What is the value of 1863 deutsche mark?

The Deutsche Mark was not used in 1863 (individual German states issued their own coinage, although copper small change was issued jointly at times). On the assumtion that you meant the 1963 deutsche mark coin, it depends on the mintmark (found below the eagle's tail) and the coin's condition. Broadly, it is worth about US$1.00 to 1.50 in circulated condition, $10 to $15 in Extremely Fine, and $110 to $200 in Uncirculated condition, with the "D" mintmark at the low end of the range, the "F" and the "G" in the middle, and the "J" at the high end of the range.