Pixel Scale Calculator Formula

Understand the math behind the pixel scale calculator. Each variable explained with a worked example.

Use the Pixel Scale Calculator

Formulas Used

Pixel Scale

pixel_scale_arcsec = 206.265 * pixel_size / focal_length

Pixel Scale (arcmin/px)

pixel_scale_arcmin = 206.265 * pixel_size / focal_length / 60

Variables

VariableDescriptionDefault
pixel_sizePixel Size(um)3.75
focal_lengthFocal Length(mm)1000

How It Works

Pixel Scale in Astrophotography

Pixel scale tells you how much sky each pixel of your camera sensor covers.

Formula

pixel_scale = 206.265 * p / f

  • *p* = pixel size in micrometres
  • *f* = focal length in mm
  • 206.265 is the conversion factor from radians to arcseconds (with the mm/um unit adjustment)

    • A good rule of thumb is to match pixel scale to about half the typical seeing (e.g., 1 arcsec/px for 2-arcsecond seeing).

    Worked Example

    3.75 um pixels on a 1000 mm telescope.

    pixel_size = 3.75focal_length = 1000
    1. 01scale = 206.265 * 3.75 / 1000
    2. 02scale = 773.5 / 1000
    3. 03scale = 0.7735 arcsec/px

    Frequently Asked Questions

    What is the ideal pixel scale?

    About one-third to one-half of the local seeing (FWHM of star images). For 2-arcsecond seeing, aim for 0.7 to 1.0 arcsec/px.

    What happens if pixels are too large?

    You under-sample the image, losing detail. Stars appear blocky and fine structure is blurred.

    What happens if pixels are too small?

    You over-sample: the extra resolution is wasted on seeing blur, while read noise and longer exposures increase.

    Ready to run the numbers?

    Open Pixel Scale Calculator