RAID triple parity (RTP) is a new algorithm for protecting against three-disk failures. It is an extension of the double failure correction Row-Diagonal Parity code. For any number of data disks, RTP uses only three parity disks. This is optimal with respect to the amount of redundant information required and accessed. RTP uses XOR operations and stores all data un-encoded. The algorithm's parity computation complexity is provably optimal. The decoding complexity is also much lower than that of existing comparable codes. This paper also describes a symmetric variant of the algorithm where parity computation is identical to triple reconstruction.