Curves began to appear in Kelly's abstract work after he returned from Paris in 1954 and moved into a studio on Broad Street in Lower Manhattan. The steep double arc in Study for Red Curves resembles the postcard collage Gauloise Blue with Red Curve (1954), which Kelly later described as his first curve. As he once remarked, “The curve was a new direction for me in New York.”

In Study for Red Curves Kelly developed the color and composition of a key early New York painting, Red Curves (1955), shown in his first one-person exhibition in New York at the Betty Parsons Gallery in 1956.