Ever wonder why getting stepped on by a heeled shoe hurts more than getting stepped on by a flat one? Under Pressure on this Moment of Science.
In physics, pressure depends on the amount of force acting on a surface and on the size of the surface. The smaller the surface, the greater the pressure. Let's say that a woman steps on your toe; she weighs 120 pounds. If she's wearing flat shoes, you would feel the force of 120 pounds spread out over the whole heel of the shoe, maybe around 4 square inches. So the pressure would be 120 divided by 4, or 30 pounds per square inch.
But when she steps on you with a high heel, the whole 120 pounds of force is concentrated on a heel that is maybe one eighth of one square inch in area. Now the pressure of her step is eight times as much, or 240 pounds per square inch instead of 30 pounds per square inch. Of course, it hurts more.
It works the other way, too. Spiked heels are painful to wear because your weight is all on the spike and the ball of the foot; therefore, the pressure is much greater on these points than in running shoes, where your weight is spread out over the whole bottom of the foot.