Angular Size & Parallax

Choose the quantity to calculate. Its number field is hidden, while its unit remains selectable. The other two values are the known quantities. Switching targets preserves the input drafts; a hidden draft is not an additional constraint.

The exact geometry is a flat segment or disk of diameter D, perpendicular to the sightline, at axial distance d from its plane: θ = 2 atan(D/(2d)). It is not the angular diameter of a sphere at its center distance. The small-angle relation is θ ≈ D/d with θ in radians. Both results refer to the chosen quantity and unit. The signed deviation is 100 × (approximate/exact − 1). At very small angles, a difference below floating-point precision can display as zero; this is not an uncertainty bound.

The astronomical unit is exactly 149597870700 m. The parsec is exactly (648000/π) au. The Julian-year light-year is 9460730472580800 m. R⊕ here is the WGS84 equatorial radius, 6378137 m, rather than a mean or nominal radius.

Annual parallax uses a one-au baseline. Positions six months apart are separated by two au; the parallax angle is half the full apparent shift. The conventional distance is d[pc] = 1/p[arcsec]. The calculator requires a reliable positive parallax and does not infer distance from noisy or negative measurements. No uncertainty or Bayesian model is included.