Born in 1766 in Newburyport, Massachusetts, a descendant of an Englishman who came to America in 1631, Perkins was a gifted and prolific inventor who had very little formal schooling. He was apprenticed to a goldsmith at age thirteen, took over his master's business at age fifteen, and went on to invent a method of plating shoe buckles. By age twenty-one, Perkins had been hired by the State of Massachusetts to make dies for copper coins.

In 1790, Perkins made what is perhaps his most important invention, a machine for cutting and heading nails in one operation. As a result, nails could be mass-produced and sold cheaply. Perkins patented his machine in 1795 and set up a nail-manufacturing company, but a subsequent lawsuit about the invention ruined the business.

Perkins next invented steel (rather than copper) plates for bank-note engraving that made counterfeiting money nearly impossible. He pursued his interest in engraving in Boston, then New York, and finally Philadelphia. With his partner, Gideon Fairman, Perkins sailed for England in 1818 to establish their engraving process in that country. They set up a factory in 1819 that for many years made plates and printed notes for local banks. In 1840 their firm was awarded the contract to produce England's first penny postage stamps; the plant printed many millions of stamps over the next 40 years.

With an ever-curious mind, Perkins continued to produce creative inventions of incredible diversity. Around 1823 he began conducting numerous experiments with high-pressure steam engines and boilers, and eventually introduced many innovations and improvements. Perkins unveiled an improved paddlewheel in 1829; in 1831 he invented a way to achieve free circulation of water in boilers; his 1834 description of the vapor compression cycle for refrigeration and ice-making was revolutionary.

Other Perkins inventions included the steam-gun; a pleometer, to measure the speed of a vessel moving through water, a bathometer, to measure the depth of water, a process of transferring engravings from one steel plate to another, a ship's pump, and a method of ventilating rooms and ships' holds. Perkins was recognized in several countries for his work, and received various awards. He died in London in 1849.