CALCULATE WITH CONFIDENCE

Astrophotography & Cameras

Astrophotography Signal-to-Noise & Exposure Calculator

Model a multi-frame source, sky, dark and read-noise budget; solve exposure or whole-frame count for an entered target; or scale a measured equal-frame SNR explicitly.

Astronomy & Space · model workbench

Keep detector electron counts, additive variance, repeated reads and ideal stack scaling visible while answering forward and inverse exposure-planning questions.

Private calculations in your browser · explicit inputs and model boundaries
Example preview · Twenty-four-frame rate modelModeled variance budget
Source14,400 e⁻²
Sky115,200 e⁻²
Dark2,880 e⁻²
Read4,320 e⁻²

Each bar is an additive variance term in square electrons for the complete stack. The square root of their sum is the modeled rms noise.

  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Enter values in e⁻/s.

Enter values in e⁻/s/pixel.

Enter values in e⁻/s/pixel.

Enter values in e⁻ rms.

Enter values in pixels.

Enter values in s.

Enter values in frames.

Calculation result

—

Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Feedback

Understand the relationship

The reasoning behind the result

Electron counts and variances must use the same aperture

V = S + Vsky + Vdark + Vread

The source rate is integrated over the complete measurement aperture. Sky and dark rates are entered per pixel, so each is multiplied by the included pixel count.

For Poisson count terms, the modeled variance in square electrons equals the expected electron count. The standard deviation is the square root of the summed variance.

Every frame adds another read-noise variance

Vread = N npix R²

Read noise is entered as an rms value per pixel per read. Squaring it produces one variance contribution; multiplying by pixels and frames accounts for every read in the ideal equal-frame stack.

Splitting a fixed total integration among more frames therefore changes read variance even when source and background electrons sum to the same totals.

Target exposure is a quadratic solve

(NC)²t² − q²N[C + npix(Bsky+Bdark)]t − q²NnpixR² = 0

For target ratio q and a fixed whole-frame count, signal grows linearly with exposure while noise is the square root of a linear count term plus a fixed per-read term.

Only the positive root is physically retained. The result belongs to the entered stationary rates and equal exposures; it is not an observing-condition forecast.

Square-root stacking has strict assumptions

SNRN = SNR1√N

The simple scaling follows when equally normalized frames carry equal signal and independent variance. The inverse squares the ratio and rounds upward to a whole frame.

Correlated pattern noise, unequal weighting, registration, resampling, clipping and changing conditions can produce different behaviour.

Follow the numbers

Reconcile a 24-frame rate model

  1. Each 300-second frame contains 2 × 300 = 600 source electrons over the aperture.
  2. Across 20 pixels, sky contributes 0.8 × 300 × 20 = 4,800 electrons and dark current contributes 0.02 × 300 × 20 = 120 electrons per frame.
  3. Read variance per frame is 20 × 3² = 180 square electrons, so one-frame variance is 600 + 4,800 + 120 + 180 = 5,700 square electrons.
  4. For 24 equal frames, signal is 14,400 electrons and variance is 136,800 square electrons.
  5. Divide 14,400 by √136,800 to obtain a modeled stacked SNR of about 38.93.

The ledger shows that sky variance dominates this entered scenario; the result does not claim those rates describe another target, filter, aperture or night.

Quick guide

How to use this calculator

  1. Use the rate model when source, sky and dark values are rates. Use the electron ledger only when those counts have already been integrated per frame.
  2. Define the source rate over the complete measurement aperture, but enter sky and dark rates per included pixel. Read noise is rms electrons per pixel for each frame read.
  3. Choose the inverse exposure or frame solve only for an explicit target ratio. The solver applies the entered stationary model and does not choose a scientifically sufficient target.
  4. Inspect the variance table: source, sky, dark and repeated-read contributions add as variances before the square root is taken.

Calculation method

Calculation and interpretation

Keep detector electron counts, additive variance, repeated reads and ideal stack scaling visible while answering forward and inverse exposure-planning questions.

For N equal frames, SNR = NCt / √[NCt + N·npix(Bsky + Bdark)t + N·npix·R²]. Target exposure uses the positive quadratic root; target frame count rounds (target SNR / single-frame SNR)² upward. A measured equal-frame ratio scales as SNRN = SNR1√N.

Worked example

Reconcile a 24-frame rate model

The ledger shows that sky variance dominates this entered scenario; the result does not claim those rates describe another target, filter, aperture or night.

For N equal frames, SNR = NCt / √[NCt + N·npix(Bsky + Bdark)t + N·npix·R²]. Target exposure uses the positive quadratic root; target frame count rounds (target SNR / single-frame SNR)² upward. A measured equal-frame ratio scales as SNRN = SNR1√N.

Supported inputs

Precision and limits

Entered expectation model

Source, sky and dark rates are visitor-supplied expectations. The calculator does not derive them from magnitude, catalog data, optics, quantum efficiency, weather or a live sky model.

Known-background approximation

The equation assumes the background under the source is estimated well enough that separate sky-estimation uncertainty need not be added. Flat-field error, scintillation, quantization and calibration uncertainty are excluded.

Independent equal frames

The rate and measured-scaling modes assume compatible equal frames and independent variance. Correlated noise, unequal weights, stacking rejection and resampling require a richer model.

No saturation or linearity decision

The tool does not compare peak-pixel charge with full well, ADC clipping or detector linearity. Use the separate full-well workflow with the relevant camera mode.

No target-quality threshold

An entered target SNR is a scenario, not a universal detection, publication, exposure or processing recommendation. The page does not guarantee a visible feature or successful observation.

Continue calculating

Related calculators