a method and apparatus for performing motion estimation in a digital video system is disclosed . specifically , the present invention discloses a system that quickly calculates estimated motion vectors in a very efficient manner . in one embodiment , a first multiplicand is determined by multiplying a first display time difference between a first video picture and a second video picture by a power of two scale value . this step scales up a numerator for a ratio . next , the system determines a scaled ratio by dividing that scaled numerator by a second first display time difference between said second video picture and a third video picture . the scaled ratio is then stored calculating motion vector estimations . by storing the scaled ratio , all the estimated motion vectors can be calculated quickly with good precision since the scaled ratio saves significant bits and reducing the scale is performed by simple shifts .