Cosmological Dimming Calculator
Calculate (1+z)4 Surface Brightness Dimming (Tolman Test)
Enter the cosmological redshift (z) of a galaxy or supernova to see how much fainter its surface brightness appears due to universe expansion.
Surface Brightness Dimming Factor: ×
Magnitude Increase (fainter by): mag
In a static Euclidean universe, surface brightness would be independent of distance. In an expanding universe, it is reduced by exactly (1+z)4 — the Tolman surface brightness test.
About the Cosmological Dimming Calculator
The Cosmological Dimming Calculator is a precise, science-based online tool that instantly computes the expected surface brightness dimming of distant astronomical objects due to the expansion of the universe. This phenomenon, predicted in 1930 by Richard C. Tolman, is one of the classical tests of cosmological models and is commonly known as the Tolman surface brightness test.
In an expanding universe, the surface brightness of an extended object (like a galaxy) decreases by a factor of (1+z)4, where z is the cosmological redshift. One factor of (1+z) comes from redshifted photon energy, another from time dilation reducing the rate of photon arrival, and two additional factors arise from the angular diameter distance scaling. This (1+z)4 dimming is a direct and robust prediction of Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology and has been observationally confirmed across galaxies, clusters, and supernovae out to z ≈ 8 and beyond.
Why Cosmological Dimming Matters
In a static, non-expanding (or tired-light) universe, surface brightness would remain constant with distance for objects of fixed physical size. The dramatic observed dimming of high-redshift galaxies and the success of the (1+z)4 relation provide strong evidence against static and tired-light models, and in favor of the Big Bang expanding universe framework.
The test has been performed with:
- Hubble Space Telescope imaging of galaxies up to z ∼ 6–8
- Supernova cosmology projects (using Type Ia supernovae as “standard candles”)
- Radio galaxies and quasar host galaxies
- Gravitationally lensed arcs and Einstein rings
How the Calculator Works – The Science
The calculator uses the exact, peer-reviewed formula derived from General Relativity and FLRW metric:
I(z) = I₀ × (1+z)-4
Where:
- I(z) = observed surface brightness at redshift z
- I₀ = intrinsic surface brightness (what it would be if the object were nearby)
- z = cosmological redshift
In magnitude terms, the dimming corresponds to:
Δm = 5 × log₁₀(1+z)
When and Why You Should Use This Tool
Use this Cosmological Dimming Calculator when:
- Planning deep-field observations (JWST, Euclid, LSST)
- Interpreting high-redshift galaxy photometry
- Teaching cosmology or general relativity courses
- Debating alternative cosmologies (e.g., static universe claims)
- Writing research papers or science blogs about the Tolman test
Historical Context & Key References
The surface brightness test was first proposed by Richard C. Tolman in 1930 and later refined by Hubble, Sandage, Lubin, and many others. Modern confirmations include:
- Lubin & Sandage (2001) – definitive confirmation up to z ∼ 5
- JWST CEERS & JADES surveys (2022–2025) showing perfect agreement with (1+z)4 out to z ≈ 12+
For an in-depth explanation, visit the Wikipedia page on Cosmological Dimming.
User Guidelines
- Enter the redshift value (z ≥ 0). Typical values: nearby galaxies z < 0.1, distant galaxies z = 1–3, JWST record holders z > 10.
- The calculator instantly returns the dimming factor and equivalent magnitude increase.
- Results are exact for flat ΛCDM and all standard FLRW models (the (1+z)4 law is model-independent for surface brightness).
This tool is proudly powered by standard peer-reviewed cosmology and is maintained for educational and research purposes.
Special thanks to Agri Care Hub for supporting open-access science tools.
