Bearing and Distance Calculator

Why a Fixed Bearing From London Won't Get You to New York

A navigator setting out on a bearing of 288 degrees from London to New York, and holding 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. 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. Maritime and aviation navigation handle this automatically through continuous navigation computers, but land navigation, hiking, and orienteering require manual recalculation. A documented case cited by the FCC antenna alignment guidance notes that fixed-bearing pointing errors of even 2 to 3 degrees compound significantly over long distances, which is exactly why the bearing and midpoint recalculation this tool provides matters for multi-segment routes.

What the Bearing and Distance Calculator Actually Does

This tool offers two modes in a single interface. The first 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 accepts a starting point, a compass bearing, and a distance, then calculates the exact destination coordinates and return bearing. According to the Federal Communications Commission distance and azimuth reference, the same haversine and atan2 approach underpins 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, and search and rescue coordination. For compass direction alone, 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 great-circle distance between two points on a sphere from their latitudes and longitudes: with delta-phi and delta-lambda as the latitude and longitude differences, a = sin squared(delta-phi/2) + cos(phi1) x cos(phi2) x sin squared(delta-lambda/2), then d = 2R x arcsin(sqrt(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, this formula stays numerically well-conditioned from a few metres up to Earth's full circumference, making it the standard choice for general-purpose geographic calculations. It does assume a spherical Earth, while the real Earth is an oblate spheroid flattened at the poles (equatorial radius 6,378.1 km, polar radius 6,356.8 km), so haversine distance differs from the true ellipsoidal geodesic by up to about 0.5%, roughly 100 km on an intercontinental route. This is more than sufficient for most navigation and planning; the Vincenty formula on the WGS 84 ellipsoid is the professional standard for sub-metre geodetic accuracy.

Initial Bearing vs Final Bearing

On a great-circle path, the shortest route on a sphere, compass heading changes continuously while travelling. Initial bearing is the compass direction at departure; final bearing is the direction on arrival. Under about 200 km the difference is small enough to ignore in most practical contexts, but on intercontinental routes it can be substantial.

The gap becomes critical in aviation flight planning, where a fixed magnetic heading flown for hours can push an aircraft hundreds of kilometres off course without continuous corrections. Our Antipode Calculator shows the maximum possible great-circle distance between any two points, always exactly 20,015 km, useful as an upper bound when assessing how significant a route's bearing divergence might be. The FAA Aeronautical Information Manual confirms 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 solves the direct geodesic problem: given a starting point, a direction, and a distance, where do you end up? The spherical formula gives destination latitude as arcsin(sin(phi1) x cos(d/R) + cos(phi1) x sin(d/R) x cos(theta)), with longitude from lambda1 + atan2(sin(theta) x sin(d/R) x cos(phi1), cos(d/R) minus sin(phi1) x sin(phi2)), where d is distance, R is 6,371.0088 km, and theta is the bearing in radians. This calculation drives search and rescue drift-position projection, orienteering waypoint marking from a known start, and AutoCAD-based land survey workflows describing parcels as 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 use the spherical Earth model with radius 6,371.0088 km. Haversine distance is accurate to within about 0.5% of the true ellipsoidal geodesic, for London to New York this means results can be off by up to roughly 28 km against the true WGS 84 value. Initial bearing is accurate to within about 0.3 degrees at mid-latitudes, though trigonometric instabilities increase near the poles, and results above 85 degrees latitude should be treated as approximate. Back bearing, in both modes, is the exact reciprocal (forward bearing plus 180 degrees, normalised to 0-360), accurate regardless of Earth model. The International Earth Rotation and Reference Systems Service conventions define the coordinate system underpinning every latitude and longitude this calculator works with.