Skip to main content
math

Great Circle Distance Calculator

Calculate the shortest distance between two points on a sphere using the Haversine formula. Enter latitude and longitude of two locations to find the great-circle distance, essential for navigation, aviation, shipping, and geography applications.

Reviewed by Chase FloiedUpdated

This free online great circle distance calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Latitude of first point in decimal degrees (N positive, S negative)

Longitude of first point in decimal degrees (E positive, W negative)

Latitude of second point

Longitude of second point

Results

Distance (km)

5570.22 km

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Great Circle Distance Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Great Circle Distance Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Great Circle Distance Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • •Use the Great Circle Distance Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • •Use it to explore the behavior of mathematical functions across a range of inputs.

About This Calculator

The Great Circle Distance Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate the shortest distance between two points on a sphere using the Haversine formula. Enter latitude and longitude of two locations to find the great-circle distance, essential for navigation, aviation, shipping, and geography applications. The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.

About Great Circle Distance Calculator

The Great Circle Distance Calculator computes the shortest path between two points on Earth's surface using the Haversine formula. A great circle is the largest circle that can be drawn on a sphere, and the shortest distance between any two points on a sphere lies along a great circle arc. This is why airplane flight paths often appear curved on flat maps: they follow great circle routes to minimize distance. The Haversine formula is numerically stable for all distances and is the standard method for geographic distance calculations in navigation, aviation, shipping logistics, and geographic information systems (GIS). Enter coordinates in decimal degrees with standard sign conventions (north/east positive).

The Math Behind It

The great circle distance is the shortest path between two points on the surface of a sphere, measured along the surface (not through the interior). It corresponds to the arc length of the great circle passing through both points. The Haversine formula computes this distance robustly: d = 2R * arcsin(sqrt(haversin(delta_lat) + cos(lat1)*cos(lat2)*haversin(delta_lon))), where haversin(x) = sin^2(x/2) = (1-cos(x))/2. The 'haversine' (half-versed-sine) function was introduced specifically for this calculation because it avoids the numerical issues that the law of cosines formula has for small distances. The derivation starts with the spherical law of cosines: cos(c) = cos(a)cos(b) + sin(a)sin(b)cos(C), where a, b, c are side lengths (in angular measure) and C is the angle opposite side c. For points on Earth, a = 90-lat1, b = 90-lat2, and C = |lon2-lon1|. Substituting and simplifying using haversine identities yields the formula. The formula assumes a perfect sphere with radius R = 6371 km (Earth's mean radius). For higher accuracy, Vincenty's formulae use the WGS-84 ellipsoid model, accounting for Earth's oblateness. The difference between spherical and ellipsoidal calculations is typically less than 0.3% but matters for precision surveying. Great circle navigation has been used since ancient times. Polynesian navigators intuitively followed great circle routes across the Pacific. Modern GPS navigation systems compute great circle distances routinely. In telecommunications, satellite coverage areas are defined by great circle geometry.

Formula Reference

Haversine Formula

d = 2R * arcsin(sqrt(sin^2((lat2-lat1)/2) + cos(lat1)*cos(lat2)*sin^2((lon2-lon1)/2)))

Variables: R = Earth radius (6371 km), lat/lon in radians

Worked Examples

Example 1: New York to London

Find the great circle distance from New York (40.7128N, 74.006W) to London (51.5074N, 0.1278W).

Step 1:Convert to radians: lat1=0.7106, lon1=-1.2918, lat2=0.8989, lon2=-0.002230
Step 2:delta_lat = 0.1883, delta_lon = 1.2896
Step 3:a = sin^2(0.0941) + cos(0.7106)*cos(0.8989)*sin^2(0.6448)
Step 4:a = 0.00886 + 0.764*0.627*0.362 = 0.00886 + 0.1733 = 0.1822
Step 5:d = 2 * 6371 * arcsin(sqrt(0.1822)) = 12742 * 0.4375 = 5574

The great circle distance is approximately 5570 km.

Example 2: Same Longitude

Find the distance from the equator (0, 0) to the North Pole (90, 0).

Step 1:delta_lat = 90 degrees = pi/2 radians
Step 2:delta_lon = 0
Step 3:a = sin^2(pi/4) + cos(0)*cos(pi/2)*sin^2(0) = 0.5 + 0 = 0.5
Step 4:d = 2 * 6371 * arcsin(sqrt(0.5)) = 12742 * pi/4 = 10008 km

The distance is approximately 10,008 km (one quarter of Earth's circumference).

Common Mistakes & Tips

  • !Forgetting to convert degrees to radians. The trigonometric functions in the formula require radian inputs. Multiply degrees by pi/180.
  • !Mixing up latitude and longitude order. Latitude measures north-south (max 90), longitude measures east-west (max 180).
  • !Assuming the result is a straight-line distance. The great circle distance follows the curved surface of the Earth, not a tunnel through it.
  • !Using the formula on a flat surface. The Haversine formula is for spherical geometry. For short distances (under 10 km), Euclidean approximation may suffice.

Related Concepts

Central Angle

The great circle distance is directly proportional to the central angle between two points: d = R * theta.

Chord Length

The chord length formula gives the straight-line distance through the Earth between two surface points.

Frequently Asked Questions

Why do airplanes follow great circle routes?

Great circle routes are the shortest paths on a sphere. On a Mercator projection map, these paths appear curved, but on the actual globe they are straight. Airlines use great circle routes (modified for winds and restricted airspace) to minimize fuel consumption and flight time.

How accurate is the Haversine formula?

The Haversine formula assumes a perfect sphere and is accurate to about 0.3% (up to about 20 km error on intercontinental distances). For higher precision, Vincenty's formulae account for Earth's ellipsoidal shape and are accurate to about 0.5 mm.

What is the longest possible great circle distance on Earth?

The maximum great circle distance is half the circumference, about 20,037 km, which is the distance between any point and its antipodal point (the point diametrically opposite on the globe).