Midpoint Calculator

What “midpoint” actually means on Earth

A midpoint is geographically halfway along a path. On a flat Cartesian plane that's easy — average the x and y values. On a sphere it is not.

The right primitive is the great-circle midpoint: the point at parameter t = 0.5 along the great-circle arc between two surface points. Equivalently: convert both endpoints to 3-vectors on the unit sphere, average the vectors, normalise back to the sphere, convert to lat/lon.

Coordinately's computation uses spherical interpolation throughout. Accuracy versus the WGS-84 ellipsoid is below 0.5 % — well inside the precision most use cases need.

The arithmetic-mean trap

Averaging coordinates feels right and is wrong. The mistake is most striking on long-distance pairs.

For New York to London, the arithmetic mean of the two coordinates lands at roughly (46.1° N, 37.1° W) — a point in the mid-Atlantic. The great-circle midpoint sits at about (52.4° N, 41.3° W), more than 700 km further north.

The arithmetic mean is genuinely useful only for tiny distances — under about 100 km in mid-latitudes. Anywhere else, use the great-circle calculation.

How the computation works

Three equivalent formulations of the great-circle midpoint, all well-documented in geodesy literature:

Vector form (used by Coordinately). Convert each endpoint to a Cartesian 3-vector on the unit sphere, take the arithmetic mean, normalise, convert back to lat/lon. Numerically stable everywhere except at exact antipodes.

Bowditch spherical form.Compute the great-circle bearing and half-distance, then apply the “direct” formula (NGA Publication 9 chapter 24). Same result, derived trigonometrically rather than via vectors.

Ellipsoidal form.Karney's 2013 algorithm computes the geodesic and samples it at parameter 0.5. Differs from the spherical midpoint by under 0.5 % on WGS-84 — indistinguishable for most use cases.

Ten ways midpoint calculation gets used in production

The midpoint is the geometric primitive behind “meet halfway”, “equidistant infrastructure”, and “neutral location” decisions. The ten cases below cover the bulk of real-world traffic; each is paired with a worked example using real coordinates.

1. “Meet halfway” consumer apps

Apps like LetsMeetHalfway, MeetWays, and the “meet halfway” feature inside Google Maps for Business compute the great-circle midpoint between two participants, then surface restaurants or venues within a short radius of it.

Worked example: Friend A at Boston Common (42.3551, -71.0656), friend B at New York's Times Square (40.7580, -73.9855). Midpoint ≈ 41.5605, -72.5360 — near Hartford, Connecticut. A quick search for restaurants near the midpoint surfaces options for a one-meal lunch meet-up.

2. Hub-and-spoke airline route planning

Carriers building hub-and-spoke networks (Delta at Atlanta, Lufthansa at Frankfurt, Emirates at Dubai) use midpoint analysis to test candidate hubs. A hub closest to the midpoint of high- traffic city pairs minimises the total network distance flown.

Worked example:Two of Emirates' major routes — Dubai → New York and Dubai → Tokyo. Without the Dubai hub, a fictional new carrier connecting NYC (40.7128, -74.0060) and Tokyo (35.6762, 139.6503) directly would midpoint near (66.0, -167.0) — near the Bering Strait, terrible for an airport. Hub planning balances geodesic midpoint against geopolitical, economic, and weather constraints.

3. Submarine cable repeater station placement

Transoceanic cables (TAT-14, Marea, FASTER) carry repeaters every 80–100 km. The midpoint of the cable is a critical engineering and political reference: it's the jurisdictional boundary for many international agreements, and it's where bidirectional protection switching converges in failure scenarios.

Worked example: Marea cable endpoints: Virginia Beach, USA (36.8516, -75.9779) ↔ Bilbao, Spain (43.2630, -2.9350). Midpoint ≈ 41.5, -39.4 — mid-Atlantic, deep ocean, where the political demarcation between US and EU jurisdiction sits.

4. Long-haul highway rest-stop planning

US state DOTs and European motorway authorities use midpoint analysis to place rest stops on long routes. Driver-fatigue research (NHTSA, EU TRL studies) recommends a break every 2 hours, which corresponds to roughly the midpoint of a 4-hour driving leg.

