Angular size API

Returns the angular size theta=2*atan(size/(2*distance)) in radians/degrees/arcminutes/arcseconds from a physical size and distance (same units). Answers 'How big does the Moon appear?', 'Angular diameter of an object at this range?'.

Price$0.02per request

MethodPOST

Route/v1/space/angular-size

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

spaceastronomyangular-sizeangular-diameterarcsecondarcminuteopticstrigonometry

API URLhttps://x402.hexl.dev/v1/space/angular-size

Integration docs

Example request

{
  "physicalSize": 3474800,
  "distance": 384400000
}

Example response

{
  "physicalSize": 3474800,
  "distance": 384400000,
  "angularSizeRad": 0.00903948059,
  "angularSizeDeg": 0.517924087,
  "angularSizeArcmin": 31.075445,
  "angularSizeArcsec": 1864.5267,
  "interpretation": "Subtends 31.08 arcmin at this distance."
}

Input schema

{
  "type": "object",
  "required": [
    "physicalSize",
    "distance"
  ],
  "properties": {
    "physicalSize": {
      "type": "number",
      "examples": [
        3474800
      ]
    },
    "distance": {
      "type": "number",
      "examples": [
        384400000
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}