Exoplanet Transit SNR Calculator

Why transit SNR matters

In transit photometry, an exoplanet produces a small, temporary drop in measured stellar flux as it crosses the stellar disk. For many planet–star combinations, the dip is only tens to thousands of parts per million (ppm). Whether you can reliably detect that dip depends on how large the signal is compared with the random fluctuations (noise) in the collected photons. This page uses a simple photon-counting model to estimate the expected signal-to-noise ratio (SNR) for a transit depth and observing time, given a star’s visual magnitude and your telescope diameter.

What this calculator estimates

• Transit signal: the fractional depth of the transit (from ppm to a unitless fraction).
• Noise: photon (Poisson) noise from the collected stellar photons.
• SNR: the transit depth multiplied by the square root of the total collected photons, under the Poisson-noise assumption.
• Detection probability (heuristic): a logistic mapping of SNR to a “confidence-like” percentage for planning and intuition (not a calibrated statistical detection probability).

Inputs (units and meaning)

• Star visual magnitude (V) (mag): approximate V-band magnitude. A difference of 5 magnitudes corresponds to a factor of 100 in flux.
• Telescope diameter (m) (diameter): assumed circular aperture; collecting area scales as D².
• Transit depth (ppm) (depth): depth in parts per million. Example: 1000 ppm = 0.001 fractional dip (0.1%).
• Observation time (hours) (hours): total on-target integration time used to measure the in-transit signal relative to baseline.

Model and formulas

The model assumes a reference photon flux for a zero-magnitude star and scales it by magnitude. Collected photons increase linearly with telescope collecting area and observing time. Photon counting noise is treated as Poisson.

Step 1: Convert magnitude to photon flux

Let the reference photon flux for a zero-magnitude star be:

F₀ = 1×10¹⁰ photons·m⁻²·s⁻¹

For visual magnitude m, the photon flux scales as:

Step 2: Telescope photon collection rate

Assuming a circular aperture with diameter D (meters), collecting area is:

A = π (D/2)²

Photon collection rate (photons per second) becomes:

R = F × A

Step 3: Total photons over the observing time

Convert observing time from hours to seconds:

t = hours × 3600

Total collected photons:

N = R × t

Step 4: Transit depth and SNR

Convert transit depth from ppm to a fractional depth:

δ = depth / 10⁶

Under Poisson statistics, photon noise scales as √N. The transit SNR estimate is:

SNR = δ × √N

Detection probability (planning heuristic)

Many surveys use a threshold near SNR ≈ 7 as a rough “detectability” dividing line in simplified discussions, though real pipelines use more detailed metrics. To give a user-friendly indicator, this calculator maps SNR to a percentage via a logistic curve:

P(%) = 100 / (1 + e^{−0.5 (SNR − 7)})

This output should be read as an intuition aid (higher SNR → more likely detection), not as a rigorously calibrated probability of discovery.

How to interpret the results

• SNR < 5: the transit is likely buried in random fluctuations; detection may be unreliable without improved precision, more time, or multiple transits.
• SNR ~ 7: a commonly cited “threshold-like” region for detectability in simplified settings; real acceptance depends on systematics and pipeline tests.
• SNR > 10: transit should be more clearly distinguishable from photon noise, assuming systematics are controlled.

Because this is a total-photon model, it is best thought of as the SNR of a combined measurement over the stated integration time. If your data are taken as many short exposures, the effective SNR also depends on how you detrend and combine points and how additional noise sources behave over time.

Worked example

Suppose you observe a V = 10 star with a 1.0 m telescope for 3.0 hours, and you expect a 1000 ppm transit depth.

1. Flux scaling: 10^−0.4×10 = 10⁻⁴ = 0.0001.
2. Photon flux at Earth: F = 1×10¹⁰ × 0.0001 = 1×10⁶ photons·m⁻²·s⁻¹.
3. Aperture area: A = π(0.5)² ≈ 0.785 m².
4. Rate: R ≈ 1×10⁶ × 0.785 ≈ 7.85×10⁵ photons/s.
5. Time: t = 3×3600 = 10800 s.
6. Total photons: N ≈ 7.85×10⁵ × 10800 ≈ 8.48×10⁹.
7. Depth fraction: δ = 1000/10⁶ = 0.001.
8. SNR: δ×√N ≈ 0.001 × √(8.48×10⁹) ≈ 0.001 × 9.21×10⁴ ≈ 92.

An SNR in this range would be extremely strong under pure photon-noise assumptions; in practice, real systematics (scintillation, guiding drift, flat-field errors, sky background, etc.) often dominate before you reach such high SNR, especially from the ground.

Comparison table: how inputs affect SNR

The table below summarizes how each input changes the SNR in this simplified model (holding other inputs fixed).

Limitations and assumptions (important)

• Photon-noise only: ignores sky background, dark current, read noise, digitization, saturation, nonlinearity, and background subtraction errors.
• No atmospheric/scintillation term: ground-based photometry often has scintillation and seeing-related noise that does not average down exactly as √t.
• No systematics (“red noise”): tracking drift, flat-field residuals, color-dependent extinction, and instrumental temperature changes can dominate at high precision.
• Spectral/throughput simplification: the reference photon flux and magnitude scaling are approximate and do not explicitly model bandpass, throughput, quantum efficiency, extinction, or airmass.
• Transit shape not modeled: ingress/egress duration, limb darkening, cadence, and detrending choices affect practical detectability.
• Heuristic detection probability: the logistic percentage is a planning indicator based on SNR only; it is not a rigorous false-alarm-controlled detection probability.

Practical tips

• If your computed photon-limited SNR is low, the most direct levers are more time, a larger aperture, or observing a brighter target.
• If your photon-limited SNR is very high but you still struggle in practice, you are likely limited by systematics; improving calibration, guiding stability, defocus strategy, and detrending may help more than adding time.
• For marginal targets, consider whether you can observe multiple transits and combine them (real pipelines often benefit substantially from repeat events).