As a general rule of thumb in stair building the sum of the tread and riser should equal around 17 1/2 inches. This is a general rule of thumb for a comfortable, easy to walk up and down set of stairs.
For example if your stair tread is 10 inches and the stair riser is 7 1/2 inches you have a comfortable stairway. Walking up and down a stairway using this formula creates a comfortable set of stairs. The next time you walk down any uncomfortable set of stairs measure the stair tread and riser. You will be amazed at what you'll find.
For public stairs or heavily used stairs this method will become one of your best friends. On public stairs you have liability issues and of course lawyer issues if you are the owner of the building. If you are not building a safe set of stairs that meets your local building codes standards you could be in for a whopping financial nightmare.
Building safe stairs as a contractor is your obligation to society. I don't know how many times I come across a loose stair tread or a broken hand rail. One of the biggest problems I find is in the poorer neighborhoods you come across some major construction problems and safety hazards. I never have been able to figure out why a building owner would not want to protect himself financially and the people that occupy and use his buildings safety.
Here's something you need to avoid when using the stair building general rule of thumb. This rule of thumb does not apply to good to an 8 inch tread with a 9 1/2 inch stair rise. You don't want to be building a latter you want to be building a safe set up stairs.
The maximum stair rise you can use for most building codes is 8 inches. You will not find the stairway to comfortable with a 9 1/2 inch stair tread and an 8 inch riser. If you have no choice and are cramped for space and you can't redesign this stairway to fit in the house or building then at least make sure you have a nice sturdy grip able stair hand rail.
This formula works great when you are working with exterior landscaping and you have a long run of stairs with a small rise. For example: if you have a 14 inch stair tread and you use a 4 inch riser this will lead to a comfortable step.
Look for stairs in your neighborhood or around some apartment complexes that don't follow these rules and have 16 inch stair treads with 7 inch risers. You will find yourself taking two steps on the stair tread on every other step and it is not a real comfortable stairway.
Happy stair building and keep this formula in mind for a nice comfortable set of stairs in your building future.