Astronomy Unit Converter

Switch between length mode (m, km, AU, ly, pc) and angle mode (rad, deg, arcmin, arcsec).

Worked example — Astronomy Unit Converter

Converted value	1.496×10⁸ km
Base-unit value	1.496×10¹¹ m
Conversion factor	1 au≈1.496×10⁸ km

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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The parsec exists so nobody has to convert anything 🖖

The parsec looks like an awkward unit until you see where it comes from: it is the distance at which 1 AU subtends exactly 1 arcsecond, so distance in parsecs = 1 / parallax in arcseconds. A star wobbling by half an arcsecond over the year is 2 pc away, and no constant is needed anywhere in that step. Because 1 arcsecond is 4.8481 × 10⁻⁶ radians, one parsec works out to 206 264.8 AU, or 3.2616 light-years. Light-years read better in prose, which is why journalism prefers them, but every parallax measurement lands in parsecs first and is converted afterwards for the reader.

Two kinds of measurement, kept apart 🖖

In astronomy you cannot lay a ruler against a star. You measure two very different things: how far apart objects are (length) and how large they appear on the sky (angle). These are not interchangeable, so this converter keeps length and angle in separate modes and never mixes them. Once you know an object's angular size and its distance, the small-angle rule size ≈ angle × distance turns arcseconds into real kilometres.

AU stopped depending on Earth's orbit 🖖

You'd expect the astronomical unit to simply be Earth's distance from the Sun — but since 2012 the International Astronomical Union has defined it as an exact fixed length, 149,597,870,700 m, by decree. It no longer tracks Earth's real orbit, which varies through the year and even drifts slowly as the Sun loses mass. So AU here is a defined constant, like the metre itself, not a fresh measurement of where Earth happens to be.

Problem solved in full

Building a parsec in metres and light-years from 1 arcsecond 6 steps
A parsec is the distance at which the radius of Earth's orbit subtends exactly 1 arcsecond. Build it from that definition — first in metres, then in light-years. This is length mode converting 1 pc to ly. Every given here is a definition rather than a measurement: 1 au = 1.495978707 × 10¹¹ m, c = 2.99792458 × 10⁸ m/s, and a year of 365.25 days.
1. Trigonometry has no idea what a degree is, so put the angle into radians first. A full turn is 2π radians and also 1,296,000 arcseconds, which fixes the conversion with no constant to look up.
  
  $1^{''} = \frac{2 π}{1 296 000} rad = \frac{π}{648 000} = 4.848137 \times 1 0^{- 6} rad$
2. Draw the right triangle: the au is the short side, the distance to the star is the long one, and the parallax angle sits at the star. The parsec is whatever d makes that angle 1 arcsecond.
  
  $tan p = \frac{1 au}{d} ⟹ d = \frac{1 au}{tan 1 ^{''}}$
3. This step is usually waved through. Replacing the tangent of 1 arcsecond by the angle itself is not free — the leading correction is θ³/3, so the relative cost is θ²/3, roughly 8 parts in 10¹². The converted value is shown to 4 significant figures, so you would need 12 before the approximation became visible.
  
  $tan θ - θ \approx \frac{1}{3} θ^{3} ⟹ \frac{tan 1 ^{''} - 1 ^{''}}{1 ^{''}} \approx 7.8 \times 1 0^{- 12}$
4. Dividing by that angle is the same as multiplying by 648,000/π. That factor is the entire content of the parsec.
  
  $1 pc = \frac{648 000}{π} \times 1.495978707 \times 1 0^{11} m = 3.086 \times 1 0^{16} m$
5. The light-year needs the same care about which year. It is the Julian one, 365.25 days exactly, and c is exact by definition, so this product is exact too.
  
  $1 ly = c t_{yr} = (2.99792458 \times 1 0^{8}) (3.15576 \times 1 0^{7}) = 9.4607 \times 1 0^{15} m$
6. Divide. Neither number came from an observation, so the ratio is exact arithmetic — its digits stop where the display stops, not where an uncertainty does.
  
  $\frac{3.085678 \times 1 0 ^{16}}{9.460730 \times 1 0 ^{15}} = 3.2616 ⟹ 1 pc = 3.262 ly$
Answer

1 pc = 3.086 × 10¹⁶ m = 3.262 ly. The factor that did all the work, 648,000/π = 206,265, is the number of arcseconds in a radian — so the parsec is not a new astronomical scale at all, it is the radian rewritten in the unit astronomers actually measure angles in. That is why a star's distance in parsecs is 1 divided by its parallax in arcseconds with no constant in front: the constant was spent when the unit was defined. The reciprocal is what makes the scale so easy to walk: shrink the parallax by 1000, to 1 milliarcsecond, and the star moves out to 1000 pc — which is 3,262 ly, the same 4 digits with the point moved.

$1 pc = \frac{648 000}{π} au = 206265 au = 3.086 \times 1 0^{16} m = 3.262 ly$

References (1)

Insight block 3 — the resolution that fixed the astronomical unit as an exact length: International Astronomical Union, Resolution B2 of the XXVIII General Assembly, Beijing, 2012 — "the astronomical unit of length … is a conventional unit of length equal to 149 597 870 700 m exactly".

By the 42Math team · Updated 2026-06-08

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

All Astronomy & Space lessons →

Example problems

Earth-Sun baseline - 1 AU converts to about 149.6 million kilometers.
Parsec to light-year - 1 parsec is about 3.26 light-years.
Moon angular size - 31 arcminutes is close to the lunar apparent diameter.
Sun to Earth mass - One solar mass in Earth masses — 3.33×10⁵ M⊕, the anchor every stellar mass is quoted against
Sun to Watts - One solar luminosity in watts — 3.828×10²⁶ W, the reference the whole stellar brightness scale is built on