Pull up a flight from New York to Tokyo on a map and the route arcs way up over the Arctic instead of heading straight across. It looks like a detour. It isn't. Flight paths look curved because the shortest route over a round Earth — a "great circle" — projects as a curve when you flatten the globe onto a rectangular map. The plane is flying about as straight as it can; it's the map that's bending the truth. Here's why.
The short answer
On a flat map (the familiar Mercator projection), a straight line is not the shortest path between two distant points. The Earth is a sphere, and the shortest path across a sphere follows a great circle — a curve that, on a flat map, sweeps toward the nearer pole. So the "curved" route is actually the straight one in reality, and the "straight" line you'd draw on the map is the longer way around.
What a great circle is
A great circle is any circle drawn on a sphere whose center is the center of the sphere — the equator is one, and so is any line of longitude. The key property: the shorter arc of the great circle connecting two points is the shortest possible path between them along the surface. For a globe, that's the equivalent of a straight line.
The reason it looks bent comes down to map projection. Mercator maps stretch the world into a rectangle, badly distorting distances toward the poles — Greenland looks as big as Africa but is a fraction of the size. A straight line drawn on that stretched rectangle (called a rhumb line, a path of constant compass bearing) is genuinely longer than the great circle. New York to Tokyo along a rhumb line is hundreds of miles further than the polar great-circle arc airlines actually fly.
Why routes aren't exactly great circles
Great circle is the baseline, but real routes deviate from it for practical reasons — which is why they rarely trace a perfect arc:
- Winds. Flights ride tailwinds and dodge headwinds; a longer path through a strong jet-stream push can be faster and cheaper than the geometric shortest one.
- Airspace and overflight. Political boundaries, restricted zones, and overflight fees push routes around certain countries.
- ETOPS and diversion airports. Twin-engine aircraft over oceans must stay within a certain flying time of a suitable airport, nudging the track.
So the honest picture is: the great circle sets the shape, and winds, airspace, and safety rules bend it a little from there.
Why do planes fly over the North Pole?
Because most of the world's big cities are in the northern hemisphere, and the great-circle path between two northern points bows toward the pole. New York–to–Beijing, Chicago–to–Delhi, London–to–Tokyo — the shortest line between them runs far closer to the Arctic than a flat map suggests. It's not that the pole is "on the way" in any intuitive sense; it's that on a sphere, up and over really is shorter than straight across.
Calculating it yourself
The math behind the shape is the same great-circle (haversine) formula that gives you distance and initial bearing between two airports. If you want the numbers — how far apart two airports are along that curve, and what heading a flight departs on — SkyLink API's distance endpoint returns great-circle distance, initial bearing, and the route midpoint from two airport codes in a single call. We walk through the formula and the API in How to Calculate Distance Between Airports, which is the natural next read if this piece made you want to plot the arc yourself.
SkyLink API gives you a free tier of 1,000 requests/month to compute great-circle routes against, with paid plans starting at $19/mo for production traffic. It's available through the free trial — sign up, grab a key, and turn the curve on the map into real distances and bearings.