Latitudinal gradients of biodiversity and macroevolutionary dynamics are prominent yet poorly understood. We derive a model that quantifies the role of kinetic energy in generating biodiversity. The model predicts that rates of genetic divergence and speciation are both governed by metabolic rate and therefore show the same exponential temperature dependence (activation energy of ≈0.65 eV; 1 eV = 1.602 × 10-19 J). Predictions are supported by global datasets from planktonic foraminifera for rates of DNA evolution and speciation spanning 30 million years. As predicted by the model, rates of speciation increase toward the tropics even after controlling for the greater ocean coverage at tropical latitudes. Our model and results indicate that individual metabolic rate is a primary determinant of evolutionary rates: ≈1013 J of energy flux per gram of tissue generates one substitution per nucleotide in the nuclear genome, and ≈1023 J of energy flux per population generates a new species of foraminifera.