The concerto is scored for solo piano, flute (third movement only), two oboes, two bassoons, two horns, and strings.

Mozart composed the concerto for performance at a series of concerts at the Vienna venues of the Trattnerhof and the Burgtheater in the first quarter of 1784, where he was himself the soloist in March 1784.

[7] It is testimony to Mozart's greatness that although this movement is extremely difficult from a technical point of view, it never sounds like a 'showpiece' meant to display the performer's skills.

Some of the demands made on the pianist include fast ascending-descending arpeggios, hand-crossing and voice highlighting in runs of semiquavers, wide jumps and towards the end a double-handed tremolo where the soloist 'battles against' the orchestra.

Simon Keefe has noted contemporary comments from Mozart's era on how the woodwind writing in this concerto showed a "newly intricate and sophisticated" character compared to Mozart's prior keyboard concerti.