How many kilometres of blood vessels are in a human body?

How to get close to this number

Work from the job the system has to do. Every cell in the body needs to sit within a very short distance of a capillary, because oxygen only diffuses a fraction of a millimetre. Fill a human-sized volume with a mesh fine enough to satisfy that constraint and the total length becomes enormous almost automatically. The geometry, not the anatomy, is what produces the answer.

People guess low because they picture the plumbing they can see. Arteries and veins are the visible, nameable part of the system, and there are not many of them; but as the explanation notes, nearly all of the length is capillaries thinner than a hair. Whenever a total is dominated by the smallest and most numerous component, intuition built on the large visible parts will undershoot badly.

Treat this as an order-of-magnitude figure rather than a measurement. Nobody has laid out a circulatory system end to end; the total is estimated from tissue samples scaled up to a whole body, and published values vary considerably depending on the method and the assumed body size. It is a genuinely useful number for understanding the scale of the system, and a genuinely imprecise one, which is an honest combination worth flagging.