Electronic digital apparatus for computing an approximation of the arctangent of a given tangent number, N, being in the range of 0 to 1 and in binary form, operates in two stages to provide a solution of the expression: ##EQU1## During the first stage, steps are taken by the apparatus to find out where within the range of 0 to 1, divided preferably into four equal increments, the known tangent number N is located. When the correct increment represented by one of a plurality of increment numbers I.sub.j stored in a ROM unit of the apparatus is found, then one of a like plurality of center numbers C.sub.k of that increment also stored in the ROM unit may be readily selected, as can also be the corresponding one of a plurality of stored numbers A.sub.i representing the arctangents of the stored center numbers C.sub.k. During the first stage, the product number C.sub.k (N) is also formed. In the second stage of operation of the apparatus, the dividend and divisor numbers N-C.sub.k and 1+C.sub.k (N) are first calculated. The quotient number,(N-C.sub.k)/[1+C.sub.k (N)],is then calculated. Finally, the Arctan (C.sub.k), such being the selected one of the arctangent numbers A.sub.i, is accessed from the ROM unit and added to the quotient which gives, as an approximation, the value of the unknown angle.