Abstract The relationship between human health and well-being, energy use and carbon emissions is a foremost concern in sustainable development. If past advances in well-being have been accomplished only through increases in energy use, there may be significant trade-offs between achieving universal human development and mitigating climate change. We test the explanatory power of economic, dietary and modern energy factors in accounting for past improvements in life expectancy, using a simple novel method, functional dynamic decomposition. We elucidate the paradox that a strong correlation between emissions and human development at one point in time does not imply that their dynamics are coupled in the long term. Increases in primary energy and carbon emissions can account for only a quarter of improvements in life expectancy, but are closely tied to growth in income. Facing this carbon-development paradox requires prioritizing human well-being over economic growth.