Real-World Use Cases

Travelers use distance calculators to estimate flight times before booking. The distance from New York to London is 5,567 kilometers, which translates to roughly 6 hours and 11 minutes of flight time at typical cruising speed. This helps set expectations for long-haul travel.

Logistics planners use great-circle distances to estimate shipping costs and transit times. A cargo route from Singapore to Dubai covers 5,841 kilometers. While actual shipping routes differ from great-circle paths, the straight-line distance provides a baseline for cost calculations.

Event organizers use it to choose venues that minimize travel for attendees. If participants are coming from Berlin, Paris, and London, knowing the pairwise distances helps identify a central meeting point. London to Paris is 343 kilometers, London to Berlin is 932 kilometers, and Paris to Berlin is 878 kilometers.

Students and educators use it for geography lessons. The distance from Tokyo to Sydney is 7,816 kilometers, illustrating the vast scale of the Pacific Ocean. Comparing distances between world cities helps build intuition for global geography.

Pilots and sailors use great-circle distances for flight and voyage planning. The shortest path between two points on Earth's surface follows a great circle, which is what the Haversine formula calculates. For long-distance routes, this can save significant fuel compared to following a line of constant compass bearing.

How It Works

The calculator uses the Haversine formula, which computes the great-circle distance between two points on a sphere given their latitude and longitude. The formula accounts for the curvature of the Earth by using trigonometric functions on the angular differences between the two points.

The Earth is modeled as a sphere with a radius of 6,371 kilometers. While the Earth is actually an oblate spheroid (slightly flattened at the poles), the spherical approximation introduces less than 0.5 percent error for most distances, which is sufficient for practical purposes.

The bearing from the origin to the destination is calculated using the forward azimuth formula. This gives the initial compass direction you would need to travel from the starting city to reach the destination city along a great-circle path. For example, the bearing from New York to London is approximately 52 degrees (northeast).

Flight time is estimated by dividing the great-circle distance by an average commercial aircraft cruising speed of 900 km/h. This is a rough estimate that does not account for takeoff, landing, wind, routing, or air traffic delays. Actual flight times are typically 10 to 20 percent longer than this estimate.

Step-by-Step Usage Guide

  1. Select the origin city from the 'From' dropdown. The city's coordinates appear below.
  2. Select the destination city from the 'To' dropdown. The city's coordinates appear below.
  3. The distance panel shows the great-circle distance in kilometers, miles, and nautical miles.
  4. The bearing panel shows the compass direction from origin to destination in degrees and cardinal direction.
  5. The flight time panel shows an estimated travel time based on average cruising speed.
  6. Click 'Swap Cities' to reverse the direction and see the return bearing and distance.

Examples

Input

New York to London

Output

5,567 km / 3,459 mi / 3,006 nm, Bearing: 52 degrees (NE), Flight: ~6h 11m

One of the busiest transatlantic routes

Input

Tokyo to Sydney

Output

7,816 km / 4,856 mi / 4,220 nm, Bearing: 199 degrees (SSW), Flight: ~8h 41m

Major Asia-Pacific route

Input

Dubai to Singapore

Output

5,841 km / 3,629 mi / 3,153 nm, Bearing: 112 degrees (ESE), Flight: ~6h 29m

Middle East to Southeast Asia connection

Input

Paris to Berlin

Output

878 km / 546 mi / 474 nm, Bearing: 63 degrees (ENE), Flight: ~58m

Short European hop between capitals

Input

Los Angeles to Tokyo

Output

8,810 km / 5,474 mi / 4,757 nm, Bearing: 305 degrees (NW), Flight: ~9h 47m

Transpacific route. Great-circle path goes north near Alaska.

Common Mistakes and Edge Cases

Things to watch out for

  • Great-circle vs driving distance: The calculator shows the shortest distance over Earth's surface (as the crow flies). Driving distance is always longer because roads follow terrain, avoid obstacles, and route through cities. For New York to London, driving is impossible. For New York to Boston, the great-circle distance is 306 km but driving distance is about 350 km.
  • Antipodal distances: For cities on nearly opposite sides of the Earth (like Auckland and Madrid), the great-circle distance approaches 20,000 km. The Haversine formula handles this correctly, but the bearing becomes less meaningful because there are multiple shortest paths.
  • Flight time estimate: The 900 km/h average speed is a rough approximation. Actual cruising speeds range from 830 km/h for older aircraft to 950 km/h for newer jets. Wind, routing, and air traffic control can add 30 minutes or more to long flights. Use this estimate for planning only.
  • Bearing changes along great-circle: The initial bearing from origin to destination is not constant along a great-circle path. For long routes, the compass heading changes continuously. The tool shows only the initial bearing, which is the direction you would start flying.
  • City coordinate accuracy: The tool uses approximate city center coordinates. For large cities like Los Angeles or Tokyo, the actual distance depends on which part of the city you measure from. The difference can be 20-30 km for sprawling metropolitan areas.

FAQ

How is the distance between cities calculated?

The calculator uses the Haversine formula, which computes the great-circle distance between two points on Earth's surface using their latitude and longitude. The great-circle distance is the shortest path between two points on a sphere, following the surface of the Earth rather than a straight line through it.

What is the difference between kilometers, miles, and nautical miles?

One kilometer equals 0.6214 miles. One nautical mile equals 1.852 kilometers or 1.1508 miles. Kilometers are used in most countries, miles in the US and UK, and nautical miles in aviation and maritime navigation. The tool shows all three.

Is the great-circle distance the same as driving distance?

No. The great-circle distance is the shortest distance over Earth's surface, as the crow flies. Driving distance is always longer because roads follow terrain, avoid obstacles, and pass through cities. For driving directions, use a mapping service like Google Maps.

How accurate is the Haversine formula?

The Haversine formula assumes the Earth is a perfect sphere with radius 6,371 km. The Earth is actually an oblate spheroid, slightly flattened at the poles. This introduces an error of less than 0.5 percent for most distances. For navigation-grade precision, use the Vincenty formula, which accounts for Earth's actual shape.

How is the flight time estimated?

The flight time is calculated by dividing the great-circle distance by an average commercial aircraft cruising speed of 900 km/h. This is a rough estimate that does not account for takeoff, landing, wind, routing, or air traffic delays. Actual flight times are typically 10 to 20 percent longer.

What does the bearing number mean?

The bearing is the initial compass direction from the origin to the destination, measured in degrees clockwise from north. A bearing of 0 degrees means north, 90 means east, 180 means south, and 270 means west. For example, New York to London has a bearing of about 52 degrees, meaning you would head northeast.

Why does the bearing change during a long flight?

On a great-circle path, the compass heading changes continuously because the path curves relative to the coordinate grid. A flight from Los Angeles to Tokyo starts heading northwest but arrives heading southwest. The tool shows only the initial bearing at the origin.

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Data Sources and Accuracy

  • Haversine formula - standard mathematical formula for great-circle distance on a sphere
  • Earth radius: 6,371 km - mean radius as defined by the International Union of Geodesy and Geophysics (IUGG)
  • City coordinates from geolocation databases and the IANA Time Zone Database

Distances are great-circle distances on a spherical Earth model, accurate to within 0.5 percent. City coordinates are approximate city center locations. Flight time estimates use a fixed cruising speed of 900 km/h and do not account for takeoff, landing, wind, routing, or air traffic delays. Actual travel times will vary.