Cosmicflows-3 Distance–Velocity Calculator(distances less than 38 Mpc)

This tool is featured in Kourkchi et al. 2020, AJ, 159, 67 (arXiv:1912.07214).

Compute expectation distances or velocities based on smoothed velocity field from the Numerical Action Methods model of Shaya et al. 2017.

Click here for acknowledgments.

*  Indicates required field
SGL [deg]
SGB [deg]
Cone [deg]

  Coordinate system
















  • Sky position, galactic, supergalactic, or equatorial (J2000 as 360° decimal) in degrees.


  • Cone (degrees) [default 15°]; plot data points within this cone angle.
  • Distance (Mpc); returns model velocity in km/s.
  • Velocity (km/s); returns model distance(s) in Mpc – potentially more than one value.


  • Model distance – velocity curve (blue) is derived from interpolation of velocities on a grid of distances with grid intervals of 0.2 Mpc at the origin increasing to 1 Mpc intervals at 38 Mpc, the outer limit of the model. The value at a grid point is averaged over the 4 nearest mass points weighted by the inverse square of separation.
  • Pause cursor over blue curve for distance and velocity information at chosen location.
  • Pause cursor over data points for extra information.


  • Data constraining the model are shown as large red circles if distance uncertainties are 5% or less (brown extra large circles for Virgo and Fornax clusters), and as small green circles if uncertainties are over 5% but not more than 15%. Data with larger uncertainties are represented by black plus signs but do not constrain the model.
  • Vgsr (km/s) is the galactic standard of rest velocity; referenced to the center of the Galaxy assuming a circular velocity of Sun of 239 km/s plus local solar motion (van der Marel et al. 2012): Vgsr = Vhelio + 11.1 cos(l) cos(b) + 251 sin(l) cos(b) + 7.25 sin(b)
  • PGC1 is the Principal Galaxies Catalog identification of the brightest member of the group contributing to the data point (Kourkchi & Tully 2017).
  • The H0=75 dashed line is only for reference. Velocities are observed and distances are determined using the scale zero-point described by Tully et al. 2016.

Numerical Action Methods model (Shaya et al. 2017)

  • Click on figure for animation of model orbits.

  • Numerical Action Methods model (Shaya et al. 2017)

How to acknowledge this work