Parallax Calculator - Stellar Distance from Parallax Angle

The parallax calculator converts a stellar parallax angle in arcseconds into a star's distance from Earth, reporting the result in parsecs, light-years, astronomical units, and kilometers.

• • Find distance from a measured parallax: Enter a Hipparcos or Gaia parallax in arcseconds or milliarcseconds and read off the distance in parsecs, light-years, AU, and kilometers.
• • Use preset nearby stars: Pick Sirius, Proxima Centauri, Alpha Centauri A, Vega, or Barnard's Star to see catalog parallax and the matching distance in a single click.
• • Reverse a known distance into parallax: Enter a distance in parsecs, light-years, AU, or kilometers to recover the parallax angle an observer would measure.
• • Compare distance units: See the same star in parsecs, light-years, AU, and kilometers side by side so unit conversions stay consistent.

Stellar parallax is the small apparent shift of a nearby star against the background sky as Earth moves from one side of its orbit to the other. The calculator handles both halves of that workflow: convert a measured parallax into a distance, or take a known distance and produce the parallax angle an observer would record.

The default mode is the standard astronomy formula D (parsecs) = 1 / P (arcseconds). A preset selector fills the parallax for nearby stars so users can verify their numbers, while a custom field accepts any positive angle for raw catalog values such as 0.13023 arcsec for Vega or 0.7685 arcsec for Proxima Centauri.

Because stellar parallax relies on Earth's year-long orbit around the Sun, the orbital period of the baseline is set by the Orbital Period Calculator rather than by any telescopic measurement.

This parallax calculator applies the IAU parsec definition: distance in parsecs equals one divided by the parallax angle in arcseconds. It then scales that distance into light-years, astronomical units, and kilometers.

• P (parallax angle, arcsec): Half of the total apparent angular shift of the star against the background sky, measured six months apart. Entered in arcseconds or milliarcseconds.
• D (distance, parsecs): The star's distance in parsecs. One parsec is the distance at which one AU subtends one arcsecond.
• ly/pc and AU/pc: Conversion factors: 1 parsec = 3.2615637769 light-years and 206,264.806 astronomical units, both fixed by the IAU.
• Reverse: D (distance, any unit): If a known distance is entered, the calculator divides by the matching unit factor to recover the parallax angle via P = 1 / D_pc.

Earth's orbit around the Sun gives a baseline of about 2 astronomical units, since observations taken six months apart sit on opposite sides of the orbit. That baseline is fixed, so measuring the angular shift of a star from two opposite positions turns the geometry into D = b / tan(θ/2). For typical stellar angles, that expression simplifies to D (parsecs) = 1 / P (arcseconds), which is what the calculator uses.

After the parsec distance is known, multiplying by 3.2615637769 converts to light-years, and multiplying by 206,264.806 converts to astronomical units. Multiplying by 149,597,870.7 km per AU produces the distance in kilometers.

According to Wikipedia Parallax, Distance to a star in parsecs equals one divided by its parallax angle in arcseconds, where one parsec is the distance at which an object has a parallax of exactly one arcsecond.

For distant stars the parallax angle shrinks below the resolution of any single telescope, so the Angular Resolution Calculator is a useful companion when discussing why only a few catalogs can reach the milliarcsecond scale.

Four ideas sit behind every parallax result. Keeping them separate makes it easier to read published values and translate between catalog units.

Stellar parallax uses Earth's own orbital motion as the baseline, while the Synodic Period Calculator tracks when two orbiting bodies line up from Earth's point of view, so the two tools describe different timing uses of the same orbit.

Six steps cover the standard forward mode (parallax to distance) and the reverse mode (distance to parallax). The calculator updates as inputs change and Reset restores the Sirius preset.

1. 1 Pick a preset star or stay on Custom: Selecting Sirius, Proxima Centauri, Alpha Centauri A, Vega, or Barnard's Star fills the parallax field with the Hipparcos catalog value. Choose Custom to enter any parallax.
2. 2 Enter the parallax angle: Type the parallax in arcseconds or milliarcseconds. Use the Parallax Input Unit menu to switch between arcsec and mas without moving the decimal.
3. 3 Read the distance row: The primary result is distance in parsecs. The next rows give light-years, AU, and kilometers so the same target can be quoted in any unit the problem set uses.
4. 4 Switch to reverse mode if you have a known distance: Enter the known distance in the Reverse Distance field, pick parsecs, light-years, AU, or kilometers, and the parallax row updates from P = 1 / D_pc.
5. 5 Compare with a lab value: Use the milliarcsecond row to compare against catalog entries, which usually list parallax in mas rather than arcsec.
6. 6 Reset between problems: Press Reset to return to the Sirius preset and clear the reverse distance field so a new problem can start without leftover values.

A student is given the Hipparcos parallax of Vega, 130.23 mas, and asked for the distance in light-years. They pick Vega in the preset menu (which fills 0.13023 arcsec) and read 25.04 light-years from the result panel without leaving the page.

When the discussion moves from a static parallax angle to the apparent angular motion of a nearby planet or asteroid, the Angular Velocity Calculator converts angular speed and orbital radius into linear velocity on the same geometry.

Five practical benefits of the calculator when working through a parallax problem or comparing distances from a catalog.

• • Fast distance checks: Swap preset stars or type a custom parallax to see the matching distance in all four common units without re-deriving any factor.
• • Catalog-friendly units: Milliarcseconds, arcseconds, parsecs, light-years, AU, and kilometers are all visible so a result can be quoted in the unit the source already uses.
• • Reverse workflow: Entering a distance returns the parallax angle an observer would measure, useful when planning telescope time or checking published figures.
• • Classroom consistency: The IAU factors are baked in, so every student gets the same numeric answer for the same input and grading is straightforward.
• • Quick sanity check on small angles: The calculator makes it obvious when a parallax falls below the rough ground-based resolution, helping students notice when Gaia or Hipparcos data is needed.

Once a star's distance is known, discussions of relativistic effects near compact objects can use the parallax distance in astronomical units as the radial input for the Gravitational Time Dilation Calculator.

The parallax formula is fixed, but several measurement choices can change whether the calculated distance matches the catalog value. The list below covers the most common sources of disagreement.

• • The simple formula D = 1 / P uses the small-angle approximation, which is excellent at typical stellar arcsecond scales but less appropriate for very wide angles, such as a spacecraft observation of a nearby asteroid, where the exact tan(θ/2) form should be used.
• • The calculator uses a fixed baseline of 2 AU. Observations from a different baseline (such as a satellite at the L2 Lagrange point) need a tailored formula rather than the standard parsec shortcut.
• • Published values for the same star can differ between catalogs by a few tenths of a milliarcsecond because of zero-point corrections and reduction-pipeline updates. The calculator reports the value the user enters without trying to choose a 'best' catalog.

According to Wikipedia Parsec, one parsec equals 206,264.806 astronomical units or about 3.26156 light-years.

According to Wikipedia Astronomical Unit, one astronomical unit is defined as exactly 149,597,870,700 meters by the 2012 IAU resolution, and one parsec is the distance at which one AU subtends an angle of one arcsecond.

The same large mirrors used for telescope imaging rely on the mirror equation, so the Mirror Equation Calculator explains how the resolving power behind parallax catalogs is set in the first place.