Parallax Calculator — Stellar Distance & Terrestrial Range
Use stellar parallax to find how far away a star is in parsecs and light-years from its annual parallax angle in arcseconds, or use terrestrial parallax to find the distance to an object from a measured baseline and angle shift.
Mode
arcsec
Distance in parsecs — d = 1 / p (p in arcseconds)
- 1
Distance d = 1 ÷ p
1 ÷ 0.7421 = 1.3475One parsec is the distance at which the parallax angle equals exactly 1 arcsecond. - 2
Distance in light-years
1.3475 × 3.26156 = 4.395
How does this calculator work?
Stellar parallax: d (parsecs) = 1 / p (arcseconds). A star with p = 0.742″ is 1/0.742 ≈ 1.35 pc ≈ 4.4 light-years away. Terrestrial parallax: d = baseline / (2 × tan(α/2)). Enter the parallax angle and baseline to get distance in parsecs, light-years, AU, and km.
Formula
How this is calculated
Parallax is the apparent shift of a nearby object against a distant background when viewed from two different positions. It is the oldest direct method for measuring astronomical distances.
For stellar parallax, astronomers observe a nearby star six months apart (from opposite sides of Earth's orbit around the Sun, giving a baseline of 2 AU ≈ 299,196,000 km). The star appears to shift by a small angle p (the annual parallax) measured in arcseconds (1/3600 of a degree). The parsec is defined so that a star at 1 parsec has a parallax of exactly 1 arcsecond: distance (pc) = 1 / p. The nearest star, Proxima Centauri, has p ≈ 0.7421″, giving d ≈ 1.35 parsecs ≈ 4.40 light-years.
For terrestrial parallax, you observe a target from both ends of a known baseline and measure the total angular shift α. The distance is d = baseline / (2 × tan(α/2)), which simplifies to d ≈ baseline / α for small angles (in radians). This underpins rangefinding in military optics, surveying, and the way human binocular vision estimates depth.
Frequently asked questions
A parsec (pc) is the distance at which the annual parallax equals exactly 1 arcsecond. It equals approximately 3.26 light-years, 206,265 AU, or 3.086 × 10¹³ km. The name is a portmanteau of "parallax arcsecond". The nearest star system (Alpha Centauri) is about 1.34 pc away.
One arcsecond is 1/3600 of one degree, or about 4.85 × 10⁻⁶ radians. It is the angular size of a golf ball seen from about 10 km away. The best ground-based telescopes achieve parallax precision of ∼0.001″; the ESA Gaia mission measures parallaxes to ∼0.00001″, reaching stars thousands of parsecs away.
The formula d = 1/p assumes the small-angle approximation (tan p ≈ p in radians) and a perfect measurement. For stars more than ∼1 kpc away, parallaxes are smaller than 0.001″ and measurement uncertainties become significant relative to the angle itself, causing large distance errors. Statistical methods such as Bayesian inference are used for precise distances to faint or distant stars from Gaia data.
Also known as
TG we-Calculate Editorial Team. (2026). Parallax Calculator — Stellar Distance & Terrestrial Range [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/parallax-calculator
TG we-Calculate Editorial Team. "Parallax Calculator — Stellar Distance & Terrestrial Range." TG we-Calculate. 2026. https://we-calculate.com/calculator/parallax-calculator.
TG we-Calculate Editorial Team, "Parallax Calculator — Stellar Distance & Terrestrial Range," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/parallax-calculator
@misc{wecalculate_parallax_calculator, title = {Parallax Calculator — Stellar Distance & Terrestrial Range}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/parallax-calculator}}, year = {2026}, note = {TG we-Calculate} }
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