Angular Size of a Galaxy Calculator

Enter the galaxy's redshift, observed angular size, and Hubble constant to calculate its physical size, distance, and lookback time.

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter Redshift (z)
Input the cosmological redshift of the galaxy. Higher values indicate greater distance and earlier epochs.
2
Enter Angular Size (arcsec)
Provide the observed angular size of the galaxy in arcseconds. This is how wide it appears in the telescope.
3
Enter Hubble Constant (km/s/Mpc)
Input the value for the Hubble constant. The standard value is approximately 70 km/s/Mpc, but recent measurements vary.
4
Review Your Results
The calculator will display the galaxy's physical size, angular diameter distance, lookback time, and other cosmological parameters.

Example Calculation

An astronomy student is analyzing a distant spiral galaxy observed by the Hubble Space Telescope, which has a redshift of 0.5 and an angular size of 30 arcseconds, and needs to determine its actual physical diameter.

Redshift (z)

0.5

Angular Size (arcsec)

Hubble Constant (km/s/Mpc)

Results

171.63 kpc

Tips

Cosmological Redshift

Redshift (z) indicates how much the universe has expanded since the light left the galaxy. A z of 0.5 means the universe was about two-thirds its current size when the light was emitted, corresponding to a lookback time of roughly 5 billion years.

Interpreting Physical Size

Compare the calculated physical size to known galaxy types. For instance, the Milky Way has a diameter of about 30 kpc. A galaxy with a physical size of 170 kpc is significantly larger than our own, suggesting it might be a giant elliptical or a large spiral.

Hubble Constant Variation

The Hubble constant (H0) is a key parameter for cosmic expansion. While 70 km/s/Mpc is a common value, recent measurements have yielded values between 67 and 74 km/s/Mpc, impacting distance and size calculations. Using the most current estimate improves accuracy.

Unveiling the True Scale of Distant Galaxies

The Angular Size of a Galaxy Calculator helps astronomers and enthusiasts alike determine the actual physical dimensions of distant galaxies by combining their observed angular size with cosmological redshift and the Hubble constant. This tool is vital for understanding galaxy evolution, morphology, and the large-scale structure of the universe. For instance, knowing that a galaxy at redshift 0.5 with an angular size of 30 arcseconds has a physical diameter of 171.63 kiloparsecs allows researchers to compare it to local galaxies like the Milky Way, which spans about 30 kpc, revealing its true cosmic scale in 2025.

Deriving Physical Size from Cosmological Observations

Calculating the physical size of a galaxy from its angular size and redshift involves a journey through cosmological principles. The process begins with the observed angular size and uses the angular diameter distance, a specific cosmological distance measure, to translate that angle into a linear dimension.

The core logic involves these steps:

Calculate Hubble Distance (DH): DH = c / H0 (where c is the speed of light, H0 is the Hubble constant).
Calculate Comoving Distance: This is a complex numerical integration based on the redshift (z) and cosmological parameters (like matter density ΩM and dark energy density ΩΛ, typically 0.3 and 0.7 for a flat universe).
Calculate Angular Diameter Distance (DA): DA = Comoving Distance / (1 + z).
Convert Angular Size: Angular Size (radians) = Angular Size (arcsec) / 206265.
Calculate Physical Size: Physical Size (kpc) = Angular Size (radians) × DA × 1000.

💡 To estimate how much light your telescope collects from faint objects, our Telescope Light Gathering Power Calculator is a useful companion tool for deep-sky observations.

Measuring a Spiral Galaxy's Extent

Consider an astronomer observing a distant spiral galaxy. They measure its redshift (z) as 0.5, its angular size as 30 arcseconds, and use a Hubble constant (H0) of 70 km/s/Mpc. The goal is to find its physical size.

Step-by-step process (simplified, as the calculator handles complex steps):

Input Redshift (z): 0.5
Input Angular Size (arcsec): 30
Input Hubble Constant (H0): 70

The calculator processes these inputs through cosmological equations.

Outputs from the calculator:

Physical Size: Approximately 171.63 kpc
Angular Diameter Distance: Approximately 1180.0 Mpc
Comoving Distance: Approximately 1770.0 Mpc
Lookback Time: Approximately 5.09 Gyr

This shows that the galaxy, appearing 30 arcseconds wide at a redshift of 0.5, has an intrinsic physical size of roughly 171.63 kiloparsecs. This is a massive galaxy, several times larger than our own Milky Way.

💡 To determine what portion of the sky your telescope can capture at once, our Telescope Field of View Calculator can help you plan your observations effectively.

Galaxy Scales Across the Universe

Galaxies exhibit a wide range of physical sizes. Dwarf galaxies can be as small as a few hundred parsecs (pc) to a few kiloparsecs (kpc), while typical spiral galaxies like the Milky Way span about 30 kpc. Giant elliptical galaxies can stretch over hundreds of kiloparsecs, sometimes exceeding 500 kpc, especially in the centers of galaxy clusters. The largest known galaxies, such as IC 1101, can have diameters exceeding 2,000 kpc (2 megaparsecs), making them thousands of times larger than the Milky Way. These vast differences in size are crucial for understanding galaxy formation and evolution processes over cosmic time.

Expert Interpretation of Galaxy Sizes

Astronomers interpret the calculated physical size of a galaxy in several ways:

Morphological Classification: The size helps in classifying a galaxy. A physical size under 10 kpc often points to a dwarf galaxy, while 20-50 kpc is typical for large spirals like the Milky Way. Sizes above 100 kpc are characteristic of giant ellipticals or the largest spirals.
Evolutionary State: By comparing the physical sizes of distant (high-redshift, thus early universe) galaxies to local ones, astronomers can trace how galaxies have grown or shrunk over cosmic time. For instance, observations suggest that high-redshift galaxies were generally smaller and more compact than their local counterparts.
Environmental Impact: Galaxies in dense environments, like galaxy clusters, often have their sizes influenced by gravitational interactions and mergers, leading to larger, more massive systems. Conversely, isolated galaxies might evolve more slowly.
Mass-Size Relation: There's a well-established relationship between a galaxy's stellar mass and its physical size. Deviations from this relation can indicate unusual formation histories or ongoing interactions. For a typical spiral galaxy, a 10^11 solar mass galaxy might have a diameter of ~30 kpc.

Frequently Asked Questions

What is the physical size of a galaxy?

The physical size of a galaxy refers to its actual diameter or extent in space, typically measured in kiloparsecs (kpc) or light-years (ly). This intrinsic dimension is inferred from its observed angular size and its cosmological distance, accounting for the expansion of the universe. For example, the Milky Way galaxy has a physical diameter of approximately 30 kiloparsecs.

How does the angular size of a galaxy change with distance?

Initially, as a galaxy gets farther away, its angular size decreases. However, due to the accelerating expansion of the universe, beyond a certain redshift (around z=1.5), the angular diameter distance starts to decrease. This means very distant galaxies can appear larger than expected, a counterintuitive effect where angular size can increase with increasing redshift.

What is lookback time in astronomy?

Lookback time is the time elapsed since the light we observe from a distant celestial object was emitted. It tells us how far back in the universe's history we are seeing that object. For example, a galaxy with a lookback time of 5 billion years is observed as it was 5 billion years ago, providing a direct window into the early universe.

Why is the Hubble constant important for galaxy size calculations?

The Hubble constant (H0) is crucial because it sets the scale of the universe's expansion. It is used to calculate the Hubble distance, which is fundamental in determining comoving distance and angular diameter distance. These distances are then directly used to convert an observed angular size into an actual physical size, making H0 integral to cosmological measurements.