Exoplanet Habitability Index Calculator
Estimate an exoplanet’s potential to support life based on its radius, orbital distance, and star type.
Formulas Used
The habitability index is calculated based on the planet’s radius and orbital distance, adjusted for the star’s habitable zone. The final index is a percentage score.
- Radius Score:
\[ \text{RadiusScore} = \min\left(1, e^{-\frac{|\text{radius} – 1|}{0.5}}\right) \]
Measures how close the planet’s radius is to Earth’s (1 Earth radius). Planets with radii between 0.8–1.4 Earth radii score higher, as they are likely rocky.
- Distance Score:
- For G-type stars: \[ \text{DistanceScore}_G = e^{-\frac{|\text{distance} – 1|}{0.3}} \]
- For K-type stars: \[ \text{DistanceScore}_K = e^{-\frac{|\text{distance} – 0.7|}{0.2}} \]
- For M-type stars: \[ \text{DistanceScore}_M = e^{-\frac{|\text{distance} – 0.3|}{0.1}} \]
Measures how close the planet’s orbital distance (in AU) is to the star’s habitable zone, where liquid water could exist. G-type stars have a habitable zone around 1 AU, K-type around 0.7 AU, and M-type around 0.3 AU.
- Habitability Index:
\[ \text{HabitabilityIndex} = (\text{RadiusScore} \times \text{DistanceScore} \times 100)\% \]
Combines the scores and converts to a percentage, rounded to two decimal places. Higher percentages indicate greater habitability potential.
Example Calculations
Example 1: Earth-like Planet (G-type Star)
Inputs: Radius = 1.0 Earth radii, Distance = 1.0 AU, Star Type = G-type
Calculations:
- Radius Score: \[ \min\left(1, e^{-\frac{|1.0 – 1|}{0.5}}\right) = 1 \]
- Distance Score: \[ e^{-\frac{|1.0 – 1|}{0.3}} = 1 \]
- Habitability Index: \[ (1 \times 1 \times 100) = 100\% \]
Result: Habitability Index: 100% (ideal Earth-like conditions)
Example 2: Large Planet (K-type Star)
Inputs: Radius = 2.0 Earth radii, Distance = 0.7 AU, Star Type = K-type
Calculations:
- Radius Score: \[ \min\left(1, e^{-\frac{|2.0 – 1|}{0.5}}\right) \approx 0.135 \]
- Distance Score: \[ e^{-\frac{|0.7 – 0.7|}{0.2}} = 1 \]
- Habitability Index: \[ (0.135 \times 1 \times 100) \approx 13.53\% \]
Result: Habitability Index: 13.53% (large radius reduces score)
Example 3: Small Planet (M-type Star)
Inputs: Radius = 0.8 Earth radii, Distance = 0.4 AU, Star Type = M-type
Calculations:
- Radius Score: \[ \min\left(1, e^{-\frac{|0.8 – 1|}{0.5}}\right) \approx 0.670 \]
- Distance Score: \[ e^{-\frac{|0.4 – 0.3|}{0.1}} \approx 0.368 \]
- Habitability Index: \[ (0.670 \times 0.368 \times 100) \approx 24.66\% \]
Result: Habitability Index: 24.66% (moderate score due to orbit deviation)
How to Use the Calculator
Follow these steps to estimate an exoplanet’s habitability:
- Enter Planet Radius: Input the planet’s radius in Earth radii (e.g., 1.0 for Earth-sized). Use positive numbers (e.g., 0.8 or 2.0).
- Enter Orbital Distance: Input the distance from the star in Astronomical Units (AU). For example, use 1.0 for an Earth-like orbit or 0.3 for a red dwarf’s habitable zone.
- Select Star Type:
- G-type (Sun-like): Habitable zone ~0.95–1.37 AU.
- K-type (Cooler): Habitable zone ~0.5–0.9 AU.
- M-type (Red Dwarf): Habitable zone ~0.1–0.4 AU.
- Calculate: Click “Calculate Habitability” to see the result.
- Interpret Result: The Habitability Index (0–100%) shows the planet’s potential to support life. Higher scores indicate Earth-like conditions. If you see “Please fill in all fields,” ensure all inputs are provided.
- Share or Embed: Use the share buttons to post results on social media, copy the result, or get an embed code for the calculator.
Note: This is a simplified model. Real habitability depends on additional factors like atmosphere and stellar radiation.