# Calculate ESI, the Earth Similarity Index

Calculator for the ESI, the similarity of a planet or other celestial body to Earth. ESI stands for Earth Similarity Index. The value indicates how closely an object resembles our home planet; the value is between 0 and 1, with the Earth itself having the value 1. The ESI is calculated from just four values, namely radius, density, escape velocity and surface temperature. So it ignores many factors, such as the magnetic field, the amount of water on the planet and the type of star around which it orbits. This is one of the reasons why the ESI is not a measure for suitability for life. Also in this respect the earth, although very good, may not be ideal. Nevertheless, exoplanets with a high ESI are often considered good candidates for extraterrestrial life.

The Earth Similarity Index is calculated as the weighted geometric mean of the deviations of the four values from those of Earth. If you change these values from those of Earth to those of another object, you can calculate the similarity to this. Please enter the mean radius in kilometers, the density in grams per cubic centimeter, the escape velocity in kilometers per second and the average surface temperature in Kelvin. The weighting indicates how strongly each value is included in the calculation. The radius has the least influence and the surface temperature has the greatest influence. The escape velocity or second cosmic velocity is calculated from mass and radius.

The internal similarity (interior ESI) and the surface similarity (surface ESI) are calculated as well as the ESI as the root of the product of these two.

Example: one of the most Earth-like known exoplanets (as of 2023), TRAPPIST-1d, has an estimated Earth radius of 4920 kilometers, a density of 4.354 g/cm³, an escape velocity of 7.911 kilometers per second, and a surface temperature of 296 Kelvin. This means its ESI is 0.9, with internal similarity and surface similarity being very close to each other. That this is not always the case becomes clear when you enter the values of Venus (6052; 5.243; 10.36; 730), where the internal similarity to Earth is very high, but the surface similarity is very low.

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