The letter is one of only four known documents containing the equation in Einstein’s own hand and the only one in a private collection, according to Boston-based auctioneers RR Auction.
The equation — energy equals mass times the speed of light squared — revolutionised physics by demonstrating that time is not absolute and that mass and energy are equivalent.
Although he first published the equation in 1905 after developing his theories on special and general relativity, Einstein included it in his letter to Polish American physicist Ludwik Silberstein, a critic and challenger of some of his work, in October 1946.
He wrote: “Your question can be answered from the E = mc2 formula, without any erudition,” in the letter written on Princeton University letterhead, according to a translation from the original German provided by RR Auction.
The page-long letter remained in Silberstein’s personal archives until they were sold by his descendants and acquired by RR Auction.
“It’s an important letter from both a holographic and a physics point of view,” Bobby Livingston, executive vice president at RR Auction, calling E = mc2 the most famous equation in the world.
The auctioneers say that five parties initially entered the bidding war for the letter and that it narrowed down to two when the price reached around $700,000 (£500,000).