Nathaniel Bowditch is the second son of former Captain Habakkuk Bowditch. His older siblings are Mary, Hab, and Lizza. The younger are Samuel, William, and Lois. In other biographies of Nathaniel Bowditch, Nat is described by people who knew him as being slight of stature, and his health was somewhat poor as a teenager and young man, probably due to privation in his youth. There is one sculpted bust of Nathaniel Bowditch in his later years, which makes him look grumpy. That might be because the artist wanted to show him in the style of a Roman statesman. His other portraits, including the one best loved by his family, depict him as a slight man with high cheekbones, a rather narrow, pointed chin, round eyes and a small mouth with the hint of an impish smile at the corners.

People who were acquainted with the real Nathaniel Bowditch, including his family, described him as invariably kind, humorous, playful, impulsive, and full of fun. He placed a high value on the most scrupulous honesty and responsibility. The dark side of his impulsiveness was a quick temper, and it took some effort on his part to overcome his occasional outbursts, particularly his frustration when trying to teach people who were slower than himself.