In standard cosmology, comoving distance and proper distance (or physical distance) are two closely related distance measures used by cosmologists to define distances between objects. Comoving distance factors out the expansion of the universe, giving a distance that does not change in time except due to local factors, such as the motion of a galaxy within a cluster. Proper distance roughly corresponds to where a distant object would be at a specific moment of cosmological time, which can change over time due to the expansion of the universe. Comoving distance and proper distance are defined to be equal at the present time. At other times, the Universe's expansion results in the proper distance changing, while the comoving distance remains constant.

Although general relativity allows the formulation of the laws of physics using arbitrary coordinates, some coordinate choices are easier to work with. Comoving coordinates are an example of such a coordinate choice. Conceptually, each galaxy in the cosmos becomes a position on the coordinate axis. As the universe expands this position moves with the expansion.

Comoving coordinates assign constant spatial coordinate values to observers who perceive the universe as isotropic. Such observers are called "comoving" observers because they move along with the Hubble flow. The velocity of an object relative to the local comoving frame is called the peculiar velocity of that object. The peculiar velocity of a photon is always the speed of light.

Most large lumps of matter, such as galaxies, are nearly comoving, so that their peculiar velocities (owing to gravitational attraction) are small compared to their Hubble-flow velocity seen by observers in moderately nearby galaxies, (i.e. as seen from galaxies just outside the group local to the observed "lump of matter").

A comoving observer is the only observer who will perceive the universe, including the cosmic microwave background radiation, to be isotropic. Non-comoving observers will see regions of the sky systematically blue-shifted or red-shifted. Thus, isotropy, particularly isotropy of the cosmic microwave background radiation, defines a special local frame of reference called the comoving frame.^{[citation needed]}

In addition to position, there is a comoving time coordinate, the elapsed time since the Big Bang according to a clock of a comoving observer. The comoving spatial coordinates tell where an event occurs while this cosmological time tells when an event occurs. Together, they form a complete coordinate system, giving both the location and time of an event.

A two-sphere drawn in 3D can be used to envision the concept of comoving coordinates. The surface of the sphere defines a two-dimensional space that is homogeneous and isotropic. The two coordinates in the surface of the sphere are independent of the radius of the sphere: as the sphere expands, these two coordinates are "comoving." If the radius expands over time, any tiny patch of the surface is unaffected, but distant points on the sphere are physically further apart across the surface.

Since comoving galaxies are the tick marks or labels for the comoving coordinate system, the distance between two galaxies denoted in terms of these labels remains constant at all times. This distance is the comoving distance. It is also called the coordinate distance, radial distance, or conformal distance. The physical distance between these galaxies would have been smaller in the past and will become larger in the future due to the expansion of the universe. The conversion factor between a comoving distance and the physical distance in an expanding Universe is called scale factor.