Tukuk-OS📏 Washington, D.C. to Montreal
| Great-circle (haversine, R = 6371.0088 km) | 786.3 km |
| Miles (international) | 488.6 mi |
| Nautical miles | 424.6 nmi |
| Initial true bearing | 20.2° NNE |
| Flight at 900 km/h (no climb, taxi or wind) | 52 min |
| Drive at 80 km/h, non-stop | 9.8 h |
| Latitude change | 6.5900° |
| Longitude change | 3.4700° |
ℹ️ What this tool does & how it works
The air line between the two is 786 km (489 statute miles, 425 nautical miles). It comes from the haversine formula on the two coordinate pairs the page carries — Washington, D.C. at 38.9100° N, -77.0400° W and Montreal at 45.5000° N, -73.5700° W — using the IUGG mean Earth radius of 6371.0088 km. Leaving Washington, D.C. toward Montreal you start on a true bearing of 20.2° (NNE); because the Earth curves, that heading drifts as you go.
How the Washington, D.C. and Montreal distance is worked out
Two points on a sphere are separated by the shorter arc of the great circle that passes through both of them, and the haversine formula is the numerically stable way to get its length: it converts the latitude difference and the longitude difference into a single chord ratio, takes its square root, and multiplies by twice the radius. Written that way it stays accurate even for pairs a few kilometres apart, which is why it is still the standard in navigation code. The radius used here is 6371.0088 km, the IUGG mean radius; on the true WGS84 ellipsoid the same Washington, D.C.–Montreal arc differs by a few tenths of a per cent depending on the route's orientation, which is well inside the error of a city-centre coordinate.
What that number means for an actual trip
It is the distance a bird flies. A 786 km line becomes roughly 1,022 km of road once hills, borders, river crossings and bypasses are counted — the 1.2 to 1.4 multiplier is the usual empirical range, and this page does not pretend to know the road you would take. Air distance is closer to the figure above, though airline routings, wind and holding add time to the 52 minutes a perfect 900 km/h cruise would take. Rail sits between the two. The latitude and longitude changes in the table show why the line is not simply "north" or "east": a 6.59° shift in latitude is about 732 km, while the same number of degrees in longitude shrinks with the cosine of the latitude.
Both positions, exactly
Washington, D.C., United States (Americas): 38° 54′ 36.0″ N, 77° 02′ 24.0″ W — decimal 38.91, -77.04, GeoHash dqcjqgm5j. Montreal, Canada (Americas): 45° 30′ 0.0″ N, 73° 34′ 12.0″ W — decimal 45.5, -73.57, GeoHash f25dvg5bw. Those two pairs are all this page needs, and everything above is derived from them; nothing is fetched, and the coordinates you can edit in the form are recalculated by your own browser, so a different pair costs nothing and stays on your device.