The recent discovery of more than a thousand planets outside our Solar System(1,2), together with the significant push to achieve inertially confined fusion in the laboratory(3), has prompted a renewed interest in how dense matter behaves at millions to billions of atmospheres of pressure. The theoretical description of such electron-degenerate matter has matured since the early quantum statistical model of Thomas and Fermi(4-10), and now suggests that new complexities can emerge at pressures where core electrons (not only valence electrons) influence the structure and bonding of matter(11). Recent developments in shock-free dynamic (ramp) compression now allow laboratory access to this dense matter regime. Here we describe ramp-compression measurements for diamond, achieving 3.7-fold compression at a peak pressure of 5 terapascals (equivalent to 50 million atmospheres). These equation-of-state data can now be compared to first-principles density functional calculations(12) and theories long used to describe matter present in the interiors of giant planets, in stars, and in inertial-confinement fusion experiments. Our data also provide new constraints on mass-radius relationships for carbon-rich planets.