Remember back in grade school when you were first learning to multiply and divide? Even though the problems all dealt with colliding trains and people who seemed to have a lot of fruit on their hands, the teacher promised this was real practical stuff that you'd need later on.

Well, the teacher was right -- at least, if there's a stair-building project in your future.

Building stairs is an art form perfected by carpenters over the centuries. There is a lot of conventional wisdom about what makes stairs comfortable and practical.

There is also a fair amount of math involved in figuring out how to build them.

Most of the math is used to fix the rise and run -- that is, the height of each stair plus the width of each tread. The rise and run distances determine how comfortable the stairs will be to use. If the rise and run are too great, the stairs will strain your legs and be hard to climb. If the rise and run are too small, you may whack your toe on the back of each step; attempting to

shorten your stride to match the stairs will wear you out.

Over the years, carpenters have determined that tread width times riser height should equal somewhere between 72 to 75 inches.

On a main stair, the maximum rise should be no more than 8 1/4 inches and the minimum run should be no less than 9 inches.

To determine how many steps, or treads, you need, measure from the top of the finished floor on the lower level to the top of the finished floor on the upper level. Don't forget to include the finish -- the flooring, the carpet, the tile, or whatever surface treatment the floor will get. Even if it adds up to just an inch or so, it will affect your calculations. A miscalculated stair with one step out of sync with the others will forever be a death trap for unwary feet.

For a multi-floor house, each flight of stairs should be figured separately -- but the rise and run have to be the same, even if the number of treads is different.

To figure the rise and run in a house with 8-foot ceilings, for instance, start by figuring the total vertical rise. By the time you add floor joists, subfloor and finish floor, the total is usually about 105 inches. A standard number of treads in a stair between first and second floors is 14. One hundred-five divided by 14 equals 7 1/2 . That means the distance from the top of each step to the top of the next step will be 7 1/2 inches.

With a riser height of 7 1/2 inches, tread width (run) should be at least 9 inches. Ten inches is a more comfortable run; when you multiply 7 1/2 inches by 10 inches, you get 75 -- within the conventional ratio of 72 to 75 inches. With 14 10-inch treads, the total run of the stair will be 140 inches. In other words, the entire stair will be 105 inches tall and 140 inches deep.

You can alter the rise and run to some extent. If you used 15 risers instead of 14, for instance, the rise would be 7 inches, and the tread width would be 10 1/2 inches (7 times 10 1/2 equals 73.5, within the rise and run guidelines).

The goal is to create comfortable stairs in the space allotted, ones that are not too steep or too shallow. While you can make small adjustments in the rise and run, you have to stay within the guidelines of 72 to 75 inches riser times run.

Another factor to consider is the head room available. On main stairs you need a minimum of 6 feet 8 inches between the top of each tread and the bottom of any obstruction above it. In older houses, you have to be especially careful about altering the rise and run. If you increase the tread width, you may decrease the head room.

Yes, it is pretty complicated. If trying to figure out how many

apples Jane gave Sally if Sally gave Tom half of them makes your head ache, you probably wouldn't enjoy building stairs. Nor will a little bit of math turn you into a master stair-builder. But knowing how the process works may help you communicate with the expert you hire to do the job.

Mr. Johnson is a Baltimore construction manager. Ms. Menzie is a feature writer for The Sun.

If you have questions, tips or experiences to share about working on houses, write to us c/o HOME WORK, The Sun, 501 N.

Calvert St. Baltimore, 21278. Questions of general interest will be answered in the column; comments, tips and experiences will be reported in occasional columns.