The importance of academic research ("AR") to economic growth is widely accepted but quantification of incremental impacts, and their attribution to any one country's expenditures, is difficult. Yet quantitative justification of government AR funding is highly desirable. We therefore attempt to quantify one impact which can be directly and causally attributed to one country's funding: spin-off companies. We focus on AR in the non-medical natural sciences and engineering (NSExm) in a whole country, Canada. 'Applied' disciplines are sometimes assumed to be the most commercializable, so we also separately investigate an especially 'basic' science, physics. Using a novel methodology, we estimate the lifetime impacts of companies spun-off directly from AR performed in 1960-1998, and compare the impacts with all government funding, direct and indirect, over the same period. This picks up virtually all funding and most company-formation since WWII, up to 1998. Such long-term studies are rare but essential, since we show that successful spin-offs grow (often exponentially) over several decades. With very conservative assumptions, and allowing for the time value of money, the impacts exceed government funding by a substantial margin. Physics actually fares 30-60% better than the combined NSExm; this reflects more successful companies, rather than greater numbers, and therefore does not seem inconsistent with earlier studies on company numbers. Firm lifetimes are long, with Canadian impacts truncated primarily by some foreign acquisitions. We argue that the spin-off impacts represent incremental contributions to GDP, much larger (even on a time-discounted basis) than the government funding and directly attributable to it; governments will also receive more in additional tax than they spent. The impacts therefore provide a quantitative justification for the public investment, allowing the much more important (but less quantifiable) long-term benefits to be regarded as a 'free' bonus. The very good showing of physics also suggests that reduced emphasis on basic work or on the basic disciplines could actually weaken the commercialization of AR.