Great Circle Distance Calculator

Calculate the shortest distance between two points on a sphere using the Haversine formula. Enter latitude and longitude coordinates to get the great circle distance in kilometers, miles, and nautical miles, plus initial and final bearing, midpoint coordinates, and step-by-step formulas with an interactive globe diagram.

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About Great Circle Distance Calculator

The Great Circle Distance Calculator computes the shortest distance between two points on the surface of a sphere using the Haversine formula. Enter the latitude and longitude of two locations to get the great circle distance in kilometers, miles, and nautical miles, along with the initial and final bearing, midpoint coordinates, estimated travel times, and a step-by-step breakdown of the Haversine formula with an interactive globe visualization.

What Is Great Circle Distance?

A great circle is the largest circle that can be drawn on the surface of a sphere — its plane passes through the center of the sphere. The great circle distance (also called orthodromic distance) is the shortest distance between two points on a sphere, measured along the surface of the sphere rather than through the interior. On Earth, great circle routes are the paths that airplanes and ships follow to minimize travel distance.

The Haversine Formula

The Haversine formula is the standard method for computing great circle distances. Given two points with latitudes \(\phi_1, \phi_2\) and longitudes \(\lambda_1, \lambda_2\):

Step	Formula	Description
Haversine	\(a = \sin^2\!\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_1) \cdot \cos(\phi_2) \cdot \sin^2\!\left(\frac{\Delta\lambda}{2}\right)\)	Compute the square of half the chord length
Central angle	\(c = 2 \cdot \text{atan2}\!\left(\sqrt{a},\; \sqrt{1-a}\right)\)	Angular distance in radians
Distance	\(d = R \times c\)	Arc length on the sphere surface

Where \(R\) is the radius of the sphere (Earth's mean radius = 6,371 km). The Haversine formula is numerically stable for both small and large distances, making it preferable to the spherical law of cosines for computer calculations.

Real-World Applications

✈

Aviation

Flight path planning and fuel estimation

🚢

Maritime Navigation

Ship routing and nautical charts

📡

Telecommunications

Satellite coverage and signal propagation

🌍

GIS & Mapping

Geospatial analysis and proximity queries

🏃

Logistics

Route optimization and delivery planning

🛰

Space Science

Orbital mechanics on planetary bodies

How to Use the Great Circle Distance Calculator

Enter Point A coordinates: Type the latitude and longitude of the starting location in decimal degrees, or click a popular route example to auto-fill both points. The interactive globe preview updates in real-time as you type.
Enter Point B coordinates: Type the latitude and longitude of the destination.
Set the sphere radius (optional): The default is Earth's mean radius (6,371 km). Change this to calculate distances on other spheres like the Moon (1,737 km) or Mars (3,390 km).
Click Calculate Distance: Press the button to compute all results.
Review results: See the distance in three unit systems, initial and final bearing with compass direction, midpoint coordinates, estimated travel times, and a step-by-step Haversine formula solution. Toggle the globe diagram layers to explore the visualization.

Haversine vs. Vincenty Formula

The Haversine formula assumes a perfect sphere and gives accuracy to within about 0.3% for Earth. The Vincenty formula models Earth as an oblate ellipsoid (WGS-84) and achieves accuracy to approximately 0.5 mm, but is more complex and computationally expensive. For most practical purposes — flight planning, logistics, educational use — the Haversine formula provides sufficient accuracy. The Vincenty formula is preferred for geodetic surveying and high-precision navigation.

Understanding Bearing

The initial bearing (forward azimuth) is the compass direction you would face when departing from Point A towards Point B along the great circle route. Bearings are measured clockwise from true north (0°–360°). Because a great circle curves along the sphere, the direction relative to north changes continuously along the route. The final bearing is the compass direction when arriving at Point B. For example, a flight from New York to London initially heads northeast (~51°) but arrives heading east-southeast (~108°).

Coordinate Format

This calculator uses decimal degrees format. Latitudes range from −90° (South Pole) to +90° (North Pole). Longitudes range from −180° (west) to +180° (east). To convert from degrees-minutes-seconds (DMS), use: decimal = degrees + minutes/60 + seconds/3600. For example, 40°42'46"N = 40.7128° and 74°0'22"W = −74.006°.

FAQ

What is a great circle distance?

A great circle distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere rather than through the interior. It follows a great circle, which is the largest circle that can be drawn on a sphere's surface and whose center coincides with the center of the sphere.

What is the Haversine formula?

The Haversine formula calculates the great circle distance between two points on a sphere given their longitudes and latitudes. The formula is: a = sin²(Δφ/2) + cos(φ₁) × cos(φ₂) × sin²(Δλ/2), c = 2 × atan2(√a, √(1−a)), d = R × c, where R is the sphere radius. It is numerically stable for all distances.

How accurate is the great circle distance for Earth?

Using Earth's mean radius of 6,371 km, the Haversine formula gives results accurate to about 0.3% because Earth is slightly oblate (flattened at the poles). For higher precision, the Vincenty formula accounts for Earth's ellipsoidal shape and achieves accuracy to about 0.5 mm.

What is the difference between initial and final bearing?

The initial bearing (forward azimuth) is the compass direction when departing from the starting point. The final bearing is the compass direction upon arriving at the destination. Because a great circle changes direction relative to north as it curves along the sphere, these two bearings are generally different.

Why do airplanes fly great circle routes?

Airplanes fly great circle routes because they represent the shortest path between two points on Earth's surface, saving fuel and flight time. On a flat map with Mercator projection, these routes appear curved, but on a globe they are the most direct paths. This is why flights from the US to Europe often fly over the North Atlantic or even near the Arctic.

Reference this content, page, or tool as:

"Great Circle Distance Calculator" at https://MiniWebtool.com/great-circle-distance-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: 2026-04-03

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

Great Circle Distance Calculator

About Great Circle Distance Calculator

What Is Great Circle Distance?

The Haversine Formula

Real-World Applications

How to Use the Great Circle Distance Calculator

Haversine vs. Vincenty Formula

Understanding Bearing

Coordinate Format

FAQ

Geometry Calculators:

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