For every 12 feet in height, you need a landing.
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Depends on how big your steps are and how long your legs are.
Well that depends on how long the steps are. If you assume a step would be 2 feet. A mile is 5280 feet so it would be 2640 steps in a mile. Three miles would then be 7920 steps.
Depends on the height you want to go up or down.
Assuming you mean steps like "footsteps", you need to know how long a "step" is. For the average person, it's somewhere around 2.2 - 2.5 feet. Let's just say 2.5 for now. To convert, divide your total number by the step length: 400 ft / 2.5 ft/step = 160 steps.
You need to know the speed before anyone can answer this.