What is an exoplanet transit?

An exoplanet transit occurs when a planet outside our Solar System passes in front of its host star as seen from Earth. The planet blocks a small fraction of the star’s light, causing a characteristic dip in the observed brightness known as a transit light curve.

How is transit depth related to planet size?

For a central transit and ignoring limb darkening, the transit depth is approximately the square of the planet-to-star radius ratio: depth ≈ (Rp/R☉)². A deeper transit implies a larger planet relative to the star.

What inputs do I need to estimate an exoplanet transit?

You typically need the star radius, planet radius, orbital period, and orbital distance or semi-major axis. With these, you can estimate the transit depth, duration, and the shape of the light curve. This calculator lets you enter either radii directly or derive the planet radius from a measured transit depth.

Can this calculator tell me if a transit is observable from Earth?

No. This tool assumes that the system is already aligned so that a transit occurs. In reality, only a small fraction of planetary systems are aligned this way. The geometric transit probability is roughly R☉/a, where R☉ is the star radius and a is the orbital distance.

Does the calculator include limb darkening or grazing transits?

For clarity and speed, the calculator uses a simple box-shaped transit model without limb darkening and assumes a central transit (impact parameter b ≈ 0). This is accurate enough for order-of-magnitude estimates and educational use. Real light-curve modeling uses more complex limb-darkening laws.

Exoplanet Transit Calculator

Explore how exoplanet transits dim a star’s light. Adjust star and planet properties to see transit depth, duration, and a synthetic light curve.

1. Star & Planet Parameters

Star radius

R☉ = solar radius, R♃ = Jupiter radius, R⊕ = Earth radius.

Planet radius

Orbital period

Orbital distance (semi-major axis)

If you change a, the period is not automatically updated (and vice versa).

Impact parameter b (0 = central transit)

0.00

b is the sky-projected distance between star and planet centers in units of star radii.

Orbital inclination i (deg)

90.0°

90° = edge-on. For simplicity, b is used directly in the duration formula.

Transit depth

– %

Relative flux drop: – ppm

Transit duration

– h

In minutes: – min

Scaled system

Rp/R★ = –
a/R★ = –

Transit probability (approx.)

– %

Geometric probability ≈ (R★ + Rp) / a

2. Synthetic Light Curve

The plot shows relative brightness vs. orbital phase for a simple box-shaped transit model (no limb darkening).

Phase 0 corresponds to mid-transit. Out-of-transit flux is normalized to 1.0.

How the exoplanet transit calculator works

This tool implements the standard analytic approximations used in introductory exoplanet transit modeling. It is designed for students, educators, and enthusiasts who want to connect the physical parameters of a star–planet system to observable quantities like transit depth and duration.

Transit depth: how much light is blocked?

For a central transit and ignoring stellar limb darkening, the fractional loss of light (transit depth) is simply the area ratio of the planet to the star:

\( \text{depth} \approx \left(\dfrac{R_p}{R_\star}\right)^2 \)

where \(R_p\) is the planet radius and \(R_\star\) is the stellar radius.

The calculator converts your chosen units (solar, Jupiter, or Earth radii) into meters internally, computes \(R_p/R_\star\), and then reports:

Depth as a fraction of the star’s flux.
Depth in percent (%).
Depth in parts per million (ppm), commonly used in space missions like Kepler and TESS.

Transit duration: how long does the dip last?

For a circular orbit and a small planet, the total transit duration (first to fourth contact) can be approximated by:

\( T \approx \dfrac{P}{\pi} \arcsin \left( \dfrac{R_\star}{a} \dfrac{\sqrt{(1 + k)^2 - b^2}}{\sin i} \right) \)

where:

\(P\) = orbital period,
\(a\) = semi-major axis (orbital distance),
\(k = R_p / R_\star\) = radius ratio,
\(b\) = impact parameter (0 for a central transit),
\(i\) = orbital inclination (90° for edge-on).

The calculator uses this expression, with your chosen values of \(P\), \(a\), \(R_\star\), \(R_p\), and \(b\), to estimate the duration in hours and minutes. For very small arguments of the arcsine, the formula reduces to:

\( T \approx \dfrac{P}{\pi} \dfrac{R_\star}{a} \sqrt{(1 + k)^2 - b^2} \)

Geometric transit probability

Only a small fraction of planetary systems are aligned so that we see transits from Earth. For circular orbits, the probability that a randomly oriented system will transit is approximately:

\( P_\text{transit} \approx \dfrac{R_\star + R_p}{a} \)

The tool reports this probability as a percentage, assuming your chosen values of \(R_\star\), \(R_p\), and \(a\).

Light-curve model used

The plotted light curve is a simple “box” model:

Out-of-transit flux is normalized to 1.0.
During transit, the flux is constant at \(1 - \text{depth}\).
Ingress and egress are not explicitly modeled; the edges are sharp.

This is sufficient to visualize how changing the planet radius or impact parameter affects the depth and duration. Professional analyses use more sophisticated models that include limb darkening and finite integration times.

Inverse mode: from depth to planet size

If you already have a measured transit depth (for example, from a light curve), you can use the inverse mode to estimate the planet radius:

\( R_p \approx R_\star \sqrt{\text{depth}} \)

The calculator:

Normalizes your depth (fraction, %, or ppm) to a fraction.
Computes \(R_p\) in the same units as the star radius.
Converts the result into Jupiter and Earth radii for intuition.

Typical transit depths for different planet types

To build intuition, here are order-of-magnitude transit depths for planets orbiting a Sun-like star:

Planet type	Radius (approx.)	Depth (fraction)	Depth (%)	Depth (ppm)
Hot Jupiter	1 R♃ ≈ 0.1 R☉	0.01	1%	10,000 ppm
Neptune-size	0.35 R♃	~0.0012	0.12%	1,200 ppm
Super-Earth	2 R⊕	~0.0003	0.03%	300 ppm
Earth-size	1 R⊕	~0.000084	0.0084%	84 ppm

FAQ

What assumptions does this calculator make?

The model assumes:

Circular orbits.
Single planet, single star.
No limb darkening (uniform stellar disk).
Small planet compared to the star.
Impact parameter b is supplied directly and used in the duration formula.

Can I use this for real data analysis?

It is best used for back-of-the-envelope estimates, classroom demonstrations, and planning. For precision modeling of real light curves, astronomers use specialized software (e.g., batman, PyTransit) that includes limb darkening, eccentric orbits, finite integration time, and noise modeling.

How do period and semi-major axis relate?

For a planet of negligible mass orbiting a star of mass \(M_\star\), Kepler’s third law gives:

\( P^2 = \dfrac{4\pi^2}{G M_\star} a^3 \)

In this calculator, period and semi-major axis are independent inputs so that you can experiment freely. For a self-consistent physical system, you would choose \(P\) and \(a\) that satisfy Kepler’s law for the assumed stellar mass.