Worked example: I-80 from San Francisco (37.7749, -122.4194) to Salt Lake City (40.7608, -111.8910). Midpoint ≈ 39.27, -117.18— Nevada, between Reno and Elko, which is where the highest- capacity rest area on the route is built.

5. Cellular relay / RF mid-link tower placement

Microwave point-to-point links cap out around 80 km without a relay. Telecom RF engineers compute the great-circle midpoint between two endpoints to scout a relay site — typically a hilltop within a few kilometres of the midpoint to ensure line-of-sight to both endpoints.

Worked example: Microwave link Denver ↔ Kansas City — endpoints at (39.7392, -104.9903) and (39.0997, -94.5786). Midpoint ≈ 39.42, -99.79 — Smith County, Kansas — a candidate area for a relay site.

6. Maritime SAR (search and rescue)

US Coast Guard and similar SAR services use last-known-position and target as the input to a search pattern. The expected location of a drifting vessel is initially the midpoint of the LKP and the target — refined by drift modelling.

Worked example: A distress signal from (24.0, -75.0) and an expected port at Nassau (25.0443, -77.3504). Midpoint ≈ 24.52, -76.18— the search pattern's first sweep centre.

7. Trans-continental pipeline pump station placement

Long-haul oil and gas pipelines (Trans-Alaska, Keystone, Druzhba) require pump stations roughly every 80–120 km along the geodesic route. The midpoint is the highest-throughput station — the one that does the most work in either direction.

Worked example: Trans-Alaska from Prudhoe Bay (70.2547, -148.3372) to Valdez (61.1308, -146.3483). Midpoint ≈ 65.68, -147.30 — Pump Station 7, near Fairbanks.

8. Diplomatic neutral venues

Cold-war and modern summits often picked venues approximately halfway between participating capitals. Reykjavík (Reagan– Gorbachev, 1986), Helsinki (multiple), and Geneva (many) are all near-midpoints between Washington and Moscow.

Worked example: Washington D.C. (38.9072, -77.0369) ↔ Moscow (55.7558, 37.6173). Midpoint ≈ 67.7, -27.6 — close to Reykjavík (64.1466, -21.9426), which is about 500 km from the computed midpoint and was the actual 1986 summit venue.

9. Yacht passage waypoint planning

Bluewater sailors crossing oceans pre-plot waypoints along the great-circle path. The midpoint is the canonical “halfway check” — celebrated on long passages as the point of no return.

Worked example: Tonga (-21.1789, -175.1982) → Fiji (-17.7134, 178.0650). Midpoint ≈ -19.45, 178.97 — in the South Pacific, near the Cikobia island group; a useful waypoint for the passage.

10. Sports league neutral host venues

The NCAA, NFL, and FIFA host neutral-site fixtures (championships, international friendlies) at venues equidistant from competing teams' fan bases. The midpoint is the planning starting point; revenue, stadium availability, and weather adjust the final choice.

Worked example: Two NFL fan bases — Seattle (47.6062, -122.3321) and Tampa (27.9506, -82.4572). Midpoint ≈ 38.13, -103.40 — central Colorado. Reasonable candidate cities within 500 km include Denver and Albuquerque.

Choosing the right tool from the “between two points” family

Why the midpoint can sometimes look wrong

• You're comparing it to the arithmetic mean. That's the wrong reference. Great-circle is correct.
• The two points are nearly antipodal. The midpoint becomes mathematically ambiguous — every point on the perpendicular great circle is a valid midpoint. The tool returns one specific result; use it as a hint, not a final answer.
• You expected the “straight line” on a Mercator map. The great-circle path is curved on Mercator; the midpoint sits on that curve. The straight-line midpoint on Mercator is a rhumb-line midpoint and is not what most use cases want.
• One endpoint is at very high latitude. Polar proximity drags the midpoint toward the pole much more than the flat-Earth intuition suggests. This is correct.

Privacy and data-flow notes

Midpoint computation runs entirely client-side using the same spherical-interpolation primitive used elsewhere on the site.

The only network traffic on this page is the optional Mapbox autocomplete on the From and To address inputs, proxied server-side via /api/geocode/suggest with Cache-Control: no-store. Mapbox responses are not cached or retained, per Mapbox ToS §19.2. Browser geolocation is button-triggered only and never automatic.