAYMENT-REQUIRED header
- HTTP 409 `payment_in_progress`: The same authorization nonce is already being settled; retry shortly
- HTTP 429 `rate_limited`: Too many requests from this client
- HTTP 503 `settlement_uncertain`: Settlement is unconfirmed; retry with the same PAYMENT-SIGNATURE
- HTTP 503 `settle_failed`: Settlement failed; retry with the same PAYMENT-SIGNATURE shortly
- HTTP 503 `facilitator_unavailable`: Payment facilitator unavailable
- HTTP 503 `facilitator_misconfigured`: Payment facilitator is not configured
- HTTP 503 `facilitator_unauthorized`: Payment facilitator rejected credentials
- HTTP 503 `ledger_unavailable`: Payment ledger unavailable
- HTTP 503 `payment_unavailable`: Payment processing unavailable

## Related tools

- [Corrected sodium](https://magentlab.com/docs/corrected-sodium) — Compute expected sodium in hyperglycemia using Katz 1.6 or Hillier 2.4. The formula argument is required.
- [Bicarbonate deficit](https://magentlab.com/docs/bicarbonate-deficit) — Estimate bicarbonate deficit from weight and measured plasma HCO3 using a 50 percent body-weight apparent space.
- [Serum osmolality](https://magentlab.com/docs/serum-osmolality) — Compute Worthley calculated serum osmolality from sodium, glucose, and BUN, plus an optional osmolar gap when a measured osm is supplied.

## Also searched as

- sodium deficit
- hyponatremia sodium deficit
- Adrogue Madias sodium
- cation deficit hyponatremia

## Payment

Required query parameters must be present and valid. 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 EIP-3009 (scheme exact, assetTransferMethod eip3009) with validBefore = now + accepts[0].maxTimeoutSeconds (600 seconds). That window starts when you sign and must cover wallet confirmation plus CDP verify and settle. Magent retries transient facilitator 429/5xx before answering. Do not send upto or batch-settlement payloads; magent does not offer those schemes.
- Retry the same URL with PAYMENT-SIGNATURE (base64 JSON echoing accepted, payload, and extensions when present).
- Success is HTTP 200 JSON plus PAYMENT-RESPONSE. Settlement happens before the tool runs. HTTP 503 settlement_uncertain or settle_failed: retry the same PAYMENT-SIGNATURE. Mint a new 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.

- 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.
- not offered `batch-settlement`: Not offered. Payment-channel vouchers claimed later in batches. Not the same as POST {items} bulk (that is still exact).

Same-path POST {items} is still scheme exact: one EIP-3009 authorization for n times the GET unit. That is not x402 batch-settlement (payment channels / vouchers).

## Guarantees

- Invalid query parameters return HTTP 400 before settlement. You are not charged.
- Settlement finishes before the tool executes (paymentFlow upfront). 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.