Exposure Time for Stars Calculator Formula

Understand the math behind the exposure time for stars calculator. Each variable explained with a worked example.

Use the Exposure Time for Stars Calculator

Formulas Used

Max Exposure Time

max_exposure = (35 * aperture_ratio + 30 * pixel_size) / (focal_length * cos(declination * pi / 180))

Variables

VariableDescriptionDefault
focal_lengthFocal Length(mm)200
pixel_sizePixel Size(um)3.75
aperture_ratiof-Number (N)4
declinationDeclination(deg)0

How It Works

Maximum Exposure Time for Point Stars

The NPF rule estimates how long you can expose before Earth's rotation causes star trailing.

NPF Formula

t = (35N + 30p) / (f * cos(dec))

  • *N* = lens f-number
  • *p* = pixel size in micrometres
  • *f* = focal length in mm
  • *dec* = declination of the target

    • Stars near the celestial equator trail fastest; those near the poles trail slowest.

    Worked Example

    200 mm f/4 lens, 3.75 um pixels, shooting the celestial equator.

    focal_length = 200pixel_size = 3.75aperture_ratio = 4declination = 0
    1. 01t = (35*4 + 30*3.75) / (200 * cos(0))
    2. 02t = (140 + 112.5) / 200
    3. 03t = 252.5 / 200
    4. 04t = 1.26 seconds

    Frequently Asked Questions

    How does the 500 rule compare?

    The classic 500 rule (t = 500/f) is simpler but less accurate, especially with modern high-resolution sensors where trailing is visible at shorter exposures.

    Does a tracking mount eliminate this limit?

    Yes. An equatorial tracking mount follows the sky, allowing exposures of many minutes without trailing.

    Why does declination matter?

    Stars near the celestial poles move in smaller circles, so they trail less per unit time. The cosine factor accounts for this.

    Ready to run the numbers?

    Open Exposure Time for Stars Calculator