What the heck does "Productivity" mean?

I'm often asked to define productivity and its algorithm. Also, I often hear productivity, production, and capacity used interchangeable. For some reason this drives me nuts because they all have different meanings.
I hope my write up below helps you understand what productivity means.

What is productivity?
Productivity is the ratio of outputs (goods and services) divided by one or more inputs (labor hours, FTEs, capital, expenses).



Improvements in productivity can be achieved by either increasing output without increasing the inputs, decreasing inputs without decreasing output, or increasing output and decreasing inputs.

Output implies production (quantity) of goods and services while input means land, labor, capital, management etc. Productivity measures the efficiency of the production system. Higher productivity means producing more from a given amount of input or producing a given amount with minimum level of inputs.
In other words, the more the output from one worker, one machine, or a piece of equipment per day per shift, the higher is the productivity (producing more output with the same resources).

In strategic operations management, productivity and production are two different terms. Productivity is the ratio between total output and the total inputs used in the production process. Production is an absolute; it refers to the volume (quantity) of output. Production volume may increase but productivity may decline as a result of inefficient use of resources. More efficient use of inputs may increase productivity but the volume of production may not increase. Production refers to the end result of production system whereas productivity reflects its efficiency.

Some of the potential benefits derived from higher productivity are as follows:
1. It helps to cut down cost per unit and thereby improve the profits.
2. Gains from productivity can be transferred to the consumers in from of lower priced products or better quality products.
3. These gains can also be shared with workers or employees by paying them at higher rate.