Stacking Signal-to-Noise Calculator Formula

Understand the math behind the stacking signal-to-noise calculator. Each variable explained with a worked example.

Use the Stacking Signal-to-Noise Calculator

Formulas Used

Stacked SNR

snr_stacked = snr_single * sqrt(num_frames)

Improvement Factor

improvement_factor = sqrt(num_frames)

Variables

VariableDescriptionDefault
snr_singleSingle-Frame SNR5
num_framesNumber of Frames100

How It Works

Signal-to-Noise Improvement from Stacking

Stacking multiple exposures averages out random noise while the signal adds coherently.

Formula

SNR_total = SNR_single * sqrt(N)

  • *N* = number of stacked frames

    • Doubling the SNR requires four times as many frames. This is the square-root law of signal averaging.

    Worked Example

    Stack 100 frames each with SNR = 5.

    snr_single = 5num_frames = 100
    1. 01SNR_total = SNR_single * sqrt(N)
    2. 02SNR_total = 5 * sqrt(100)
    3. 03SNR_total = 5 * 10 = 50

    Frequently Asked Questions

    Is stacking better than one long exposure?

    For the same total time, ideally they are equivalent. In practice, stacking is better because it allows rejection of satellite trails, cosmic rays, and bad frames.

    Does this assume noise is random?

    Yes. The sqrt(N) law applies to uncorrelated random noise (shot noise, read noise). Systematic patterns (e.g., vignetting) must be removed separately.

    How many frames do I need?

    For a 10x SNR improvement you need 100 frames. For 3x you need only 9. Diminishing returns set in at high frame counts.

    Ready to run the numbers?

    Open Stacking Signal-to-Noise Calculator