—In a proceeding pursuant to CPLR article 78 to review a determination of the Zoning Board of Appeals of the Village of Grand-View-on-Hudson, dated April 17, 1990, denying the petitioner a variance and a certificate of occupancy, and vacatur of a stop-work order, the Zoning Board of Appeals of the Village of Grand-View-on-Hudson appeals from stated portions of a judgment of the Supreme Court, Rockland County (West, J.), dated November 14, 1990, which, inter alia, directed it to issue the petitioners an area variance, and a certificate of occupancy, and the petitioners cross-appeal from so much of the judgment as declined to vacate the underlying stop-work order, which vacatur would have obviated the need for a variance.
Ordered that the judgment is affirmed, without costs or disbursements.
This appeal is the culmination of a long and acrimonious battle between the petitioners and the Village of Grand-View-on-Hudson concerning the petitioners’ construction of a single-family dwelling upon a lot they own in the village. In essence, this appeal concerns whether the ceiling in one-half of the petitioners’ basement will be seven feet six inches high or five feet eleven inches high.
A decision by a zoning board to grant or deny a variance will not be set aside absent a showing of illegality, arbitrariness, or an abuse of discretion (see, Matter of Fuhst v Foley, 45 *711NY2d 441; Consolidated Edison Co. v Hoffman, 43 NY2d 598; Matter of Brucia v Planning Bd., 157 AD2d 657). A zoning board’s decision will be sustained if it has a rational basis and is supported by substantial evidence (see, Matter of Fuhst v Foley, 45 NY2d 441, supra; Consolidated Edison Co. v Hoffman, 43 NY2d 598, supra). Here, the reasons stated by the Board of Zoning Appeals for denying the petitioners’ request for a variance concerning an aggregate floor area in excess of the applicable zoning limit are not supported by substantial evidence. Consequently, the Supreme Court’s ruling, directing the respondent to grant a variance and issue a certificate of occupancy, is affirmed.
In light of this determination, we need not reach the merits of the petitioners’ cross appeal. Thompson, J. P., Rosenblatt, Miller and Pizzuto, JJ., concur.