How is the distance between two coordinates calculated?

It uses the haversine formula for great-circle distance on a sphere: a = sin^2(dLat/2) + cos(lat1) * cos(lat2) * sin^2(dLon/2), c = 2 * asin(sqrt(a)), d = R * c, with mean Earth radius R = 6371.0088 km. This gives the shortest path over the Earth's surface between two points given in decimal degrees.

What is the distance between New York and Los Angeles?

Using the haversine formula with R = 6371.0088 km, New York City (40.7128, -74.0060) to Los Angeles (34.0522, -118.2437) is approximately 3,935.75 km (2,445.56 miles). The initial bearing from New York is about 273.7 degrees, roughly due west.

Is the haversine distance accurate for short distances?

Yes. The haversine formula is numerically stable for short distances, unlike the spherical law of cosines which loses precision below a few meters. The remaining error comes from modelling the Earth as a sphere: up to about 0.5% versus the more exact ellipsoidal Vincenty formula.

How do I convert the result to miles or meters?

This calculator shows kilometers, miles, meters, nautical miles, feet, and yards simultaneously. Conversions use exact definitions: 1 mile = 1.609344 km, 1 nautical mile = 1.852 km, 1 foot = 0.3048 m.

What is the maximum possible distance between two points on Earth?

The maximum is half the Earth's circumference - the antipodal distance - which is pi x 6371.0088 = about 20,015.11 km (12,436.82 miles). For example, Madrid to Wellington (New Zealand) is about 19,854.82 km, close to the theoretical maximum.

Why does my GPS app show a slightly different distance than haversine?

GPS apps often use ellipsoidal formulas (Vincenty or Karney) on the WGS84 ellipsoid rather than a sphere, and many report driving distance along roads rather than straight-line distance. Haversine versus ellipsoidal results typically differ by less than 0.5%.

Can I enter coordinates as degrees minutes seconds?

This calculator accepts decimal degrees. To convert: decimal = degrees + minutes/60 + seconds/3600, using a negative sign for South latitudes and West longitudes. For example, 40 deg 42 min 46 sec N = 40 + 42/60 + 46/3600 = 40.7128.

What is the difference between great-circle distance and driving distance?

Great-circle distance is the shortest straight-line path over the Earth's surface ('as the crow flies'). Driving distance follows actual roads and is always longer - typically 15-40% more depending on terrain and road networks. For example, New York to Los Angeles is 3,935.75 km great-circle but about 4,500 km by road.

How long does it take to travel between two points?

This calculator estimates travel time from the great-circle distance using typical speeds: walking 5 km/h, cycling 20 km/h, driving 80 km/h, and flying 900 km/h. These are straight-line estimates - actual driving takes longer because roads are not straight. For New York to Los Angeles (3,935.75 km): about 4h 22m flying or 49h 11m driving non-stop.

What is the midpoint between two coordinates?

The geographic midpoint is the point halfway along the great-circle path between two coordinates, computed with spherical trigonometry. For example, the midpoint between New York (40.7128, -74.0060) and Los Angeles (34.0522, -118.2437) is approximately (39.5103, -97.1601), which falls in Kansas. This calculator shows the midpoint for every calculation.

What is a nautical mile and when is it used?

A nautical mile is defined as exactly 1,852 meters. It equals one minute of latitude, which makes it convenient for navigation: 1 degree of latitude = 60 nautical miles. It is the standard unit in aviation and maritime contexts.

How do I find the coordinates of a city?

Use the built-in city picker on this page - select from 32 major world cities and the coordinates fill in automatically. For other places, search the place name followed by 'coordinates' in any search engine, or right-click a location in Google Maps to see its latitude and longitude.

What are antipodal points?

Antipodal points are diametrically opposite each other on the globe - the farthest two points can be, about 20,015 km apart. The antipode of a point (lat, lon) is (-lat, lon +/- 180). For example, Madrid, Spain is nearly antipodal to Wellington, New Zealand (19,854.82 km apart).

Does the haversine formula account for altitude or elevation?

No. The haversine formula computes surface distance on a sphere of fixed radius and ignores elevation differences. For most purposes this is negligible - even the 8.8 km height of Mount Everest changes the result by far less than 0.1%.

What is the difference between haversine and Vincenty formulas?

Haversine assumes a spherical Earth (one radius, R = 6371.0088 km) and is simple and fast, with up to about 0.5% error. Vincenty uses the WGS84 ellipsoid (equatorial radius 6378.137 km, flattening 1/298.257) and is accurate to millimeters but more complex and can fail to converge for near-antipodal points. For everyday distance questions, haversine is more than accurate enough.

Distance Calculator

Q: What is the initial bearing between two coordinates?

The initial bearing is the compass direction you would set out on from point A toward point B along the great-circle path: bearing = atan2(sin(dLon) * cos(lat2), cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(dLon)), normalized to 0-360 degrees. On long routes the bearing changes as you travel, so this is the bearing at departure only.

Distance between two GPS coordinates or cities (haversine great-circle), with travel time estimates, halfway midpoint, and initial bearing. 100% client-side.

Point A

Latitude A (decimal deg, -90 to 90)

Longitude A (decimal deg, -180 to 180)

Point B

Latitude B (decimal deg, -90 to 90)

Longitude B (decimal deg, -180 to 180)

Kilometers

Miles

Meters

Nautical miles

Feet

Initial bearing

Halfway midpoint

Estimated travel time (straight-line distance)

Mode	Typical speed	Time

haversine: a = sin^2(dLat/2) + cos(lat1)*cos(lat2)*sin^2(dLon/2); d = 2*R*asin(sqrt(a)), R = 6371.0088 km
bearing: b = atan2(sin(dLon)*cos(lat2), cos(lat1)*sin(lat2) - sin(lat1)*cos(lat2)*cos(dLon))

Worked examples

Route	Distance	Bearing	Flight time*

*Flight time estimated at 900 km/h cruise from great-circle distance; actual flights vary with routing and wind.

Great-circle vs driving distance

The haversine formula computes the great-circle distance: the shortest path over the surface of a sphere between two points. This is the "as the crow flies" distance. Driving distance follows real roads and is always longer, typically by 15-40%.

Route	Great-circle	Typical driving	Ratio
New York - Los Angeles	3,935.75 km	~4,500 km	1.14x
London - Paris	343.56 km	~460 km	1.34x
Singapore - Jakarta	905.36 km	no road (sea crossing)	-

Use this calculator for straight-line distance questions ("how far apart are these cities?"). For trip planning with actual routes, use a routing or maps tool.

About this method

The haversine formula computes the great-circle distance between two points from their latitudes and longitudes. This calculator uses the mean Earth radius R = 6371.0088 km (IUGG value). The initial bearing is the compass heading at departure along that path (0 deg = North, 90 deg = East).

Note: the Earth is an oblate ellipsoid, not a perfect sphere. For distances beyond ~1,000 km, haversine can differ from ellipsoidal (Vincenty) results by up to ~0.5%. The midpoint shown is the geographic halfway point along the great-circle path, computed with spherical trigonometry.

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