Stellar Parallax Distance
Worked example: p = 1 arcsec → d = 1 pc = 3.0857e16 m — press Try an example to run it live, then adjust anything.
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Stellar Parallax Distance explained
As Earth swings from one side of its orbit to the other, a nearby star appears to shift against the distant background by twice the parallax angle p. Trigonometry gives d = AU/tan p, but real stellar parallaxes are so tiny — always under one arcsecond — that tan p ≈ p in radians, and the small-angle form d = AU/p is exact to better than one part in 10¹⁰. The nearest star system, Proxima Centauri, has p = 0.7685″ = 3.726 × 10⁻⁶ rad, so d = 1.496 × 10¹¹ / 3.726 × 10⁻⁶ ≈ 4.02 × 10¹⁶ m — about 4.25 light-years.
This geometry defines the parsec: the distance at which the parallax is exactly one arcsecond, 3.086 × 10¹⁶ m, so that d in parsecs is simply 1/p in arcseconds. Friedrich Bessel made the first successful measurement in 1838 (61 Cygni, p ≈ 0.31″), finally proving the Earth moves; today ESA's Gaia mission measures parallaxes to a few microarcseconds, pinning down distances for nearly two billion stars and anchoring every rung of the cosmic distance ladder.
Stellar Parallax Distance formula
- = Distance to the star (m)
- = Parallax angle (°)
Missing one of these? Work it out first, then come back
- Distance to the star — Speed, Distance & Time, Gravitational Field Strength
- Parallax angle — Torque with a Lever Arm (τ = rF sin θ), Angular Velocity (ω = θ/t)