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Great Circle Distance Calculator

Calculate the shortest distance between two points on Earth using the Haversine formula. Includes initial course, final bearing, and midpoint.

About this calculator

This calculator finds the shortest path between two points on Earth's surface using the Haversine formula, which treats Earth as a perfect sphere (mean radius 3,440.065 nautical miles) rather than the more precise oblate spheroid (WGS84 ellipsoid) that GPS and aviation-grade navigation systems use -- for most practical flight-planning distances this introduces only a small error, typically well under half a percent, but it means results won't match an FMS or GPS receiver to the last tenth of a mile. Initial True Course is the compass heading at DEPARTURE only; a genuine property of great-circle navigation is that the true course changes continuously along the route (except when flying due north/south or along the equator), so Final Bearing at the destination is generally different from Initial True Course -- not a rounding artifact. An aircraft actually flying the great circle route must continuously adjust heading, which is why real long-haul flight plans break the great circle into a series of straight rhumb-line segments rather than flying one constant heading the whole way. Midpoint is the geographic halfway point along the great circle path itself (not a simple average of the two latitude/longitude pairs), useful for identifying enroute alternates.

Est. Time at 120 kt and Est. Time at 450 kt are simple distance-over-speed estimates at two representative cruise speeds, ignoring wind, climb/descent, and routing deviations entirely.

Inputs

°
°
°
°

Results

Distance

747.8 NM

Initial True Course

246°

Distance860.5 SM
Distance1,384.8 km
Final Bearing238°
Est. Time at 120 kt374 min
Est. Time at 450 kt100 min
Midpoint Latitude37.1°
Midpoint Longitude-111.81°
How to Use This Calculator
  1. Enter departure and destination coordinates in decimal degrees.
  2. North latitude and East longitude are positive; South and West are negative.
  3. Look up airport coordinates on SkyVector or AirNav.
  4. Results show great circle distance, initial true course, final bearing, and the route's midpoint coordinates.

How the result changes across these scenarios

ScenarioDistanceInitial True Course
DEN → LAX747.8 NM246°
JFK → LHR2,991.4 NM51°
SFO → NRT4,442.3 NM303°

What each input means

Departure Latitude
Latitude in decimal degrees. North is positive, South is negative. Example: Denver = 39.8561
Departure Longitude
Longitude in decimal degrees. East is positive, West is negative. Example: Denver = −104.6737
Destination Latitude
Destination latitude in decimal degrees. Example: LAX = 33.9425
Destination Longitude
Destination longitude in decimal degrees. Example: LAX = −118.4081

How this is calculated

Worked example, using the default values

  1. Great Circle Distance
    Haversine: d = R × 2 × atan2(√a, √(1−a))
    From 39.8561°N, 104.6737°W to 33.9425°N, 118.4081°W = 747.8 NM
  2. Initial True Course
    θ = atan2(sin(Δlon)·cos(lat₂), cos(lat₁)·sin(lat₂) − sin(lat₁)·cos(lat₂)·cos(Δlon))
    From departure coordinates = 246°
  3. Midpoint
    Calculated from spherical geometry
    Halfway along the great circle = 37.0973°N, 111.8085°W

Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why is Final Bearing different from Initial True Course for the same route?

Because a great circle route is not a single constant compass heading -- except when flying due north/south or along the equator, the true course changes continuously as you travel along the shortest path over a sphere. Initial True Course is only the heading at departure; Final Bearing is the heading you'd be flying on arrival, and for two genuinely different points the two are generally different by design, not by error. (If you enter identical departure and destination coordinates as a sanity check, both bearings correctly read 0° -- there's no course to fly between a point and itself.)

How accurate is this calculator's distance compared to a GPS or flight-planning system?

Close, but not identical. This calculator uses the Haversine formula on a spherical-Earth model (a fixed mean radius), while GPS receivers and certified flight-management systems use the WGS84 ellipsoid, which accounts for Earth's actual oblate shape. The difference is typically well under half a percent for most routes -- fine for flight planning and estimation, but not a substitute for certified navigation data.

What is Midpoint useful for?

It marks the geographic halfway point along the actual great circle path between your two coordinates -- not a simple average of the latitude and longitude values, which would not generally sit on the route at all. Midpoint Longitude is normalized to the standard ±180° range, so a route that crosses the antimeridian (the trans-Pacific case pilots most often use this for) still reports a valid coordinate instead of a value outside ±180°. Pilots and dispatchers use a route's midpoint to help identify enroute alternates or evaluate ETP (equal-time point) planning for long overwater or remote-area legs.

Do the flight-time estimates account for wind or actual routing?

No. Est. Time at 120 kt and Est. Time at 450 kt are simple great-circle-distance- divided-by-speed calculations -- they ignore headwind or tailwind components, climb and descent segments, and any real-world routing that deviates from the direct great circle path (which airspace structure and air traffic control routing almost always require). Treat them as rough planning estimates, not a replacement for a real flight-planning computation.

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