Not a stair expert but this is from the International Building Code.
There maybe a better section that applies
1009.9 Spiral stairways. Spiral stairways are permitted to be used as a component in the means of egress only within dwelling units or from a space not more than 250 square feet (23 m2) in area and serving not more than five occupants, or from galleries, catwalks and gridirons in accordance with Section 1015.6.
A spiral stairway shall have a 71/2 -inch (191 mm) minimum clear tread depth at a point 12 inches (305 mm) from the narrow edge. The risers shall be sufficient to provide a headroom of 78 inches (1981 mm) minimum, but riser height shall not be more than 91/2 inches (241 mm). The minimum stairway clear width at and below the handrail shall be 26 inches (660 mm).
Spiral stairways are generally constructed with a fixed center pole that serves as either the primary or the only means of support from which pie-shaped treads radiate to form a winding stairway.
The commentary to Section 1009.4.3 regarding the possible event of nonconcentric movement on stairways with winders also applies to spiral stairways. The nature of stairway construction is such that it does not serve well when used in emergencies that require immediate evacuation, nor does a spiral stairway configuration permit the handling of a large occupant load in an efficient and safe manner. Furthermore, it is impossible for fire service personnel to use a spiral stairway at the same time and in a direction opposite that being used by occupants to exit the premises, possibly causing a serious delay in fire-fighting operations. Therefore, this section allows only very limited use of spiral stairways when part of a required means of egress. Spiral stairways may be used in any occupancy as long as such stairways are not a component of a required means of egress.
Spiral stairways are required to have dimensional uniformity. The stairway must have a clear width of at least 26 inches (660 mm) at and below the handrail. The depth of the treads must not be less than 71/2 inches (191 mm) measured at a point that is 12 inches (305 mm) out from the narrow edge (see Figure 1009.9). Riser heights are required to be the same throughout the stairway, but are not to exceed 91/2inches (241 mm). Minimum headroom of 6 feet, 6 inches (1981 mm) is required.
There is a picture::: see figure 1009.9
http://publicecodes.cyberregs.com/icod/ibc/2009f2cc/icod_ibc_2009f2cc_10_par107.htm?bu2=undefined