One formula · your inputs
Angular separation calculator
Two sky positions lie on a sphere, so their separation follows a spherical cosine relation rather than flat x–y distance.
Enter right ascension in decimal hours and declination in signed decimal degrees for each position.
Formula
How it is calculated
cos θ = sin δ₁ sin δ₂ + cos δ₁ cos δ₂ cos(α₁ − α₂)- Convert right ascension hours to degrees.
- Convert all angles to radians.
- Apply the spherical cosine relation and convert back.
What the result represents
Great-circle separation on a unit sphere.
The page keeps every decision-bearing quantity visible as an input. It does not look up a product catalogue, current market value or hidden recommended preset.
Limits of the model
The result uses the coordinates exactly as entered. It does not reconcile epoch, reference frame, proper motion, parallax or catalogue uncertainty.
Use the number to compare transparent scenarios. Verify critical observations, equipment combinations and coordinates independently.
Questions about this calculation
Does this angular-separation calculator choose equipment for me?
No. It evaluates only the displayed formula with the numbers you enter and does not make a purchase, compatibility or safety decision.
Why can the observed result differ?
Real optics and observing conditions add obstructions, transmission losses, aberrations, seeing, focus and measurement uncertainty that are outside the arithmetic model.
Can I use the result for navigation or safety-critical work?
No. SkyClock tools are transparent planning estimates, not certified navigation, engineering or safety instruments.
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