Exoplanet Discovery Calculator

Enter a host star's mass, radius, and temperature plus the planet's orbital period to find its orbital distance and speed (Kepler's third law), its equilibrium temperature, and whether it falls in the star's habitable zone.

Quick Facts

Kepler's third law
a³ = M☉ × P²
Semi-major axis (AU) from stellar mass (solar masses) and orbital period (years).
Orbital velocity
v = √(GM☉ / a)
Circular-orbit speed from the star's gravitational parameter and orbital distance.
Equilibrium temperature
T = T☉√(R☉/2a) × (1-A)¹⁄⁴
Blackbody temperature from stellar temperature, radius, distance, and planet albedo.
Habitable zone (conservative)
≈ 0.95√L to 1.37√L AU
Simplified estimate for Sun-like stars, where L is stellar luminosity relative to the Sun.

Your Results

Calculated
Semi-Major Axis
-
Orbital distance from Kepler's third law (AU)
Orbital Velocity
-
Circular-orbit speed (km/s)
Equilibrium Temperature
-
Blackbody temperature estimate (K)
Habitable Zone Status
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Position relative to the conservative habitable zone

Ready

Enter the star's mass, radius, and temperature plus the orbital period, then press Calculate.

How the Exoplanet Calculator Works

Astronomers rarely see an exoplanet directly. Instead, methods like the transit method (a periodic dip in starlight as the planet crosses in front of its star) and the radial-velocity method (a periodic wobble in the star's spectrum) reveal the planet's orbital period with high precision. Combined with the host star's own mass, radius, and temperature — known from spectroscopy and stellar models — that period is enough to derive the planet's orbital distance, orbital speed, and a rough estimate of its temperature and habitability, all from well-established physics.

Finding the orbital distance and velocity

Kepler's third law, combined with Newton's law of gravitation, ties a planet's orbital period directly to its distance from its star. In solar units (astronomical units, solar masses, and years) it simplifies to a³ = M★ × P², so the semi-major axis is a = (M★ × P²)1/3. This calculator converts your orbital period from days to years, applies that formula to get the distance in AU, then finds the circular orbital speed from v = √(GM★ / a), using the Sun's standard gravitational parameter (GM☉ ≈ 1.327 × 1011 km³/s²) scaled by the star's mass.

Estimating equilibrium temperature and habitability

A planet's equilibrium temperature — the temperature it would settle at as an airless blackbody balancing incoming starlight — follows Teq = T★ × √(R★ / (2a)) × (1 − A)1/4, where A is the planet's Bond albedo (the fraction of light it reflects rather than absorbs). To flag whether that distance is broadly favorable for liquid water, the calculator also compares the semi-major axis to a simplified conservative habitable zone, scaled from the star's luminosity (via the Stefan-Boltzmann relation, L ∝ R²T⁴) as roughly 0.95√L to 1.37√L AU.

What this model does not capture

These formulas assume a circular orbit, a planet whose mass is negligible next to its star's, and a star similar enough to the Sun for the simplified habitable-zone scaling to apply. They ignore orbital eccentricity, axial tilt, atmospheric greenhouse warming, and tidal heating — all of which can shift a real planet's temperature and climate well away from this baseline estimate. Treat the results as an order-of-magnitude starting point, not a substitute for a full climate or dynamical model.

Frequently Asked Questions

How do you calculate an exoplanet's orbital distance from its period?
This calculator applies Kepler's third law in solar units: a³ = M★ × P², where a is the semi-major axis in astronomical units (AU), M★ is the star's mass in solar masses, and P is the orbital period in years. Because the planet's mass is negligible next to the star's, this gives an accurate first-order distance directly from the transit or radial-velocity period astronomers measure.
What is an exoplanet's equilibrium temperature?
The equilibrium temperature is the temperature a planet would reach as an airless blackbody in balance with incoming starlight: Teq = T★ × √(R★ / (2a)) × (1 − A)1/4, where A is the planet's albedo (fraction of light reflected). It is a useful baseline, but a real atmosphere's greenhouse effect can push the actual surface temperature well above this value — Earth's equilibrium temperature is about 255 K, yet its surface averages about 288 K.
How is the habitable zone estimated in this calculator?
This tool uses a simplified, widely cited estimate for Sun-like stars: the conservative habitable zone spans roughly 0.95√L to 1.37√L astronomical units, where L is the star's luminosity relative to the Sun. It is a rough guide to where liquid water could exist on an Earth-like planet, not a precise boundary — real habitable-zone limits depend on the star's spectral type and detailed atmospheric modeling.
Does this calculator assume a circular orbit?
Yes. It treats the orbit as circular (eccentricity = 0) and uses the semi-major axis as the orbital radius for both the velocity and temperature calculations. Real exoplanet orbits can be eccentric, which makes the planet's distance from its star — and therefore its temperature — vary over the course of one orbit.

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