Great Circle Calculator - Shortest Distance Between Two Points
Calculate the great-circle distance — the shortest path along the Earth's surface — between any two geographic coordinates.
Enter the latitude and longitude of two points on Earth. The calculator uses the Haversine formula to compute the shortest surface distance.
Great Circle Calculator - Shortest Distance Between Two Points
Calculate the great-circle distance — the shortest path along the Earth's surface — between any two geographic coordinates.
About the Great Circle Calculator
A great circle is the largest possible circle that can be drawn on the surface of a sphere — the circle whose plane passes through the center of the sphere. On Earth, great circles are the shortest paths between any two points on the surface. Airline flight paths, ocean shipping routes, and submarine cable corridors all follow great circles because they minimize the total distance traveled.
The most common formula for computing great-circle distance is the Haversine formula, which was developed for nautical navigation in the nineteenth century and remains in wide use today because it is numerically stable for all distances, including very short ones where other formulas can suffer from catastrophic cancellation. The Haversine formula computes the central angle θ between two points on a unit sphere and then multiplies by the Earth's radius to get the arc length.
The formula works as follows. Given point 1 at (φ₁, λ₁) and point 2 at (φ₂, λ₂) in decimal degrees, convert to radians by multiplying by π/180. Compute Δφ = φ₂ − φ₁ and Δλ = λ₂ − λ₁. Then a = sin²(Δφ/2) + cos(φ₁)·cos(φ₂)·sin²(Δλ/2), and c = 2·arcsin(√a). The great-circle distance d = R·c, where R is Earth's mean radius. This calculator uses R = 6371 km (6371.009 km is the IUGG mean radius), which converts to 3958.8 miles or 3440.1 nautical miles.
Latitude is measured in degrees north (+) or south (−) of the Equator, ranging from −90° (South Pole) to +90° (North Pole). Longitude is measured in degrees east (+) or west (−) of the Prime Meridian through Greenwich, England, ranging from −180° to +180°. Coordinates are commonly given in decimal degree format (e.g., 40.7128° N, 74.0060° W becomes 40.7128, −74.0060).
The initial bearing (or forward azimuth) is the compass direction you would face at the starting point if you were to travel the great-circle route. It is computed as θ = atan2(sin(Δλ)·cos(φ₂), cos(φ₁)·sin(φ₂) − sin(φ₁)·cos(φ₂)·cos(Δλ)), then converted to a bearing in the range 0–360°.
The midpoint of a great-circle arc is the geographic point equidistant between the two endpoints along the shortest surface path. It is NOT simply the arithmetic average of the latitudes and longitudes — that gives the midpoint of a chord through the Earth, not a point on the surface arc. The correct midpoint formula uses spherical trigonometry.
This calculator is useful for aviation route planning, maritime navigation, geospatial analysis, mapping, and any application that needs accurate surface distances on a sphere rather than straight-line or map-projected distances.
Great Circle Distance Examples
Four real-world city pairs demonstrating the great-circle calculation.
| City Pair | Great-Circle Distance | Notes |
|---|---|---|
| New York (40.7128, −74.0060) → London (51.5074, −0.1278) | ≈ 5,570 km / 3,461 mi | Typical transatlantic flight distance. Flight time is about 7 hours eastbound. |
| Sydney (−33.8688, 151.2093) → Tokyo (35.6895, 139.6917) | ≈ 7,822 km / 4,861 mi | Major Asia-Pacific air corridor. The route curves north over the Pacific. |
| Dubai (25.2770, 55.2962) → Cape Town (−33.9249, 18.4241) | ≈ 7,648 km / 4,752 mi | Long-haul Africa route, frequently used by airlines connecting the Gulf to South Africa. |
| Quito (−0.1807, −78.4678) → Singapore (1.3521, 103.8198) | ≈ 19,729 km / 12,259 mi | A very long transoceanic route crossing the equator, spanning nearly halfway around Earth. |
How to Use the Great Circle Calculator
- Enter the latitude and longitude of the origin point (Point 1) in decimal degrees. Use negative values for South latitudes and West longitudes.
- Enter the latitude and longitude of the destination point (Point 2) in decimal degrees.
- Select the desired distance unit: kilometers, miles, or nautical miles.
- Click 'Calculate Distance'. The calculator applies the Haversine formula and displays the great-circle distance, initial bearing, and midpoint coordinates.
- Use the Reset button to clear all fields, or click one of the example buttons to load a preset city pair.
Great Circle Calculator FAQ
What is a great circle?
A great circle is the intersection of a sphere with a plane that passes through the sphere's center. On Earth, every meridian of longitude is a great circle, and so is the Equator. The great-circle path between two points is always the shortest route along the surface.
Why do flights follow curved paths on flat maps?
On most flat maps (Mercator projection) great-circle routes appear curved because straight lines on a Mercator map are rhumb lines (constant compass bearing), not great circles. Great-circle routes look straight only on a gnomonic projection. In reality the great-circle path is the shorter route.
What is the Haversine formula?
The Haversine formula computes the central angle between two points on a sphere using the formula a = sin²(Δφ/2) + cos φ₁·cos φ₂·sin²(Δλ/2), then c = 2·arcsin(√a), then distance = R·c. It is numerically stable for both very short and very long distances.
What is the difference between great-circle distance and straight-line distance?
Straight-line (Euclidean) distance cuts through the Earth's interior, which is not a usable path. Great-circle distance is measured along the surface of the sphere and represents the actual shortest route any surface vehicle or aircraft would travel.
What Earth radius does the calculator use?
The calculator uses Earth's mean radius of 6371 km (per the International Union of Geodesy and Geophysics, IUGG). This is an approximation — Earth is an oblate spheroid, so the true distance can vary by up to about 0.3% from the spherical model depending on the latitudes involved.
What is the initial bearing?
The initial bearing (or forward azimuth) is the compass direction you would need to face at Point 1 to travel the great-circle route toward Point 2. It is measured clockwise from north (0°) through east (90°), south (180°), and west (270°). The bearing changes continuously along a great-circle route.