{
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  "question": "What is the great-circle distance between (51.5074, -0.1278) and (48.8566, 2.3522)?",
  "answer": "343.56 km",
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    {
      "label": "Geodetic Reference System 1980 (IUGG mean Earth radius)",
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    }
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    "kind": "doi",
    "value": "Moritz, H. (2000). Geodetic Reference System 1980. Journal of Geodesy, 74(1), 128-133.",
    "retrieved_utc": "2026-09-30T19:44:00Z"
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  "deck_id": "method-deck",
  "deck_title": "Method Deck",
  "method": {
    "name": "Great-circle distance (haversine)",
    "version": "1",
    "source_url_or_file": "methods/great-circle-distance-haversine.cjs",
    "sha256_of_method_file": "6b1abc8a8bc4026026102cdce0324710aa8d59f677a951d587bf9b2fa869a741"
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  "method_deck": {
    "inputs": [
      {
        "name": "lat1",
        "type": "number",
        "unit": "degrees",
        "required": true,
        "description": "Latitude of point 1.",
        "min": -90,
        "max": 90
      },
      {
        "name": "lon1",
        "type": "number",
        "unit": "degrees",
        "required": true,
        "description": "Longitude of point 1.",
        "min": -180,
        "max": 180
      },
      {
        "name": "lat2",
        "type": "number",
        "unit": "degrees",
        "required": true,
        "description": "Latitude of point 2.",
        "min": -90,
        "max": 90
      },
      {
        "name": "lon2",
        "type": "number",
        "unit": "degrees",
        "required": true,
        "description": "Longitude of point 2.",
        "min": -180,
        "max": 180
      }
    ],
    "outputs": [
      {
        "name": "distance_km",
        "unit": "km",
        "description": "Great-circle distance between the two points."
      }
    ],
    "steps": [
      "Convert both points' latitudes and longitudes to radians.",
      "Haversine formula: a = sin^2(dLat/2) + cos(lat1)*cos(lat2)*sin^2(dLon/2), where dLat and dLon are the differences in latitude and longitude.",
      "c = 2 * atan2(sqrt(a), sqrt(1-a)).",
      "distance = R * c, where R is the mean Earth radius, 6371.0088 km (IUGG).",
      "Round to 2 decimals.",
      "This treats Earth as a sphere; true geodesic distance on the actual ellipsoid can differ by a small fraction of a percent."
    ],
    "constants": [
      {
        "name": "mean_earth_radius_km",
        "value": 6371.0088,
        "unit": "km",
        "source": 0
      }
    ],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "lat1": 51.5074,
          "lon1": -0.1278,
          "lat2": 48.8566,
          "lon2": 2.3522
        },
        "expected": {
          "answer": "343.56 km"
        },
        "check": "London to Paris is commonly cited as about 344 km great-circle distance; the computed 343.56 km matches that commonly cited figure to within a kilometer."
      },
      {
        "name": "test vector: quarter of the equator",
        "inputs": {
          "lat1": 0,
          "lon1": 0,
          "lat2": 0,
          "lon2": 90
        },
        "expected": {
          "answer": "10007.56 km"
        },
        "check": "Two points on the equator 90 degrees of longitude apart are exactly a quarter of the equatorial great circle apart, so the distance must equal (pi/2) * R = 1.5707963268 * 6371.0088 = 10007.56 km, which the formula reproduces analytically."
      }
    ],
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          "value": "Moritz, H. (2000). Geodetic Reference System 1980. Journal of Geodesy, 74(1), 128-133.",
          "retrieved_utc": "2026-09-30T19:44:00Z"
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        "added_utc": "2026-09-30T22:39:30.722Z",
        "added_by": "method:Great-circle distance (haversine)",
        "why": "the method that computed this answer",
        "check": null,
        "status_label": "pending",
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}