What is the maximum elevation mountains can reach on Earth, the Moon, and Mars?

The purpose of this paper is to compare the maximum theoretical and actual height of mountains on the Earth, Moon and Mars. This comparison requires a new definition of a mountain in which the reference to a global vertical datum is replaced by a local datum that is used for each topographic positive relief. Submarine topographies on Earth are also included as mountains. Although the Moon is the most likely to have the tallest mountains it has not had the effective geological processes required for mountain building. On Mars there is a high similarity between the maximum theoretical height and the heights of its giant volcanoes. On Earth, the geological factors of isostasy, fluvial and glacial erosion prevent mountains reaching their maximum theoretical height. On the Moon the highest mountains have been built by impact tectonics, whereas on Earth and Mars volcanism is the most efficient way of building a single mountain. • Comparison of maximum mountain height on the Earth, the Moon and Mars. • Simple answer based on the critical factor of rock strength. • New mountain definition in which absolute elevation is not considered. • Images of the highest mountains on Earth, the Moon and Mars are provided. • Volcanism is the most efficient mountain building mechanism on Earth and Mars. • Impact tectonics is the most efficient mountain building mechanism on the Moon.