Great Circle Calculator - Haversine Distance and Bearing Solver

A great circle calculator finds the shortest surface distance between two points on a sphere, the initial compass bearing to follow that path, and the midpoint of the arc. It treats the Earth as a sphere, takes two latitude/longitude pairs, and uses the haversine formula to turn the angular separation into a real distance.

• • Long-haul flight and shipping planning: Estimate the great circle distance between two cities to compare with the route actually flown, factor in fuel, or sanity-check an airline's claim.
• • Marine and sailing navigation: Compute the orthodrome (the shortest path on the ocean) between two ports in nautical miles, with the initial bearing to set on departure.
• • Geography and homework problems: Confirm a textbook answer about the distance between two capitals, two landmarks, or two latitude/longitude pairs.
• • GPS and mapping tools: Build or check a small GPS script that needs a fast, accurate spherical distance without a full library.

A great circle is the largest circle on a sphere and the geodesic between any two points, which is why the great circle is the path an airline plotter draws on a long-haul map.

If the surface distance comes out in kilometers and you need statute miles, nautical miles, or feet, the Distance Converter page changes the unit of the result without recomputing the haversine.

The page implements the haversine formula in JavaScript. It takes the two latitude/longitude pairs, converts them to radians, builds the difference terms, and applies the formula to get the angular separation c. Multiplying c by the mean Earth radius converts the angle into a surface arc length in kilometers.

• lat1, lon1: Latitude and longitude of the first point, in decimal degrees.
• lat2, lon2: Latitude and longitude of the second point, in decimal degrees.
• φ1, φ2, Δφ, Δλ: Latitudes and the latitude/longitude differences, in radians, used inside the trig functions.
• R = 6371.0088 km: Mean Earth radius used to convert the angular distance c into a surface distance d.

All four coordinates go in as decimal degrees, but the trig functions inside the haversine formula work in radians. The page multiplies each input by π/180 before any sine or cosine runs, and converts the final bearing back to degrees.

According to Movable Type Scripts (Chris Veness), the great circle distance between two latitude/longitude points is computed with the haversine formula d = 2·R·atan2(√a, √(1−a)) where a = sin²(Δφ/2) + cos(φ1)·cos(φ2)·sin²(Δλ/2) and all angles are in radians.

If your coordinates are in degrees-minutes-seconds or in UTM and not in the decimal degrees the haversine formula expects, the Coordinates Converter page changes the format of the input before you type the numbers into this one.

Four ideas explain what a great circle really is and how the bearing and midpoint follow from the same inputs.

The page only uses spherical geometry, so it ignores the small flattening of the Earth. The error is well under 0.5%, the same approximation used by most airline and nautical calculators.

The angular distance c in radians is the same as the central angle between the two points, and the Central Angle Calculator page turns that angle into a planar fraction of a circle, sector area, and chord length.

Five short steps take you from two coordinates to a distance, bearing, and midpoint.

1. 1 Look up the latitude and longitude of point 1: Use decimal degrees, positive for north and east, negative for south and west. New York is (40.7128, -74.0060); London is (51.5074, -0.1278).
2. 2 Look up the latitude and longitude of point 2: Same format. The defaults are New York and London so the example starts as a familiar transatlantic great circle.
3. 3 Read the great circle distance: The primary output is the surface arc length in kilometers, updated as you type. Statute miles and nautical miles appear below.
4. 4 Read the initial bearing and midpoint: The initial bearing is in degrees from true north; the midpoint is a latitude and longitude. Use the bearing as the heading to set on departure; use the midpoint to plot a waypoint.
5. 5 Check the result against a known example: Run the New York to London example first. The page should return about 5570 km, a bearing near 51°, and a midpoint near (52.37°, -41.29°).

For a flight from Sydney (-33.8688, 151.2093) to Tokyo (35.6762, 139.6503), the calculator returns a great circle distance of about 7826 km, an initial bearing near 350°, and a midpoint near (0.91°, 145.49°).

The haversine formula runs on radians, so the Angle Converter page is the right place to confirm the degree-to-radian step that happens inside the calculation when you want to follow the math by hand.

These benefits matter most when planning a route, checking a claim, or running a script that needs a known-correct spherical distance.

• • Use the shortest path on a sphere: The haversine formula gives the orthodrome between two coordinates, the geodesic on a sphere. That is shorter than any straight line on a flat projection and matches what airline and marine charts plot as a great circle route.
• • Get the bearing and midpoint for free: From the same four inputs, the page returns the initial bearing, the midpoint, and the surface distance, enough information to plan a route without a separate navigation tool.
• • Return all three common distance units: The same calculation gives you kilometers, statute miles, and nautical miles in one pass, useful for both land travel and marine or air navigation.
• • Stay numerically stable at short and long distances: The haversine form avoids the floating-point loss that the plain spherical law of cosines suffers when the points are very close. The same code path works for a 100-meter hop and a 20015-km antipodal route.
• • Plug straight into a small script: The pure calculation function in the page is self-contained JavaScript, so you can paste it into a Node script or a small web app to compute spherical distances.

The page is most useful as a check, not as a replacement for understanding the formula. Use it to confirm a homework answer, sanity-check an airline's trip length claim, or pre-validate a coordinate pair.

If your two points have a real altitude or a z-coordinate and you want the straight-line distance through space rather than the surface arc, the 3D Distance Calculator page runs the same Pythagorean formula on a 3D vector.

The haversine formula is the same in every case, but a few factors change how the result should be read.

• • The page is the spherical case only. Vincenty's formula on the WGS84 ellipsoid gives a result correct to about a meter, but is more code to maintain and falls apart for nearly antipodal points.
• • The bearing shown is the initial heading. On a great circle, the heading changes continuously as the path curves relative to the meridians, which is why long-haul flights update the heading at every waypoint.
• • The result is the surface distance, not the chord through the Earth and not the route distance along a road or a shipping lane. For road distance you need a routing engine with a road graph.

According to NASA National Space Science Data Center, the mean radius of the Earth is 6371.0088 km, which is the standard value used to convert a great-circle angular distance in radians into a surface arc length in kilometers.

When the path between the two points follows a known curve other than a great circle, the Arc Length Calculator page integrates the distance along that curve instead of returning the chord or the surface arc.