Star Motion Exposure Calculator
Estimate the local time for an entered pixel-motion budget from focal length, pixel pitch and stellar declination on a stationary camera.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Convert the angular sampling near the image center into a pixel-motion time using Earth’s sidereal rotation rate and declination.
t=pixels×2 atan(pixel pitch/(2 focal length)) / [(2π/86164.0905) cos(declination)]
Worked example
A 14 mm lens with 4 μm pixels at declination 0° gives about 3.918 seconds per pixel of local motion. Doubling the permitted pixel motion doubles that model time.
Assumptions and input details
Stationary untracked camera, local image-center approximation, at most 600 seconds and 0.01 rad of angular motion. This is not the 500 rule or an optimum exposure recommendation. Output does not model wide-field edge motion, tracking error, seeing, sky brightness, noise or perceived sharpness.
References: NASA/JPL: sidereal rotation period of Earth
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Estimate near and far acceptable-focus limits using focal length, aperture, focus distance and an explicit circle-of-confusion criterion.
Find an equivalent shutter time, aperture or ISO, or compare two camera settings. Separate the light-exposure ratio from the ISO-adjusted brightness index.
Calculate horizontal, vertical and diagonal field angles and scene coverage from sensor dimensions, focal length and subject-plane distance.
Reserved advertising space.