Redshift to Distance Calculator

Calculate Luminosity, Angular Diameter, and Comoving Distances from a given redshift.

Redshift ($z$):

Cosmological Parameters (Flat $\Lambda$CDM)

Hubble Constant ($H_0$ in km/s/Mpc):

Matter Density ($\Omega_M$):

Dark Energy Density ($\Omega_\Lambda$):

Results:

Luminosity Distance ($D_L$):

Angular Diameter Distance ($D_A$):

Comoving Distance ($D_C$):

Understanding Cosmological Distances

This tool calculates various cosmological distances based on a specified redshift and a flat Lambda-CDM ($\Lambda$CDM) cosmological model. The $\Lambda$CDM model is the current standard model of big-bang cosmology.

What is Redshift ($z$)?

Redshift is a phenomenon where the light from distant galaxies appears "shifted" towards the red end of the electromagnetic spectrum. This is primarily caused by the expansion of the universe, stretching the wavelength of light as it travels towards us. Higher redshift values correspond to greater distances and earlier times in the universe's history.

Cosmological Parameters:

Hubble Constant ($H_0$): Represents the current rate of expansion of the universe. It's typically given in kilometers per second per megaparsec (km/s/Mpc). A higher $H_0$ implies faster expansion.
Matter Density ($\Omega_M$): The fraction of the universe's total energy density that is composed of matter (both baryonic and dark matter).
Dark Energy Density ($\Omega_\Lambda$): The fraction of the universe's total energy density attributed to dark energy, which is responsible for the accelerating expansion of the universe. In a flat universe, $\Omega_M + \Omega_\Lambda = 1$.

Types of Distances:

Comoving Distance ($D_C$): This is the distance between two objects that remains constant despite the expansion of the universe, as if measured on a fixed grid that expands with the universe. It's the proper distance at the present time ($z=0$) if expansion could be "stopped."
Angular Diameter Distance ($D_A$): This distance relates the physical size of an object to its apparent angular size in the sky. For distant objects, $D_A$ can actually *decrease* beyond a certain redshift (around $z \approx 1.6$) because of the expansion of space and the light travel time. $D_A = D_C / (1+z)$.
Luminosity Distance ($D_L$): This distance relates the absolute luminosity of an object (how much light it actually emits) to its apparent brightness as observed from Earth. It's crucial for measuring distances to supernovae. For a flat universe, $D_L = D_C \times (1+z)$.

How This Tool Works:

This calculator uses the standard flat $\Lambda$CDM cosmological model. The calculation involves numerically integrating the Friedmann equation to determine the comoving distance, which then allows for the calculation of angular diameter and luminosity distances. All calculations are performed client-side in your browser, ensuring your privacy.