{
    "name": "Bearing Between Coordinates Calculator",
    "url": "https://calculators.geekmidst.com/calculators/bearing-between-coordinates-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/bearing-between-coordinates-calculator.md",
    "category": "Algebra, geometry & advanced math",
    "description": "Find the initial and final great-circle bearing from one latitude/longitude to another, in degrees from true north, with the compass point.",
    "summary": "The initial bearing is the direction to set off along the great circle, measured clockwise from true north. On a sphere the bearing changes along the way, so the final bearing usually differs.",
    "also_called": [
        "Azimuth calculator",
        "Forward azimuth calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "lat1",
            "label": "Start latitude",
            "type": "number",
            "default": "35",
            "unit": "°"
        },
        {
            "name": "lon1",
            "label": "Start longitude",
            "type": "number",
            "default": "45",
            "unit": "°"
        },
        {
            "name": "lat2",
            "label": "Destination latitude",
            "type": "number",
            "default": "35",
            "unit": "°"
        },
        {
            "name": "lon2",
            "label": "Destination longitude",
            "type": "number",
            "default": "135",
            "unit": "°"
        }
    ],
    "outputs": [
        {
            "key": "initial",
            "label": "Initial bearing",
            "format": "number"
        },
        {
            "key": "compass",
            "label": "Compass point (16-wind)",
            "format": "text"
        },
        {
            "key": "initial_dms",
            "label": "Initial bearing in DMS",
            "format": "text"
        },
        {
            "key": "final",
            "label": "Final bearing on arrival",
            "format": "number"
        },
        {
            "key": "back_bearing",
            "label": "Reverse of initial bearing",
            "format": "number"
        },
        {
            "key": "distance_km",
            "label": "Great-circle distance",
            "format": "number"
        }
    ],
    "formula": {
        "text": "θ = atan2(sin Δλ · cos φ₂, cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ), normalised to 0–360°;  final bearing = (bearing from 2 to 1 + 180°) mod 360°",
        "variables": {
            "φ₁, φ₂": "start and destination latitudes",
            "Δλ": "difference in longitude",
            "θ": "bearing clockwise from true north"
        }
    },
    "worked_example": {
        "inputs": {
            "lat1": "35",
            "lon1": "45",
            "lat2": "35",
            "lon2": "135"
        },
        "steps": [
            "Δλ = 90°, so sin Δλ = 1 and cos Δλ = 0.",
            "θ = atan2(cos 35°, cos 35° × sin 35°) = atan(1 ÷ sin 35°) = atan(1.743447) ≈ 60.1624°.",
            "Both points share a latitude, so by symmetry the final bearing is 180° − 60.1624° = 119.8376°."
        ],
        "result": "From 35°N 45°E to 35°N 135°E you set off on 60.16° (ENE) and arrive heading 119.84° (ESE)."
    },
    "interpretation": "A great-circle route changes heading continuously. A constant compass heading (a rhumb line) is easier to steer but longer, except along the equator or a meridian.",
    "assumptions": [
        "Spherical Earth (mean radius 6,371.0088 km for the distance).",
        "Bearings are from true north, not magnetic north; add or subtract the local magnetic declination for a compass."
    ],
    "limitations": [
        "Undefined at a pole and for identical or antipodal points.",
        "Ellipsoidal (WGS-84) azimuths can differ by a fraction of a degree."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why is the final bearing different from the initial one?",
            "answer": "Meridians converge towards the poles, so a great circle crosses each one at a different angle. Only routes along the equator or a meridian keep a constant bearing."
        },
        {
            "question": "Is the return bearing just the initial bearing plus 180°?",
            "answer": "Only on a flat map. On the sphere the bearing for the return trip is the final bearing plus 180°, which generally differs."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Great Circle Distance Calculator",
            "url": "https://calculators.geekmidst.com/calculators/great-circle-distance-calculator"
        },
        {
            "name": "Coordinate Midpoint Calculator",
            "url": "https://calculators.geekmidst.com/calculators/coordinate-midpoint-calculator"
        },
        {
            "name": "Degrees Minutes Seconds Converter",
            "url": "https://calculators.geekmidst.com/calculators/degrees-minutes-seconds-conversion-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}