Great Circle Distance Calculator

What This Great Circle Distance Calculator Does

This calculator finds the shortest path between two locations on Earth, given their latitude and longitude. That shortest path, traced over the surface of the globe, is called a great circle route. It is the basis for how airlines choose efficient flight paths, how shipping companies plan ocean crossings, and how engineers estimate distances for undersea cables and communication links.

Enter the coordinates of two points in decimal degrees and the tool returns the great circle distance, typically in both kilometers and miles. The result represents the idealized shortest surface distance on a spherical Earth, not a driving route or step-by-step navigation.

The Haversine Formula

The calculator uses the haversine formula, a standard equation in navigation for estimating distances on a sphere. It works by converting the difference in latitude and longitude between two points into an angular distance, then multiplying by the Earth’s radius to get a linear distance.

In symbolic form, using radians:

• φ₁, φ₂: latitudes of point 1 and point 2
• λ₁, λ₂: longitudes of point 1 and point 2
• Δφ = φ₂ − φ₁
• Δλ = λ₂ − λ₁

The haversine formula is:

Then the central angle c (in radians) between the two points is:

Finally, the great circle distance d is:

d = R × c

where R is the Earth’s mean radius (often taken as about 6,371 km). The calculator may internally convert this to miles or nautical miles for additional outputs.

How to Enter Coordinates

The calculator expects coordinates in decimal degrees:

• Latitude ranges from −90° (South Pole) to +90° (North Pole).
• Longitude ranges from −180° (west) to +180° (east).

If you have degrees, minutes, and seconds (DMS), convert to decimal degrees first:

• decimal = degrees + minutes / 60 + seconds / 3600

Examples:

• 40° 42′ 46″ N → 40 + 42/60 + 46/3600 ≈ 40.7128
• 74° 00′ 21″ W → −(74 + 0/60 + 21/3600) ≈ −74.0060

Interpreting the Result

The output from the calculator is the shortest distance over the Earth’s surface between the two coordinates. This has a few important implications:

• It is not a driving or walking distance. Real-world routes are longer because of roads, terrain, and waypoints.
• It assumes a smooth spherical Earth, so the number is an approximation.
• When shown in multiple units (for example, kilometers and miles), each value is simply a conversion of the same great circle distance.

You can use the value to compare potential routes, estimate travel times given an average speed, or sanity-check distances between cities, airports, or waypoints.

Worked Example: New York to London

Suppose you want the great circle distance between New York City and London. Using approximate city-center coordinates in decimal degrees:

• New York: latitude 40.7128, longitude −74.0060
• London: latitude 51.5074, longitude −0.1278

Steps:

1. Convert each latitude and longitude from degrees to radians.
2. Compute Δφ and Δλ in radians.
3. Apply the haversine formula to find a.
4. Compute c = 2·atan2(√a, √(1−a)).
5. Multiply by Earth’s radius, e.g. R = 6,371 km, to get d.

Using this process, you get a distance of roughly 5,580–5,600 km, or about 3,470 miles. This explains why flight paths between the U.S. East Coast and Europe often arc northward over the North Atlantic when plotted on a flat map: the curved path you see is actually the shortest great circle route on a sphere.

Great Circle vs. Rhumb Line

In navigation, a great circle route is not the only possible path between two points. Another important path type is the rhumb line (or loxodrome), which crosses all meridians at a constant bearing. The two differ in several ways:

This calculator focuses on great circle distance, not rhumb line distance, because the great circle is usually preferred for efficiency in long-distance travel and engineering estimates.

Real‑World Applications

Great circle distance is useful in many scenarios:

• Aviation: Airlines use great circle routes as the basis for long-haul flight planning, then adjust for winds, airspace restrictions, and safety considerations.
• Shipping: Cargo and tanker routes across the oceans are often planned close to great circle paths to save time and fuel, subject to weather and navigational constraints.
• Telecommunications: Engineers designing undersea fiber cables and microwave links estimate span lengths using great circle distances between landing points or towers.
• GIS and mapping: Analysts compare distances between cities, study spatial relationships, or validate location data with straightforward spherical distance calculations.
• Education and hobby use: Teachers illustrate spherical geometry and map projections, while enthusiasts explore how far radio signals, flights, or voyages might reach.

Assumptions, Limitations, and Accuracy

While the haversine-based great circle distance is very useful, it relies on a few simplifying assumptions:

• Spherical Earth: The method treats Earth as a perfect sphere with a single radius R. In reality, Earth is slightly flattened (an oblate spheroid).
• Mean radius: A constant mean radius (about 6,371 km) is used. Actual radius varies slightly with latitude.
• Coordinate accuracy: The quality of the result depends directly on how accurate your input coordinates are.

For most everyday purposes—high-level planning, education, and quick checks—the error introduced by these assumptions is small, often on the order of fractions of a percent. For short to medium distances the numbers are typically within a few hundred meters of more precise ellipsoidal models. Over intercontinental distances, differences of up to a few kilometers can appear.

If you need survey-grade, legal, or engineering precision, or you must account for local geodetic datums, you should use an advanced geodesic calculator based on an ellipsoidal model such as WGS84 (for example, algorithms by Vincenty or Karney).

Using the Calculator Effectively

To get the most out of the tool:

• Enter latitudes between −90 and +90, and longitudes between −180 and +180, in decimal degrees.
• Verify that north and east are positive, while south and west are negative.
• Interpret the output as the idealized shortest surface distance, usually shown in kilometers and miles, not as a turn‑by‑turn route.
• Use the result for comparisons, estimates, and teaching—not as the sole basis for safety‑critical navigation.

With these points in mind, great circle distance is a powerful way to understand how far apart places really are on our curved planet, and why global routes often look surprising when projected onto a flat map.