Great Circle Distance Calculator

Frequently Asked Questions

What is the haversine formula?

a = sin²(Δφ/2) + cos φ₁ × cos φ₂ × sin²(Δλ/2); c = 2 × atan2(√a, √(1−a)); d = R × c, where R = 3,440 NM (or 6,371 km, 3,959 sm) for Earth's mean radius.

A worked example?

KJFK (40.64° N, 73.78° W) to EGLL (51.47° N, 0.46° W): great-circle distance ≈ 2,997 NM (5,551 km). The rhumb-line (constant heading) route would be ~150 NM longer.

How is initial bearing calculated?

θ = atan2(sin Δλ × cos φ₂, cos φ₁ × sin φ₂ − sin φ₁ × cos φ₂ × cos Δλ), normalized 0–360°. The initial heading toward EGLL from KJFK is ≈ 051° (northeast), curving south as you near London.

Why does the great-circle curve north on a Mercator map?

The shortest path on a sphere lies along a great circle. Mercator flattens latitude lines, so a great circle between two mid-latitude points appears as a curve north of the straight rhumb line. Educational only - for navigation, use certified flight planning software.

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Aviation & Marine Disclaimer: Educational only. Not for flight or navigation operations.

This calculator is for educational and informational purposes only and is not a substitute for official flight or navigation planning. Always use current performance charts, an approved POH/AFM, certified navigation tools, and follow all applicable FAA, ICAO, USCG, and other regulatory guidance. Verify all results independently before operating any aircraft or vessel.

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How This Calculator Works

Flat-map distances mislead at intercontinental scale - the shortest path between two points on Earth is the great-circle route, an arc on the surface of the sphere, which on a Mercator chart curves dramatically toward the pole. New York to Tokyo over Anchorage is shorter than the equator-hugging straight line you might draw on a wall map. This calculator implements the haversine formula, a numerically-stable version of the spherical law of cosines, to return the great-circle distance in nautical miles, statute miles, and kilometres from two latitude/longitude pairs (decimal degrees). It also reports the initial true bearing - the heading you would steer at the start of the great circle - which continuously changes along the route. Use for planning study; airline flight planning systems also account for wind, restricted airspace, and ETOPS waypoints.

Formula / Method

Let φ₁, φ₂ be the latitudes and λ₁, λ₂ the longitudes (radians). Haversine: a = sin²(Δφ÷2) + cosφ₁·cosφ₂·sin²(Δλ÷2), c = 2·atan2(√a, √(1−a)), distance d = R·c, where R is the mean Earth radius ≈ 6,371 km (3,440 nm). Initial bearing θ = atan2(sinΔλ · cosφ₂, cosφ₁·sinφ₂ − sinφ₁·cosφ₂·cosΔλ), normalised to 0–360°. Haversine is preferred over the law-of-cosines form because it remains accurate for very small distances where cosine differences are tiny.

Worked Example

JFK (40.6413, −73.7781) to LHR London Heathrow (51.4700, −0.4543). Convert all four values to radians; compute Δφ and Δλ. The haversine yields c ≈ 0.8665 rad, so distance = 6,371 × 0.8665 ≈ 5,520 km, or about 2,980 nm (3,430 sm). Initial true bearing from JFK is about 51° (northeast) - over the course of the flight that bearing rotates through more easterly headings as the great circle curves up toward the North Atlantic and back down to London. At a 450-kt TAS this is roughly 6.6 hours in still air; westbound headwinds typically add 1–1.5 hr to the return leg.

Common Mistakes

Entering longitudes as positive in the western hemisphere - west longitudes are negative in the standard convention (use −73.78, not 73.78W). Mixing decimal-degree and degrees-minutes-seconds formats - convert DMS to decimal first (40° 38′ 28″ → 40 + 38÷60 + 28÷3600). Reading the result as “flight distance” without adjusting for cruise-altitude winds - great-circle distance is a still-air figure. Forgetting that the initial bearing is not the constant heading you actually fly along a great circle - only along the equator or a meridian is bearing constant. Confusing nm with sm - 1 nm = 1.15 sm; mixing them costs 15% of any distance.

Tips & FAQ

How accurate is the spherical model? The Earth is an oblate spheroid; haversine errors are under 0.5% for any pair of points - well below the precision of typical flight planning. For survey-grade work use Vincenty's formulae on the WGS-84 ellipsoid. Why does the bearing change? A great circle is the intersection of a plane through the centre of the Earth with the surface; only the equator and meridians have constant heading. Rhumb line vs. great circle? A rhumb line keeps a constant bearing but is longer - useful at sea for steering by compass, less so for long-distance flying. Disclaimer: planning study only; cross-check against official flight-planning tools and account for current winds, NOTAMs, and airspace.

Great Circle Distance Calculator

Frequently Asked Questions

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