Great Circle Distance Calculator
Free Great circle distance Converter for geography & distance units. Enter a value to see equivalent measurements across systems.
Formula
d = 2R * arcsin(sqrt(sin((lat2-lat1)/2)^2 + cos(lat1)*cos(lat2)*sin((lon2-lon1)/2)^2))
The Haversine formula calculates the great circle distance by first computing the haversine of the central angle between two points. It uses latitude and longitude in radians, with R being Earth's mean radius of 6,371 km. The formula handles antipodal points correctly and avoids numerical issues at small distances.
Worked Examples
Example 1: New York to London Flight Distance
Problem: Calculate the great circle distance from New York (40.7128 N, 74.006 W) to London (51.5074 N, 0.1278 W).
Solution: Using Haversine formula with R = 6,371 km:\ndLat = 10.7946 deg, dLon = 73.8782 deg\na = sin(5.3973)^2 + cos(40.7128) * cos(51.5074) * sin(36.9391)^2\nc = 2 * atan2(sqrt(a), sqrt(1-a))\nDistance = 6371 * c
Result: Distance: 5,570.25 km | 3,461.05 miles | 3,007.69 nautical miles | Bearing: 51.37 degrees
Example 2: Sydney to Tokyo
Problem: Find the distance from Sydney (-33.8688, 151.2093) to Tokyo (35.6762, 139.6503).
Solution: dLat = 69.545 deg, dLon = -11.559 deg\nApply Haversine formula with Earth radius 6,371 km.\nCompute intermediate value a, then angular distance c.
Result: Distance: approximately 7,823 km | 4,861 miles | Initial bearing: 338.68 degrees
Frequently Asked Questions
What is the great circle distance?
The 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 it. On Earth, this represents the shortest flight path between two locations. The concept comes from the fact that the shortest path on a sphere always lies along a great circle, which is a circle whose center coincides with the center of the sphere. Airlines use great circle routes to minimize fuel consumption and flight time.
Can I use Great Circle Distance Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
How accurate are the results from Great Circle Distance Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.