Calculating small changes in distance.

Okay so here is the problem. I need to calculate a small change 3in>dx>1in then display that change in distance.

The distance would be measured from a compression pad, with a single axis accelerometer placed in the middle of it.

I am having trouble converting the raw data into a distance measurement and then getting the distance measurement to the output in time.

Is there an easier way to calculate the distance, something that would cut down on processing time?
Or an easier way to calculate distance in compression?

a compression pad, with a single axis accelerometer placed in the middle of it

What do you mean by this? Can you post a drawing?
How is it being compressed, and what sort of acceleration values do you expect?

It is a separate area with an accelerometer glued to the middle. Basically the mat is just an area of flexible material where the accelerometer can be placed so that compressions in the isolated area will not effect the rest of the design.

It is being pushed down by human hands and rapid acceleration is expected.