Exoplanet Calculator — Orbital Period, Temperature & Transit Depth
Enter a host star's mass, radius and temperature, plus the planet's orbital distance, radius and albedo to get the orbital period (Kepler's 3rd law), equilibrium temperature, transit signal depth and the geometric probability the planet transits across its star.
M☉
AU
R☉
K
R⊕
Period via Kepler's 3rd law: T = a^1.5 / M^0.5 (years) = 1 years
- 1
Semi-major axis^1.5
1^1.5 = 1From Kepler's 3rd law: T² = a³ / M★. - 2
√(stellar mass)
√(1) = 1 - 3
Orbital period (years)
1 ÷ 1 = 1 - 4
Orbital period (days)
1 × 365.25 = 365.25
How does this calculator work?
Exoplanet orbital period: T = a^1.5 / M★^0.5 (years in solar units). Equilibrium temperature: T_eq = T★ × √(R★/2a) × (1−albedo)^0.25. Transit depth: δ = (Rp/R★)² in ppm. Transit probability: P ≈ R★/a. For an Earth-twin around the Sun: 365 days, 255 K, 84 ppm, 0.47%.
Formula
How this is calculated
The orbital period follows from Kepler's third law in solar units: T² = a³ / M★, so T = a^1.5 / √M★ in years, where a is the semi-major axis in AU and M★ is the stellar mass in solar masses. This form of the law assumes the planet's mass is negligible compared to the star, which is true for planets orbiting Sun-like stars.
The planetary equilibrium temperature is the blackbody temperature at which the planet radiates away as much energy as it absorbs from the star. It is given by T_eq = T★ × √(R★ / 2a) × (1 − α)^0.25, where R★ is the stellar radius and a is the orbital distance both measured in the same units (this calculator uses AU, converting R★ from solar radii), and α is the Bond albedo — the fraction of incoming starlight reflected. For Earth-Sun values (T★ = 5778 K, R★ = 1 R☉ ≈ 0.00465 AU, a = 1 AU, α = 0.3) the formula gives about 255 K, consistent with the observed mean effective radiating temperature.
For transit observability, the fractional drop in stellar brightness during a transit (transit depth δ) equals the ratio of disk areas: δ = (Rp/R★)², expressed in parts per million. The geometric transit probability — the chance that a randomly oriented orbit is aligned so that the planet crosses the stellar disk as seen from Earth — is P ≈ R★/a.
Frequently asked questions
The equilibrium temperature ignores the greenhouse effect and atmospheric heat redistribution. Earth's actual mean surface temperature is about 288 K, considerably warmer than its equilibrium temperature of 255 K, because atmospheric greenhouse gases trap outgoing infrared radiation. Planets with thick atmospheres (like Venus at ~735 K) can be far hotter than T_eq predicts.
Space-based missions such as Kepler, TESS, and CHEOPS can detect transit depths of roughly 10–50 ppm or smaller for bright, quiet stars. An Earth-sized planet transiting a Sun-like star produces about 84 ppm — detectable from space but challenging. Hot Jupiters produce depths of 1–3%, easily detected even from the ground.
Transit probability is approximately the stellar radius divided by the orbital distance: P ≈ R★/a. At 1 AU from a Sun-like star this is about 0.47%, meaning fewer than 1 in 200 randomly oriented Earth-twin orbits will happen to align with our line of sight. This is why transit surveys must monitor hundreds of thousands of stars to find a statistically significant sample of Earth-like planets.
Also known as
TG we-Calculate Editorial Team. (2026). Exoplanet Calculator — Orbital Period, Temperature & Transit Depth [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/exoplanet-calculator
TG we-Calculate Editorial Team. "Exoplanet Calculator — Orbital Period, Temperature & Transit Depth." TG we-Calculate. 2026. https://we-calculate.com/calculator/exoplanet-calculator.
TG we-Calculate Editorial Team, "Exoplanet Calculator — Orbital Period, Temperature & Transit Depth," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/exoplanet-calculator
@misc{wecalculate_exoplanet_calculator, title = {Exoplanet Calculator — Orbital Period, Temperature & Transit Depth}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/exoplanet-calculator}}, year = {2026}, note = {TG we-Calculate} }
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