Why does a change in depth in water give a far greater difference in pressure than the same change in height in air?

Begin by explain that pressure is described by the amount of force exerted on a given area (N/m²). The force in this equation is given by the weight of everything directly above the point you are measuring. We may calculate this force as follows: Force = Height x Area x Density x g. Dividing both sides by Area gives us an equation that calculates pressure: (Remember Pressure = Force/Area). Pressure = Height x Density x g. Because water is much denser than air (almost 1000x), a much smaller difference in height is needed for the same change in pressure in water. Conclude by giving a tangible example: a bottle of water exerts a much greater pressure on your hand than a bottle of air.