You can't have one riser that is shorter than the rest because it's a trip hazard. That's why you round up to the next whole number.
Any opening in a floor weakens the structure. Consult a professional before cutting out the opening.
A correctly sized opening for a stairwell allows sufficient width for a person to walk up and down, and enough headroom to avert the sickening "thwack" that occurs when a person's head makes unexpected contact with the ceiling. According to the National Safety Council 984,000 people suffered injuries as a result of using stairs during 1996. Calculate the optimal opening for stairs that looks right in the space and also reduces the possibility of injury.
Measure the stairway width, or consult the building plans. The generally accepted minimum width for a stairway is 36 inches. The width of the stair opening is 36 inches or the actual width of the stairway, whichever is greater.
Measure the distance from the floor where the base of the stairs will be to the ceiling. Record it. Cut a small hole through the ceiling, within the area you know will be removed for the stairs. Make the hole big enough to let you easily measure the distance from the ceiling to the surface of the upper floor. Call this distance the floor thickness. Add the two measurements together to determine the total height, or rise, of the stairs. For example, if the floor to ceiling distance is 110 inches and the floor thickness is 10 inches, the total height is 120 inches.
Divide the rise of the stairs by the height of the risers, the vertical backs of the steps. The maximum permitted height of a riser is usually 8 1/4 inches, so divide the total rise of the stairs by 8 1/4, and round up to the next whole number. The result is the number of risers required. For example, if the total rise is 120 inches, divide 120 by 8 1/4 to obtain 14.54. Rounded up, that becomes 15.
Subtract one from the number of risers -- there is one less tread than there are risers on any stairway -- and multiply it by the depth of each tread. For example, if the treads are 10 inches deep and there are 15 risers, multiply 10 by 14. The result is the run or horizontal distance covered by the stairs. In the example, the run is 140 inches, or 10 inches times 14.
Decide upon the minimum headroom clearance needed. The common value used is 6 feet 8 inches, but you may prefer a greater value, such as 7 feet (84 inches).
Substitute the values calculated in the previous steps into the following equation:
Stair opening = ((floor thickness + headroom clearance) x stair run) / stair rise.
The length of the stair opening is represented by the following equation.
Opening = ((10 + 84) x 140) / 120
Progressively simplifying the equation gives (94 x 140) / 120, then 13,160 / 120, and finally 109.67. The example stair opening needs to be 109.67 inches, or 9 feet 1 2/3 inches.
David Robinson has written professionally since 2000. He is a Fellow of the Royal Geographical Society and the Royal Meteorological Society. He has written for the "Telegraph" and "Guardian" newspapers in the U.K., government publications, websites, magazines and school textbooks. He holds an honors Bachelor of Arts in geography and education and a teaching certificate from Durham University, England.