Age of the Universe

The rough answer is one over the Hubble constant — the "Hubble time" of 14.5 billion years you get by running the expansion backwards at today's rate. The precise answer requires integrating the expansion history through radiation domination, matter domination and the late acceleration caused by dark energy, and the Planck satellite's map of the cosmic microwave background constrains those ingredients tightly enough to give 13.797 ± 0.023 billion years.

The result is checked by two independent clocks: the oldest globular clusters, dated from where their stars turn off the main sequence, come in around 13 billion years, and radioactive dating of thorium and uranium in ancient halo stars agrees. Both would flatly contradict the model if the universe were younger, and in the 1990s they briefly did — before the discovery of dark energy raised the calculated age above that of the oldest stars.