While piano concertos were previously composed prolifically, over a year elapsed between this work and its predecessor. The scarcity of piano concertos, a genre composed for public concerts, indicates a decline in Mozart's activity as a performer. Indeed, in 1787, no subscription concerts were held due to a lack of subscribers. A major reason for this was likely the cooling of the Viennese audience's enthusiasm for Mozart, coupled with the significant blow to Vienna's musical culture caused by Austria's entry into the war against Turkey in February 1788, precisely when this work was completed.

Due to these circumstances, the concerto could not be performed after its completion, and it is believed to have finally premiered in April 1789, at the Dresden court, en route to Berlin.

The nickname “Coronation” originates from its performance on October 15, 1790, at the celebratory banquet for Leopold II's coronation, alongside two symphonies and Piano Concerto No. 19, K. 459.

In the autograph manuscript of this work, the piano part is somewhat incomplete, with some sections appearing in sketch form. Specifically, the right-hand part of the second movement contains only the main melody, and nothing is written for the left hand. For this left-hand section, the version written in by J. A. André for the first edition in 1794 is generally used.

No cadenza for the first movement by the composer himself has survived.

First Movement: Allegro, D major, 4/4 time. Concerto-sonata form.

While possessing brilliance with trumpets and timpani, their overall use is restrained, revealing instead a chamber music-like aspect. It is widely believed that these two instruments were added later for performance, suggesting that Mozart originally conceived this concerto in a form that could be performed by a smaller ensemble.

Second Movement: [Larghetto], A major, 2/2 time. Ternary form.

A movement consisting of generally gentle themes. The solo piano begins with a simple theme and plays a leading role throughout the movement.

Third Movement: [Allegretto], D major, 2/4 time. Rondo form.

A typical rondo finale that emphasizes a light, brisk rhythm while occasionally showing moments of shadow. Brilliant passages for the solo piano are also prominent.