Latitude Longitude Distance Calculator - Great-circle distance from two GPS coordinates

A latitude longitude distance calculator finds the great-circle distance between two points on Earth from their GPS coordinates in decimal degrees. Enter the latitude and longitude of a starting point and a destination point, and the page returns the shortest surface distance in kilometers and miles, the initial compass bearing, and the latitude and longitude of the half-way point along the great-circle path. It is the everyday answer to the question, "how far apart are these two places on the globe, and which way do I head from the first to the second?"

• • Travel planning between cities: Get the great-circle distance and the initial compass bearing from your home city to a destination city to sanity-check a flight path, a road trip detour, or a sea route.
• • Hiking, geocaching, and field GPS: Measure the distance from your current GPS reading to a trailhead, geocache, or survey marker without redrawing the route on a separate mapping app.
• • Logistics and delivery radius: Estimate delivery distances between warehouses, drop zones, and customer addresses from coordinates exported from a routing tool or spreadsheet.
• • GIS, mapping, and data prep: Compute pairwise distances from a list of decimal-degree coordinates before clustering, nearest-neighbor search, or a radius filter in a geographic dataset.

Because the page accepts coordinates in the same decimal-degree format used by GPS devices, mapping apps, and GIS exports, the workflow is the same whether the coordinates come from a phone, a spreadsheet, or a hand-typed value.

The output is the shortest path along the surface of a sphere, not the driving, walking, or flight distance, so treat the great-circle answer as the lower bound of the actual trip.

If you want to express the result in feet, nautical miles, or yards instead of km and miles, the Distance Converter page handles the unit math.

The page implements the haversine formula, the standard spherical-trigonometry method for great-circle distance. It converts each latitude and longitude from decimal degrees to radians, builds the angular differences, runs the haversine intermediate, and multiplies the central angle by the Earth's radius.

• φ1, φ2: Latitude of point 1 and point 2 in radians after converting from decimal degrees.
• λ1, λ2: Longitude of point 1 and point 2 in radians after converting from decimal degrees.
• Δφ, Δλ: Differences (φ2 − φ1) and (λ2 − λ1) in radians, used as the inputs to the half-angle sines.
• a: Haversine intermediate, sin²(Δφ/2) + cos(φ1) · cos(φ2) · sin²(Δλ/2). Always in [0, 1].
• c: Central angle in radians, c = 2 · atan2(√a, √(1 − a)).
• R: Mean Earth radius, R = 6371.0088 km (the value recommended by NOAA).
• d: Great-circle distance on the surface, d = R · c, in kilometers and converted to statute miles.

According to Movable Type Scripts, the haversine formula computes great-circle distance on a sphere using d = 2 · R · atan2(√a, √(1 − a)) with a = sin²(Δφ/2) + cos(φ1) · cos(φ2) · sin²(Δλ/2).

If you want to see why the spherical approach is preferred over a straight 3D subtraction through the Earth, the 3D Distance Calculator page runs the Cartesian (x, y, z) version of the same two points.

Four ideas explain why the formula uses radians, sines, and a fixed radius instead of a simpler subtraction.

Together these four ideas let the same formula return the distance, the bearing, and the midpoint from one set of inputs, which is why the page shows all five numbers from the same four coordinate fields.

The planar, flat-Earth version of the same two points uses just x and y instead of latitude and longitude, and the 2D Distance Calculator page shows the formula and midpoint side by side.

Five short steps cover every common case, from a single named city pair to coordinates copied from a spreadsheet.

1. 1 Enter latitude 1 and longitude 1: Type the first point in decimal degrees. The defaults are New York City (40.7128, -74.0060), so the page starts with a recognizable example.
2. 2 Enter latitude 2 and longitude 2: Type the second point in decimal degrees. The defaults are London (51.5074, -0.1278), which gives the classic transatlantic distance.
3. 3 Read the distance in km and miles: The primary outputs are the great-circle distance in kilometers and the same value in statute miles. Both update live as you edit any input field.
4. 4 Read the bearing and the midpoint: Below the distance, the page shows the initial compass bearing from point 1 toward point 2 and the latitude and longitude of the half-way point along the great-circle path.
5. 5 Convert units or rerun with new inputs: For feet, nautical miles, or yards, open the Distance Converter in a new tab. Click Reset on this page to return to the New York to London default.

Try (1.3521, 103.8198) as point 1 (Singapore) and (35.6762, 139.6503) as point 2 (Tokyo). The latitude longitude distance calculator returns about 5311.23 km (≈ 3300.25 mi), an initial bearing near 232.23°, and a midpoint near (19.3787, 111.8200), over the South China Sea.

If your coordinates arrive in degrees-minutes-seconds form like 40° 42' 46", the Coordinates Converter page converts them to decimal degrees before you paste them here.

These benefits matter most when you need a fast, trustworthy number from a coordinate pair without opening a full GIS package.

• • Skip the trig and the arithmetic: Manual haversine problems are easy to get wrong on the radians conversion or the half-angle sines. The calculator handles the trig so you can focus on the inputs and the meaning of the answer.
• • Get km and miles in one pass: Most searches mix metric and US customary units. The page returns both from the same four inputs, using the exact 1 mi = 1.609344 km factor.
• • See the bearing and midpoint alongside the distance: A great-circle answer alone is not enough for trip planning. The page adds the initial compass heading and the half-way point so the distance is immediately useful.
• • Validate coordinates before they reach another tool: Latitude outside [-90, 90] or longitude outside [-180, 180] is rejected with a clear error before any trig runs, so the page doubles as a coordinate validator.
• • Use the same decimal-degree format as GPS devices and GIS exports: Paste a value straight from a phone screenshot, a Google Maps pin, or a CSV export and the page accepts it without re-formatting first.

The page is most useful as a quick check, not as a replacement for a routing engine. Use it to validate a coordinate, to estimate a flight or sea distance, or to pre-compute a radius before the points reach a longer script.

For the same haversine calculation but with nautical miles and a waypoint-style result layout, the Great Circle Calculator page sits next to this one in the math category.

The haversine formula is the same in every case, but a few factors change how the result should be read or what input format you should use.

• • The page is the spherical case only. For sub-percent accuracy on a flat-projection map, switch to an ellipsoidal method (Vincenty) or to a planar distance on a local projection.
• • The great-circle answer is the shortest surface distance, not the road, rail, or flight distance. Real travel paths follow roads, airways, or shipping lanes and are almost always longer.
• • The initial bearing is the heading at point 1 only. The compass heading changes continuously along the great circle, so the bearing at the midpoint is different from the initial value.

According to NOAA National Hurricane Center, the mean radius of the Earth used for spherical distance calculations is 6371.0088 km.

According to NIST, 1 international mile equals exactly 1.609344 kilometers, the value used to convert the great-circle result between metric and US customary units.

When the two points straddle the antimeridian and a flat-projection distance is more useful than a global great circle, convert the pair to UTM first and run the distance there with the Lat Long to Utm Calculator page.