William Thomson's father, James Thomson, was a teacher of mathematics and engineering at Royal Belfast Academical Institution and the son of a farmer. James Thomson married Margaret Gardner in 1817 and, of their children, four boys and two girls survived infancy. Margaret Thomson died in 1830 when William was six years old.]
William and his elder brother James were tutored at home by their father while the younger boys were tutored by their elder sisters. James was intended to benefit from the major share of his father's encouragement, affection and financial support and was prepared for a career in engineering.
In 1832, his father was appointed professor of mathematics at Glasgow and the family moved there in October 1833. The Thomson children were introduced to a broader cosmopolitan experience than their father's rural upbringing, spending mid-1839 in London and, the boys, being tutored in French in Paris. Mid-1840 was spent in Germany and the Netherlands. Language study was given a high priority.

Thomson had heart problems and nearly died when he was 9 years old. He attended the Royal Belfast Academical Institution, where his father was a professor in the university department, before beginning study at Glasgow University in 1834 at the age of 10, not out of any precociousness; the University provided many of the facilities of an elementary school for able pupils, and this was a typical starting age.