Calciro

Sky Background Electron Rate Calculator

Enter sky brightness in mag/arcsec², an electron-rate photometric zero point, pixel scale, exposure settings, aperture size, dark current, and read noise.

Sky Electron Rate per Pixel
6.279716 e−/s/pixel
Sky Rate per Arcsec²
25.118864 e−/s/arcsec²
Pixel Area
0.25
Sky Electrons in Aperture
7,535.659 e−
Dark Electrons in Aperture
12 e−
Read-Noise Variance
180 e−²
Total Background Noise
87.907 e− RMS

Use this calculator on your website

Add this free Sky Background Electron Rate Calculator to your blog, article, or business website. Copy the embed code and publish it in minutes.

Perfect for blogs, WordPress, Webflow, and business websites.

The calculator returns sky rate per arcsec² and per pixel, total sky electrons in the aperture, dark electrons, read-noise variance, and total background noise.

Need a calculator like this?

Calciro can build a custom calculator around your formulas, pricing rules, or lead-generation process.

How to Use This Calculator

Use a zero point defined so that a source with magnitude equal to the zero point produces 1 electron per second. Enter sky surface brightness in the same magnitude system and filter. Pixel scale is arcseconds per pixel. Aperture size is the number of pixels included in the measurement.

Formula & Methodology

The sky electron rate per square arcsecond is 10^((ZP − μsky)/2.5). Multiplying by pixel scale squared gives electrons per second per pixel. Sky and dark electrons scale with exposure time, aperture pixels, and number of exposures. Read-noise variance scales with pixels and exposures.

Example: 21.5 mag/arcsec² sky with a 25 mag electron zero point

At 0.5 arcsec/pixel, the sky rate is about 6.28 e−/s/arcsec² and about 1.57 e−/s/pixel. A 60-second exposure collects about 94 e− of sky per pixel.

This is a broadband calibrated-rate model. It assumes the sky surface brightness and zero point refer to the same filter, magnitude system, atmospheric convention, aperture convention, and detector units. It does not model source signal, extinction, color terms, flat-field error, scintillation, correlated noise, saturation, nonlinearity, or sky-subtraction geometry.

For observation planning only. Confirm the instrument zero point, gain convention, detector properties, observing conditions, and official exposure-time calculator before scheduling or interpreting scientific observations.

Related Calculators

Related Guides

Frequently Asked Questions

What zero point does this calculator require?
It requires the magnitude that produces one electron per second in the same filter and magnitude system as the sky brightness.
What if my zero point is in ADU per second?
Convert it to an electron-rate zero point using the detector gain and the same photometric convention before using this calculator.
Why is pixel scale squared?
Sky brightness is per square arcsecond, while one square pixel covers pixelScale × pixelScale square arcseconds for square pixels.
How is read noise combined?
Independent read-noise variance is readNoise² multiplied by the number of aperture pixels and the number of exposures.
Does binning change the calculation?
Yes. Use the effective binned pixel scale, effective aperture pixel count, and correct read-noise behavior for the instrument readout mode.

Last updated 7/20/2026