Math & Numbers
Heat Radiation Calculator (Stefan-Boltzmann Law, Q=εσA·T⁴)
Compute thermal radiation from a blackbody/grey body (Stefan-Boltzmann law): blackbody emissive power E_b = σ·T⁴ (W/m²), total radiated power Q_rad = ε·σ·A·T⁴ (W); with an optional surrounding temperature T₀ it also computes the net radiative exchange Q_net = ε·σ·A·(T⁴-T₀⁴) (W). σ = 5.670374419e-8 W/(m²·K⁴); ε is the emissivity (0 < ε ≤ 1, blackbody ε=1); T is the ABSOLUTE temperature (K) — °C and °F are first converted to K (this is an absolute temperature, not a difference); A is the radiating area. Area in m²/cm².
Quick start
Call this tool from your code in three languages.
curl -X POST 'https://api.elysiatools.com/en/api/tools/heat-radiation-calculator' \
-H 'Content-Type: application/json' \
-d '{"emissivity":1,"temperature":300,"tempUnit":"K","area":1,"areaUnit":"m2","coldTemperature":0,"decimalPlaces":4}'API reference
Send a POST request with your inputs as JSON. File parameters require a separate upload first.
Endpoint
POST https://api.elysiatools.com/en/api/tools/heat-radiation-calculatorParameters
| Name | Type | Required | Description |
|---|---|---|---|
| emissivity | number | Yes | Emissivity ε of the surface (0 < ε ≤ 1). Use ε = 1 for an ideal blackbody. |
| temperature | number | Yes | ABSOLUTE temperature T of the radiating surface, in the selected Temperature Unit. Must be > 0 K after conversion. |
| tempUnit | select | No | Unit of the surface temperature. This is an ABSOLUTE temperature, not a difference: °C→K adds 273.15, °F→K uses (T-32)·5/9+273.15. |
| area | number | No | Radiating surface area A, in the selected Area Unit. |
| areaUnit |
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:
{
"mcpServers": {
"elysiatools-heat-radiation-calculator": {
"name": "heat-radiation-calculator",
"description": "Compute thermal radiation from a blackbody/grey body (Stefan-Boltzmann law): blackbody emissive power E_b = σ·T⁴ (W/m²), total radiated power Q_rad = ε·σ·A·T⁴ (W); with an optional surrounding temperature T₀ it also computes the net radiative exchange Q_net = ε·σ·A·(T⁴-T₀⁴) (W). σ = 5.670374419e-8 W/(m²·K⁴); ε is the emissivity (0 < ε ≤ 1, blackbody ε=1); T is the ABSOLUTE temperature (K) — °C and °F are first converted to K (this is an absolute temperature, not a difference); A is the radiating area. Area in m²/cm².",
"baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=heat-radiation-calculator",
"command": "",
"args": [],
"env": {},
"isActive": true,
"type": "sse"
}
}
}List available tools
After connecting to the SSE endpoint, list the exposed tools:
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Call this tool
Invoke the tool by its id, passing arguments built from its parameters:
{
"jsonrpc": "2.0",
"id": 2,
"method": "tools/call",
"params": {
"name": "heat-radiation-calculator",
"arguments": {
"emissivity": 1,
"temperature": 300,
"tempUnit": "K",
"area": 1,
"areaUnit": "m2",
"coldTemperature": 0,
"decimalPlaces": 4
}
}
}