Suppose you dug a shaft straight down from your feet to the exact centre of the Earth. How many kilometres deep would it be?

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Answer

About 6,400 km

The deepest hole ever drilled, the Kola Superdeep Borehole in Russia, reached just 12.2 km before the heat made further drilling impossible.

How to estimate it

The shaft's depth is simply Earth's radius, and the radius follows from the circumference. A trip around the planet is 40,000 km, and circumference equals 2 × 3.14 × radius. So the radius is 40,000 / 6.28, about 6,370 km. The accepted average is about 6,400 km, slightly more at the equator than at the poles because the planet bulges.

Source: NASA Earth Fact Sheet

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