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Exoplanet Habitability Score

Calculate the Earth Similarity Index (ESI) for an exoplanet based on radius, density, escape velocity, and surface temperature relative to Earth.

About this calculator

This calculator computes the Earth Similarity Index (ESI), a metric introduced by Schulze-Makuch et al. (2011) in the journal Astrobiology that astrobiologists use to summarize how physically Earth-like a candidate exoplanet is, on a scale from 0 to 1. Rather than a simple average, ESI multiplies together four separately scored components — planet radius, bulk density, escape velocity, and surface temperature — each scored by how closely it matches Earth's own reference value (all set to 1, or 288 K for temperature) using the formula (1 − |x − x₀|/(x + x₀)) raised to a weighting exponent. The weights (5.58 for temperature, 1.07 for density, 0.70 for escape velocity, 0.57 for radius, normalized by their sum) come directly from that paper's published exponents, chosen so that temperature dominates the overall score, reflecting its outsized importance for surface liquid water and thus habitability as currently understood.

Because the four component scores are multiplied rather than added, one badly mismatched parameter — say, a scorching surface temperature — can drag the whole index down even if the planet is otherwise Earth-sized and Earth-dense; ESI rewards balanced similarity, not any single strong match. The calculator also reports an Interior ESI (radius and density combined) and Surface ESI (escape velocity and temperature combined) as sub-scores, plus a rough surface gravity estimate (density times radius) and a simple water-state guess based on whether surface temperature falls between 273 K and 373 K. Remember that ESI measures physical resemblance to Earth, not confirmed habitability or life — a planet can score high on ESI while having an atmosphere, radiation environment, or geological history that makes it entirely uninhabitable.

Inputs

R⊕
ρ⊕
V⊕
K

Results

Earth Similarity Index

1

Classification

Earth-like

Interior ESI1
Surface ESI1
Surface Gravity1 g⊕
Surface Temperature14.9 °C
Water StateLiquid (possible)

Figures current as of 2011. Source: D. Schulze-Makuch, A. Méndez, A. G. Fairén, P. von Paris, C. Turse, G. Boyer, A. F. Davila, M. Resendes de Sousa António, L. N. Irwin, and D. Catling, "A Two-Tiered Approach to Assessing the Habitability of Exoplanets," Astrobiology 11(10): 1041-1052 (2011)

How to Use This Calculator
  1. Enter Planet Radius (R⊕) relative to Earth — values near 1.0 indicate a rocky, Earth-sized world.
  2. Enter Planet Density (ρ⊕) relative to Earth's 5,515 kg/m³ to characterize interior composition.
  3. Enter Escape Velocity (V⊕) relative to Earth's 11.2 km/s — this determines ability to retain an atmosphere.
  4. Enter Surface Temperature (K): Earth is 288 K; values between 273 K and 373 K allow liquid water.
  5. Read the Earth Similarity Index (ESI) from 0 to 1 — values above 0.8 are considered Earth-like, and check Water State for habitability clues.

How the result changes with Surface Temperature

Surface TemperatureEarth Similarity IndexClassification
1440.7515Potentially Habitable
2160.8971Earth-like
4320.8545Earth-like
7200.6742Potentially Habitable

What each input means

Planet Radius
Planet radius in Earth radii (Earth = 1, Mars = 0.53, Jupiter = 11.2)
Planet Density
Bulk density relative to Earth (Earth = 1 = 5,515 kg/m³, Mars = 0.71)
Escape Velocity
Escape velocity relative to Earth (Earth = 1 = 11.2 km/s, Mars = 0.45)
Surface Temperature
Estimated equilibrium surface temperature in Kelvin (Earth = 288 K, Mars = 210 K)

How this is calculated

Formula

ESI = ∏(1 - |xᵢ - xᵢ₀| / (xᵢ + xᵢ₀))^(wᵢ/n)

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Planet Radius = 1, Planet Density = 1, Escape Velocity = 1, Surface Temperature = 288 = 4 input(s) provided
  2. Calculate Earth Similarity Index
    Earth Similarity Index
    1 = 1
  3. Calculate Classification
    Earth-like = Earth-like
  4. Calculate Interior ESI
    Interior ESI
    1 = 1
  5. Calculate Surface ESI
    Surface ESI
    1 = 1

Figures and sources

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does one badly mismatched parameter tank the whole ESI score even if the others are Earth-like?

The four component scores — radius, density, escape velocity, and temperature — are multiplied together rather than averaged, so the formula rewards balanced similarity across all four rather than strength in any single one. A planet with Earth-like radius and density but a scorching surface temperature will still get a low overall ESI, because that one term near zero drags the entire product down.

Why is temperature weighted so much more heavily than the other three parameters?

The calculator uses a weight of 5.58 for temperature versus 0.57 for radius, 1.07 for density, and 0.70 for escape velocity, normalized by their sum. This weighting reflects the outsized importance surface temperature has for supporting liquid water, which is considered the single most critical factor for habitability as currently understood in astrobiology.

What's the difference between Interior ESI and Surface ESI in the results?

Interior ESI is the geometric mean of just the radius and density scores, characterizing how similar the planet's bulk composition and size are to Earth's. Surface ESI is the geometric mean of the escape velocity and temperature scores, characterizing surface and atmospheric conditions. Together they let you see whether a planet's overall ESI is being driven by its interior structure or its surface environment.

Does a high Earth Similarity Index mean the planet is actually habitable?

No — ESI only measures physical resemblance to Earth across four bulk parameters, not confirmed habitability or the presence of life. A planet can score above 0.8 on ESI while having an atmosphere, radiation environment, or geological history that makes it entirely uninhabitable; the score is a similarity metric, not a habitability guarantee.

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