Why twice as tall is not twice as heavy
Make a person twice as tall with the same proportions and every area, including the cross-section of their bones and muscles, grows four times, while their volume and weight grow eight times. Each square inch of bone then carries twice the load. That is the square-cube law, which Galileo described in 1638.
Draw Robert Wadlow beside the average manThe law in numbers
Height ×1.5 gives area ×2.25 and volume ×3.375. Height ×2 gives area ×4 and volume ×8; height ×3, area ×9 and volume ×27. Weight follows volume, and the strength of a bone or a muscle follows its cross-section, an area.
So the load on every square inch of bone grows as fast as the height itself: half as tall again, half as much load again on each square inch.
The tallest person on record
Robert Wadlow stood 8 ft 11.1 in (2.72 m), 1.55 times the height of an average US man of 5 ft 9 in. Scaled up with the same proportions, the average man would have 2.4 times the bone cross-section and weigh 3.7 times as much. Wadlow weighed 439 lb (199 kg) at his death at 22.
Real tall people are not scaled-up copies of anyone: proportions differ from person to person at every height. The law describes what scaling alone does.
Why an elephant is not a big mouse
Large animals have proportionally thicker bones than small ones, because each bone carries more weight for its cross-section. J. B. S. Haldane made the point in his 1926 essay “On Being the Right Size” with a giant 60 ft tall: weighing 1,000 times as much as a man, every square inch of his bones would carry 10 times the load, enough to break a thigh bone at each step.
The same arithmetic is why each taller skyscraper is harder to build, and why a monster many times human height could not stand up in the real world.
Wikipedia, Square–cube law · Wikipedia, On Being the Right Size
What the drawings here show
The charts on this site scale standing height only. A figure drawn twice as tall is not drawn to carry eight times the weight; outlines are symbols, and width is illustrative.
Try the same example
Draw Robert Wadlow beside the average man. The names, units and values carry into the editable chart.
For the arithmetic alone, use the height difference calculator. For a different unit, use the height converter.
The next useful step
How the charts work explains the shared scale, source precision and custom inputs.