How Far Is a Degree?

Miles Off scores you on kilometres, but you aim on a grid of degrees. Converting between the two is one small number and one cosine, and holding them turns the reveal screen's distances from a verdict into information you can actually use.

The 111-kilometre rule

One degree of latitude is almost exactly 111 kilometres, everywhere on Earth (it drifts between about 110.6 and 111.7 km because the planet bulges, but never enough to matter at game scale). This is not a coincidence so much as a family history: the metre was originally defined as one ten-millionth of the distance from the equator to the North Pole, so the pole-to-equator arc is 10,000 km, spread over 90 degrees. Ten degrees of latitude is 1,110 km; the width of a fingernail against a desktop globe is a few hundred.

Longitude shrinks

A degree of longitude is 111 km only at the equator, because the circles of longitude converge at the poles. The rule is 111 km times the cosine of the latitude: at 45° a degree of longitude is about 79 km, and at 60° (Oslo, Anchorage, St. Petersburg) it is exactly half, about 55 km. This is why east-west misses in the far north are cheaper than they look on a flat map, and why the flat map exaggerates them (the Mercator guide is the long version of that complaint).

The scale of a miss

• 30 km: the game's bullseye radius, about a quarter of a degree. City-level precision.
• 300 km: under three degrees of latitude. Right region, wrong neighbourhood; the scoring curve barely minds.
• 1,000 km: nine degrees. Wrong country in Europe, wrong state in big countries. Survivable.
• 5,000 km: a wrong continent. The exponential curve has already taken nearly everything.
• 20,000 km: the theoretical maximum. Half the planet's circumference (40,000 km around, and yes, that round number is the metre's definition again) puts you at the antipode: the exact opposite point on Earth. Madrid to Wellington is close to this worst case.

Great circles, or why the arc looks bent

The dashed arc on the reveal screen is a great circle: the shortest path between two points on a sphere, the line a stretched string would take. On the globe it looks straight; on a flat map it looks like a detour. The shortest route from New York to Tokyo arcs up past Alaska; London to Los Angeles passes over Greenland. Airlines are not being scenic, they are being spherical. Miles Off measures every distance this way, so your miss is always the honest, string-pulled-tight number.

Using the numbers mid-game

Two habits pay off. First, calibrate your zoom: before you pin, know roughly how many kilometres the visible map spans, so a "small nudge" is a known quantity rather than a hope. Second, read your reveal distances in degrees: a 220 km miss is two degrees, an aiming error; a 2,200 km miss is twenty degrees, a knowledge error. The first kind wants a steadier hand, the second wants an evening with the anchor scaffold. Knowing which lesson a miss is teaching is most of improving.