Born in Darlton near Tuxford, Nottinghamshire, Calvert, was the son of Charles Calvert senior, an amateur artist and agent for the Duke of Norfolk. Henry had eight brothers and sisters of which three, Charles, Michael Pease, and John, were also artists. As a child Henry moved to Manchester where he spent most of his working life until the 1860’s when he moved to Southport, where he eventually died.
He is comparatively little known and underestimated as an artist whose ability deserves greater recognition. His work is of a high standard, his horses well drawn, his composition good and his detail of items such as saddlery is accurate; as well as painting horses and sporting scenes he painted a variety of other animals including cattle portraits, and a few landscapes. Calvert "is a comparatively little known and underestimated artist whose ability deserves greater recognition. His work is of a high standard, his horses well drawn, his composition good and his detail...accurate. Although he would seem to have led a fairly active artistic life his work is now fairly rare" (Dictionary of Equestrian Artists). His best known works are of Hunt Meets (all of which were engraved): 'The Cheshire Hunt' 1839, 'The Vine Hunt Meeting' 1843 and 'The Wynnstay Hunt' 1855.