Yes, the best formula is T = 20-(4R/3) which results in a 6" Riser and a 12" Tread.

I checked further into the above stair formula and found that it only applies at a riser height of 7" or greater.

For a 6" riser a comfortable tread would be 13 1/2".

At a riser height of 5 1/2" the stair will be at a "critical angle" where a ramp would be more appropriate.

The minimum stair riser is 5".

All dimensions taken from the AIA's Architectural Graphic Standards.

check with your local building dept as there are building codes for stairs.

Modern building codes set a maximum riser height and minimum tread depth but no longer offer a riser/tread ratio formula for comfort.

Thanks for the great info. Follow-up question: On open stairs there often is a little overlap at the back of the step, where the risers would be if you had them. Do you think the 13.5 inches for 6" riser height can include that overlap? In other words, say the tread is 13.5 inches, but overlaps 1.5 inches, for an effective tread depth of 12 inches (even though your foot could, technically, go past 12 inches to hit the back of the tread, or even over the edge of the back of the tread. Why that might happen I don't know, ;) but it could). Would that be appropriate, considering the formula?

When an open riser stair is designed to have a 13.5" tread, the horizontal dimension from the leading edge of one tread to the leading edge of the tread below will be 13.5 regardless of how much you overlap the treads so the actual physical size of each tread will be 13.5" plus the overlap dimension.

If you overlap 13.5" treads 1.5" you would have a stair with an effective tread dimension of 12" which is allowed by code but would be awkward to use with a 6" riser. If 13.5" is too large for your layout you should reduce the riser height as well as the tread depth using a stair design chart.

Open risers are permitted, provided that the opening between treads does not permit the passage of a 4-inch diameter sphere. For your stair you could add a partial riser under each tread back from the leading edge of the treads (creating a nosing) or place a rigid rod or dowel to create the same restriction.

Keep in mind that such a slowly rising stair, especially if it has open risers, will be one that many people will find uncomfortable to use. Codes only prevent excessively small treads and tall risers; the purpose of the stair design formulas and charts is to avoid stairs that force people to walk in an unnatural, unbalanced manner. The normal range of a tread is 9" (where allowed by code) to 11". In my opinion, a stair with a tread of 11" or larger should have handrails on both sides (code requires only one handrail in a residence).

Okay, thanks for that great explanation. I don't really understand the ergonomics of the tread/riser ratio - can you explain it to me? And ... if I planned on a 12" tread, what would be the optimum riser height? And would I have to have extremely thick treads in order to make the 4" sphere requirement?

If you wish to design a non-standard stair you need to know enough about how a foot moves on a stair to be able to avoid creating a dangerous condition.

The idea that you suggest of thickening the tread until the opening is only 4" is a good example of a dangerous condition because it is likely to cause the heel of someone descending to catch on the bottom of the thickened tread and cause a fall. A thickened tread could also cause someone to catch their toe when ascending but the fall would probably be less serious. In the site linked below, the author says the most dangerous condition is the "heel-catch" shown in figure 4. The study says, "During a heel-catch fall, the victim frequently tumbles disastrously all the way to the landing."

The only two code approved ways of meeting the maximum open riser requirement is 1) to use a "partial riser" as shown in Figure 1c where the RO is 4 inches or less and the nosing of the upper tread is a standard design as prescribed by the code (nosing length between 3/4" and 1 1/4", and the max. nosing radius 9/16" Look at the PDF at this URL: jself.com/stair/StairCodes.pdf), or 2) to use a metal or wood rod to achieve the same results which is shown in the document linked above.

Poorly designed stairs can be very dangerous and open riser stairs are the most dangerous kind. I will not use them not only because of the unnecessary risk of injury but because of the awkward space created below them.

Here is a link that might be useful: Stair Fall Injuries

A glance over the previous posts did not find a mention of the very long horizontal area required for stairs with 6" riser. If exterior, it may not matter. If interior, it will require huge amounts of floor space- on every floor served by the stairs.

It would be about 9 ft longer, difficult to carpet, and would create an awkward space underneath. What's not to like?

There have been studies of the proper design of stairs since the ancient Greeks. What is accepted today is that the angle of rise is not a factor within the range of about 20 to 40 degrees with the middle of that range being preferred for comfort and safety and that there is a desirable average gait when ascending and descending stairs that does not change for all stairs in that angle range. The gait is measured vertically and horizontally over 2 risers and 2 treads often with the vertical movement value being increased relative to the horizontal movement value because it is generally slower.

Therefore, as the design riser height is reduced, the forward travel distance is normally increased in order to avoid a reduction in the gait. In general, it is better to lengthen the standard gait for a slow rising "grand" stairway rather than allowing it to be shortened as you are proposing.

The formulas used by designers to determine the best riser and tread ratios is a matter of design choice rather than building code requirements although most codes limit the tallest riser and the shortest tread but those limitations should not be taken as a recommendation for a stair design. For professional designers over the past 50 years the generally accepted best riser and tread has been 7.5"/10" and more recently 7"/11" for public uses. For other stair angles within the code limits, designers use many different formulas:
R + T = 17 to 18
R X T = 70 to 75
2R + T = 25
Arch. Graphic Standards chart
These formulas are listed in the order of increasing usefulness. Since you would use the larger value of these formulas, a 6" riser height would require a 12", 12.5", 13", or 13.25" tread depth which is a large range so you could pick a value in the middle like 12.5". If everyone in your house is short you could use 12" but a taller person might find the rate of ascent and descent frustratingly slow.

IMHO if you want a slow rising "grand" stairway you must lengthen rather than shorten the gait so it is better to err on the long side and use a 13" tread.

I have found that the 2R + T = 25 formula works best because it recognizes the greater importance of vertical foot movement relative to horizontal foot movement in maintaining a comfortable gait but the Arch. Graphic Standards chart is even better.