Latitude Longitude Distance Calculator

What the Latitude Longitude Distance Calculator Measures

This calculator computes the great circle distance between two or more points on Earth's surface given their latitude and longitude coordinates. The great circle distance is the shortest possible surface path between any two points -- the path you would travel if you could fly in a perfectly straight line ignoring all terrain, roads, and air corridors. It is sometimes called the "as the crow flies" distance, and it is what aviation, maritime, and GPS navigation systems use as their baseline distance measurement.

The result is different from driving distance, which follows road networks and is always longer. For two points in the same city, the great circle distance may be 5 km while the driving distance is 7 or 8 km. For two points separated by a mountain range or bay, the straight-line distance might be 30 km while the driving route is 80 km or more. According to the NOAA National Geodetic Survey, the great circle (geodesic) distance is the internationally agreed reference measurement for any two geographic coordinates, forming the basis for all aviation and maritime distance reporting.

The Haversine Formula: Step by Step

The haversine formula calculates the great circle distance between two points from their latitude and longitude in four steps. Step 1: convert all coordinates from degrees to radians (multiply by π/180). Step 2: compute a = sin²(Δφ/2) + cos(φ₁) × cos(φ₂) × sin²(Δλ/2), where φ is latitude and λ is longitude. Step 3: compute c = 2 × arcsin(√a). Step 4: multiply by Earth's mean radius: d = R × c = 6,371.0088 km × c.

The haversine function, sin²(x/2), is numerically preferred because it remains well-behaved for very small angles (nearby points) where the simpler law of cosines formula would divide nearly equal numbers and lose precision. The maximum error of the spherical haversine formula compared to the WGS84 ellipsoidal Vincenty formula is approximately 0.3%, or about 22 km on a 7,300 km route. For distances under 2,000 km this error is under 6 km. The USGS Map Projections reference details the difference between spherical and ellipsoidal distance calculations for those requiring sub-metre accuracy.

How Many Kilometres Per Degree? Scale Reference by Latitude

Understanding the degree-to-kilometre scale helps you estimate coordinate distances mentally. One degree of latitude is approximately 111.32 km anywhere on Earth (ranging from 110.57 km at the equator to 111.69 km at the poles). One degree of longitude depends on latitude: it equals 111.32 × cos(latitude) km. At the equator, one degree of longitude is 111.32 km -- the same as latitude. At 45° N (central France, Oregon), it is 78.7 km. At 60° N (Oslo, Anchorage), it is 55.7 km. At 80° N (northern Greenland), it is 19.3 km.

This latitude dependence of longitude scale is why you cannot compare a coordinate difference in latitude directly to the same difference in longitude at high latitudes. A 0.1-degree change in latitude always means about 11.1 km, but a 0.1-degree change in longitude means 11.1 km at the equator and only 1.9 km at 80°N. The USGS arc-second distance guide provides the full table for all major latitudes, and this calculator shows the values for your specific midpoint latitude in the scale reference panel.

Multi-Stop Routes: Calculating Total Distance with Waypoints

A multi-stop route calculation works by computing the haversine distance for each consecutive pair of points separately, then summing all the segment distances. For a route with points A, B, C, and D, the total distance is d(A,B) + d(B,C) + d(C,D). Each segment is calculated independently using the coordinates of just those two endpoints. This is how trail GPS devices, flight planning software, and shipping route optimisers calculate accumulated track distance.

The per-segment breakdown is valuable for spotting anomalies: a segment that is disproportionately long (shown as a high percentage of total in the table) often indicates a GPS recording error, a missed waypoint, or a route detour. Trail race certification bodies, including those following World Athletics technical specifications, require accumulated GPS waypoint distances rather than single start-to-finish great circle measurements precisely because the multi-segment method captures every turn and elevation change in the course profile.

Straight-Line vs Driving Distance: What This Calculator Gives You

This calculator gives straight-line surface distance (great circle), not driving distance. For most planning purposes, the straight-line distance is the correct starting point: it tells you the minimum possible distance between two locations and gives an upper-bound estimate for travel time at any given speed. Driving distances are typically 20 to 40% longer in urban and suburban areas and can be 2 to 5 times longer in mountainous or island terrain.

The travel time display in this calculator uses the straight-line distance with a selected speed. For driving scenarios, the displayed time should be treated as a theoretical minimum; actual driving time will be longer. For aviation scenarios, the great circle distance is the correct basis for block-time estimation because commercial aircraft fly geodesic routes (adjusted for wind), not road-following paths. Maritime distances are typically calculated in nautical miles along established routes, and the International Maritime Organization uses great circle distance as the standard datum for voyage planning and search-and-rescue radius calculations.

Accuracy: When the 0.3% Spherical Error Matters and When It Does Not

The haversine formula treats Earth as a perfect sphere of radius 6,371.0088 km (the IUGG mean radius). Earth is actually an oblate spheroid slightly flattened at the poles, with an equatorial radius 21 km larger than the polar radius. This difference causes the haversine formula to overestimate or underestimate distances by up to 0.3% compared to the WGS84 ellipsoid model used by GPS systems. For a 500 km distance, the maximum error is 1.5 km. For a 10 km distance, the maximum error is 30 metres.

For navigation planning, logistics, route estimation, and most engineering applications, a 0.3% error is entirely negligible. For land surveying, legal boundary determination, and geodetic reference work, the more precise Vincenty or Karney ellipsoidal formulas are required. The NOAA NGS inverse tool uses the Vincenty formula for professional geodetic work and gives results to millimetre precision. For all practical distance estimation needs, haversine with Earth's mean radius gives results accurate enough for confident decision-making.