Math & Numbers

Magnetic Permeability Converter (H/m ↔ relative μ_r)

Convert magnetic permeability (μ) between absolute permeability in henry per metre (H/m, SI unit; equivalently N/A² or T·m/A) and relative permeability μ_r (dimensionless). Vacuum permeability μ₀ = 4π×10⁻⁷ H/m ≈ 1.25663706×10⁻⁶ H/m (defined pre-2019; since the 2019 SI redefinition it is a measured quantity with relative uncertainty 1.6×10⁻¹⁰, so the 4π×10⁻⁷ form is still exact for all engineering purposes). Relations used: μ = μ_r × μ₀ and μ_r = μ / μ₀ (magnetic susceptibility χ_m = μ_r − 1). Reference: vacuum μ_r = 1, copper 0.999994 (diamagnetic), aluminum 1.000022 (paramagnetic), iron ≈ 5000 (ferromagnetic).

json· JSON resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/permeability-converter' \
  -H 'Content-Type: application/json' \
  -d '{"inputUnit":"relative","value":5000,"outputUnit":"H/m","decimalPlaces":10}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/permeability-converter

Parameters

Name	Type	Required	Description
inputUnit	select	No	—
value	number	Yes	Permeability in the selected Input unit. Must be non-negative.
outputUnit	select	No	—
decimalPlaces	number	No	—

Response format

JSON result

JSON

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-permeability-converter": {
      "name": "permeability-converter",
      "description": "Convert magnetic permeability (μ) between absolute permeability in henry per metre (H/m, SI unit; equivalently N/A² or T·m/A) and relative permeability μ_r (dimensionless). Vacuum permeability μ₀ = 4π×10⁻⁷ H/m ≈ 1.25663706×10⁻⁶ H/m (defined pre-2019; since the 2019 SI redefinition it is a measured quantity with relative uncertainty 1.6×10⁻¹⁰, so the 4π×10⁻⁷ form is still exact for all engineering purposes). Relations used: μ = μ_r × μ₀ and μ_r = μ / μ₀ (magnetic susceptibility χ_m = μ_r − 1). Reference: vacuum μ_r = 1, copper 0.999994 (diamagnetic), aluminum 1.000022 (paramagnetic), iron ≈ 5000 (ferromagnetic).",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=permeability-converter",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "permeability-converter",
    "arguments": {
  "inputUnit": "relative",
  "value": 5000,
  "outputUnit": "H/m",
  "decimalPlaces": 10
}
  }
}

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Magnetic Permeability Converter (H/m ↔ relative μ_r)

json· JSON resultOpen tool

curl -X POST 'https://api.elysiatools.com/en/api/tools/permeability-converter' \ -H 'Content-Type: application/json' \ -d '{"inputUnit":"relative","value":5000,"outputUnit":"H/m","decimalPlaces":10}'

Name

Type

Required

Description

inputUnit

select

—

value

number

Yes

Permeability in the selected Input unit. Must be non-negative.

outputUnit

select

—

decimalPlaces

number

—

{ "mcpServers": { "elysiatools-permeability-converter": { "name": "permeability-converter", "description": "Convert magnetic permeability (μ) between absolute permeability in henry per metre (H/m, SI unit; equivalently N/A² or T·m/A) and relative permeability μ_r (dimensionless). Vacuum permeability μ₀ = 4π×10⁻⁷ H/m ≈ 1.25663706×10⁻⁶ H/m (defined pre-2019; since the 2019 SI redefinition it is a measured quantity with relative uncertainty 1.6×10⁻¹⁰, so the 4π×10⁻⁷ form is still exact for all engineering purposes). Relations used: μ = μ_r × μ₀ and μ_r = μ / μ₀ (magnetic susceptibility χ_m = μ_r − 1). Reference: vacuum μ_r = 1, copper 0.999994 (diamagnetic), aluminum 1.000022 (paramagnetic), iron ≈ 5000 (ferromagnetic).", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=permeability-converter", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "permeability-converter", "arguments": { "inputUnit": "relative", "value": 5000, "outputUnit": "H/m", "decimalPlaces": 10 } } }