Understanding the trade-offs between organisms' life history traits has been a major goal of physiology, ecology and evolution. In the last few decades, two types of intra-specific studies have highlighted the trade-off between growth and longevity. First, diet restriction (DR), as an environmental intervention, has been shown to suppress growth and extend the lifespan of a broad range of animals. Second, genetic studies have also shown that mice, whose growth hormone function is genetically modified (GM), grow slower and live longer than their wild-type siblings. Despite a wealth of empirical data, still largely missing is a theoretical framework that specifies and makes quantitative predictions on this trade-off. Here, I present a mechanistic model based on the principles of energy conservation. The model quantifies explicitly how DR and GM alter the animal's energy budget, and channel metabolic energy to somatic maintenance by suppressing growth, thereby extending lifespan. Data from a diverse set of empirical studies on small rodents supports the predictions of the model. More importantly, the model reveals that although DR and GM are two different methods to extend lifespan, i.e., environmental vs. genetic, the underlying mechanisms of them are the same from the energetic viewpoint.