Circunferência da Terra na Latitude

Circumference of the Earth at a given latitude

The parallel at latitude φ is a circle smaller than the equator. Its circumference is C = 2π·R·cos(φ), with R = 6,371 km (Earth's mean radius) and φ in radians or degrees (using the right cosine). At the equator (φ = 0°), C ≈ 40,075 km; at the Tropic of Cancer (~23.4°), C ≈ 36,788 km; at latitude 60°, C ≈ 20,038 km (half the equator); at the poles, cos(90°) = 0 and C = 0. The result tells you the total east-west distance you would travel by going once around the planet at that latitude, which is also useful to convert longitude differences into kilometers.

Applications

Celestial navigation, map projection design (Mercator stretches the higher latitudes precisely because the real parallels shrink), GPS calculations, satellite ground-track analysis and estimating east-west separation in degrees on the ground for logistics or aviation.

FAQ

Why is the equator the biggest circle? Because it sits in the same plane as Earth's center — any other parallel is a "small circle" cut by a plane that does not pass through the center.

How does this help find east-west distance? Divide the parallel circumference by 360° to get km per degree of longitude at that latitude (~111.32·cos(φ) km/°).

Does the formula account for Earth's flattening? No — it assumes a perfect sphere. The real ellipsoid is ~21 km flatter at the poles, an error under 0.3% for most uses.