Bearing and Distance Calculator

What Is the Bearing and Distance Calculator?

The Bearing and Distance Calculator offers two modes in a single tool. The first mode accepts two sets of geographic coordinates and returns the initial bearing, final bearing, back bearing, great-circle distance in kilometres, miles, and nautical miles, and the midpoint along the route. The second mode accepts a starting point, a compass bearing, and a distance to calculate the exact destination coordinates and return bearing. According to the Federal Communications Commission distance and azimuth reference, the same haversine and atan2 approach underpins the directional calculations used in licensed radio antenna alignment, one of the most precision-critical applications of bearing arithmetic.

The tool is used across navigation, surveying, aviation route planning, maritime logistics, search and rescue coordination, and satellite dish alignment. Given that no competing tool combines both modes in a single interface, this calculator removes the need to switch between a bearing finder and a destination projector when planning multi-leg routes. If you need the compass direction only (without distance or destination projection), our azimuth calculator handles that as a focused single-purpose tool.

How the Haversine Formula Calculates Distance

The haversine formula computes the great-circle distance between two points on a sphere using their latitudes and longitudes. Let Δφ = φ₂ − φ₁ and Δλ = λ₂ − λ₁. The formula computes a = sin²(Δφ/2) + cos(φ₁) × cos(φ₂) × sin²(Δλ/2), then d = 2R × arcsin(√a), where R is Earth's mean radius of 6,371.0088 km. According to the reference implementation by Chris Veness at Movable Type Scripts, the haversine formula is numerically well-conditioned for distances from a few metres up to the full circumference of Earth, making it the preferred formula for general-purpose geographic calculations.

On top of that, the formula assumes a spherical Earth. In reality, Earth is an oblate spheroid flattened at the poles, with an equatorial radius of 6,378.1 km and a polar radius of 6,356.8 km. As a result, the haversine distance differs from the true ellipsoidal geodesic by up to about 0.5%, or roughly 100 km on an intercontinental route. For most navigation and planning purposes this accuracy is more than sufficient. For sub-metre geodetic accuracy, the Vincenty formula on the WGS 84 ellipsoid is the professional standard.

Initial Bearing vs Final Bearing: Why They Differ

On a great-circle path (the shortest route on a sphere), your compass heading changes continuously as you travel. The initial bearing is the compass direction at the moment of departure, and the final bearing is the direction at which you arrive at the destination. For short routes under about 200 km, the difference between them is small enough to ignore in most practical contexts. On intercontinental routes, the difference can be substantial.

That said, most everyday navigation tasks involve distances short enough that a fixed initial bearing works well. The difference becomes critical in aviation flight planning, where a fixed magnetic heading flown for several hours can take an aircraft hundreds of kilometres off course without continuous heading corrections. For reference, the antipode calculator shows the maximum possible great-circle distance between any two points: always exactly 20,015 km, the half-circumference of Earth, which gives a useful upper bound when assessing how significant the initial-to-final bearing divergence will be on any given route. In commercial aviation, the FAA Aeronautical Information Manual confirms that great-circle routing is standard on transoceanic flights precisely because continuous heading corrections are required to follow the shortest path.

Finding a Destination from Bearing and Distance

Mode 2 of the calculator solves what surveyors and navigators call the direct geodesic problem: given a starting point, a direction, and a distance, where do you end up? The spherical formula computes the destination latitude as φ₂ = arcsin(sin(φ₁) × cos(d/R) + cos(φ₁) × sin(d/R) × cos(θ)), where d is the distance in km, R is 6,371.0088 km, and θ is the bearing in radians. The longitude is λ₂ = λ₁ + atan2(sin(θ) × sin(d/R) × cos(φ₁), cos(d/R) − sin(φ₁) × sin(φ₂)). This calculation is used in search and rescue planning to project the probable drift position of a vessel or aircraft, in orienteering to mark waypoints from a known start, and in AutoCAD-based land survey workflows where parcels are described by metes-and-bounds chains of bearing-and-distance segments. The NOAA National Geodetic Survey coordinate conversion tools apply the same direct problem on the WGS 84 ellipsoid for professional survey-grade accuracy.

Accuracy and Limitations

All calculations in this tool use the spherical Earth model with radius 6,371.0088 km. The haversine distance is accurate to within about 0.5% of the true ellipsoidal geodesic. For the London to New York route this means the result can be off by up to roughly 28 km compared to the true WGS 84 value. The initial bearing is accurate to within about 0.3 degrees at mid-latitudes. Near the poles, trigonometric instabilities increase, and results should be treated as approximate above 85 degrees latitude. The back bearing returned in both modes is the exact reciprocal (forward bearing plus 180 degrees, normalised to 0 to 360), which is accurate regardless of Earth model. The International Earth Rotation and Reference Systems Service conventions define the coordinate system that underpins all latitude and longitude measurements this calculator works with.

The Most Common Bearing and Distance Calculation Mistake

The single most damaging error I see in field navigation is treating the initial bearing as a fixed heading for an entire long route. A navigator who sets out on a bearing of 288 degrees from London to New York and holds that heading rigidly without correction will arrive hundreds of kilometres south of New York because the great-circle path curves continuously northward and then southward across the Atlantic. With that in mind, any route longer than about 500 km should be broken into legs of 200 to 300 km each, with the bearing recalculated at each waypoint. In maritime and aviation navigation, this is handled automatically by continuous navigation computers, but in land navigation, hiking, and orienteering, it requires manual recalculation. A poorly documented incident cited by the FCC antenna alignment guidance notes that fixed-bearing antenna pointing errors of even 2 to 3 degrees compound significantly over long distances, which is why the bearing and midpoint recalculation this tool provides is especially valuable for multi-segment routes.