I’m sure you’re right. No way actual spending during the calendar year 1861 went down as a percent of GDP.!
Massive federal spending started to ramp up in May and continued accelerating through the rest of that year. Although much of the initial expense was paid by the states, possibly with later reimbursement by the feds.
I note your numbers show GDP doubling in three years. You will excuse me if I take that with a grain of salt. Especially when a very large part of the 1860 economy was no longer part of the equation.
During the equivalent period of WWII GDP increased only by about 50%.
I couldn't tell you how those numbers are determined, but note that US GDP remained in the $8 billion per year range from 1863 through 1873, when it began climbing towards $20 billion in 1900.
Also note that US GDP rose from $38 billion in 1914 to $88 billion in 1920.
GDP also rose from $92 billion in 1939 to $223 billion in 1945.
Clearly there has long been a strong correlation between major wars and US GDP increase.