Angular Parallax

Relate linear size, angular size and distance (small-angle and exact atan forms) for astronomy and optics estimates.

About this tool

Three relationships between linear size, angular size and distance:

  • Angular size: θ = 2·atan(D / 2d); small-angle limit θ ≈ D/d (radians).
  • Annual parallax → distance: d[pc] = 1 / p[arcsec]. By definition 1 pc is the distance at which 1 AU subtends 1 arcsec.
  • Conversion: 1 pc ≈ 3.0857 × 10¹⁶ m ≈ 3.2616 ly; 1 rad = 206 264.806 arcsec.

Examples

  • Moon: D ≈ 3 474 km, d ≈ 384 400 km → θ ≈ 0.518° ≈ 31'.
  • Proxima Centauri parallax 0.7687" → d ≈ 1.301 pc ≈ 4.245 ly.
  • Sun seen from Pluto: θ ≈ 49.5".