The expansion in the supply of energy services over the last couple of centuries has reduced the apparent importance of energy in economic growth despite energy being an essential production input. We demonstrate this by developing a simple extension of the Solow growth model, which we use to investigate 200 years of Swedish data. We find that the elasticity of substitution between a capital-labor aggregate and energy is less than unity, which implies that when energy services are scarce they strongly constrain output growth resulting in a Malthusian steady-state. When energy services are abundant the economy exhibits the behavior of the “modern growth regime” with the Solow model as a limiting case. The expansion of energy services is found to be a major factor in explaining the industrial revolution and economic growth in Sweden, especially before the second half of the 20th century. In the latter period, labor-augmenting technological change becomes the dominant factor driving growth.