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Calcimator

Planetary Transit Calculator

Calculate transit depth, duration, probability, and timing for exoplanet transits.

About this calculator

This calculator models the geometry of an exoplanet transit -- a planet passing in front of its host star as seen from Earth -- using the standard formulas from transit photometry (see Winn 2010, "Transits and Occultations"). Transit Depth is the simplest relationship: it is the square of the ratio of Planet Radius to Star Radius. Because it is a squared ratio, both inputs move it by the same relative amount for the same percentage change -- doubling the planet's radius quadruples the dip in starlight, and halving the star's radius also quadruples it, since Planet Radius sits in the numerator and Star Radius in the denominator of the same squared term. Transit Probability is the geometric chance that the planet's orbital plane happens to be aligned edge-on enough for a transit to occur at all, computed as Star Radius divided by Semi-Major Axis (converted to the same units): a bigger star or a tighter orbit both raise the odds of catching a transit.

Transit Duration uses a simplified circular-orbit approximation that assumes a roughly edge-on crossing; it does not fully account for how far off-center the crossing is. That off-center distance is what Impact Parameter reports, in units of the star's own radius: it is Semi-Major Axis divided by Star Radius, multiplied by the cosine of Orbital Inclination. A value under 1 means the planet's disk genuinely crosses the star's disk as seen from Earth -- a real transit; a value of 1 or more means the geometry misses the star entirely at that inclination, even though the other outputs still compute a number. Because Semi-Major Axis to Star Radius ratios are typically large (Earth's is over 200), Impact Parameter climbs quickly as Orbital Inclination departs from a perfect 90 degrees (edge-on), which is why real transiting-planet searches are so sensitive to orbital alignment.

Inputs

Solar Radii
Earth Radii
days
AU
degrees

Results

Transit Depth

0.0000008386

Transit Duration

12.98 hours

Transit Probability

0.00465%

Impact Parameter0
Ingress Duration0.0005 days
Orbital Velocity29,785.68 m/s
How to Use This Calculator
  1. Enter Star Radius (solar radii) and Planet Radius (Earth radii) for the target system.
  2. Enter Orbital Period (days) and Semi-Major Axis (AU) — use Kepler's law if only one is known.
  3. Set Orbital Inclination (°): 90° is perfectly edge-on; values below 90° reduce transit probability.
  4. Read Transit Depth (fraction of stellar flux dimming) — a 1% dip means the planet covers 1% of the star's disk.
  5. Use Transit Duration (hours) to plan observation windows and Transit Probability to assess detection likelihood.
  6. Check Impact Parameter (in stellar radii): values below 1 mean the planet's disk actually crosses the star as seen from Earth; 1 or above means the geometry misses the star entirely at that inclination.

How the result changes with Star Radius

Star RadiusTransit DepthTransit DurationTransit Probability
0.50.00000335456.49 hours0.00233%
0.750.00000149099.73 hours0.00349%
1.50.000000372719.46 hours0.00698%
2.50.000000134232.44 hours0.01163%

What each input means

Star Radius
Radius of the host star
Planet Radius
Radius of the transiting planet
Orbital Period
Orbital period of the planet
Semi-Major Axis
Average orbital distance
Orbital Inclination
Orbital inclination (90° = edge-on)

How this is calculated

Formula

Transit Depth = (R_planet / R_star)²

Worked example, using the default values

  1. Identify Input Parameters
    5 parameters
    Star Radius = 1, Planet Radius = 0.1, Orbital Period = 365.25, Semi-Major Axis = 1, Orbital Inclination = 90 = 5 input(s) provided
  2. Calculate Transit Depth
    Transit Depth
    8.386e-7 = 8.386e-7
  3. Calculate Transit Duration
    Transit Duration
    12.98 = 12.98
  4. Calculate Transit Probability
    Transit Probability
    0.00465 = 0.00465%
  5. Calculate Impact Parameter
    Impact Parameter
    0 = 0
  6. Calculate Ingress Duration
    Ingress Duration
    0.0005 = 0.0005

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

Do Planet Radius and Star Radius affect Transit Depth the same way?

They move it in opposite directions but by the same relative amount: Transit Depth is literally (Planet Radius / Star Radius) squared, so growing Planet Radius deepens the transit while growing Star Radius shallows it, and a given percentage change in either input produces the same-size percentage swing in Transit Depth because both sit inside the same squared ratio. A Jupiter-sized planet around a Sun-sized star produces a dip roughly 100 times deeper than an Earth-sized planet around that same star, purely from the radius ratio.

What does an Impact Parameter of 1 or greater mean?

It means the planet's disk misses the star's disk entirely from Earth's vantage point, even though this calculator still reports a Transit Depth, Duration, and Probability as if a transit were happening. Impact Parameter is (Semi-Major Axis / Star Radius) times the cosine of Orbital Inclination, so at a perfectly edge-on 90-degree inclination it is exactly 0 (a dead-center crossing), and it grows quickly as inclination departs from 90 degrees because most stars are tiny compared to a planet's orbital distance.

Does Orbital Inclination change Transit Depth?

No. Transit Depth depends only on the ratio of Planet Radius to Star Radius -- how much of the star's disk the planet covers once it is in front of the star. Orbital Inclination instead controls whether a transit happens at all (via Impact Parameter) and, more subtly, how close to the star's center the crossing is, which this calculator's simplified duration formula does not fully model.

Why does a larger Semi-Major Axis lower Transit Probability?

Transit Probability is Star Radius divided by Semi-Major Axis (in matching units), so it is a pure geometric ratio: a planet orbiting farther from its star sweeps out a much larger circle, and the star's disk covers a proportionally smaller sliver of the possible orbital-plane orientations that would produce a transit. This is why hot, close-in planets are found by transit surveys far more often than distant, cold ones -- not because they are more common, but because their transit geometry is far more probable to catch.

Is the Transit Duration figure exact?

No -- it uses a simplified circular-orbit approximation (arcsin of Star Radius over Semi-Major Axis, scaled by Orbital Period) that assumes a roughly edge-on crossing and does not fully account for the crossing's Impact Parameter or orbital eccentricity. Real transit-duration calculations used in mission planning also fold in the planet's own radius and the exact impact parameter; treat this output as a reasonable first estimate, not a substitute for full orbital-mechanics software.

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