Why is the night sky dark? If stars filled an infinite, unchanging universe, every line of sight would end on a star. The resolution: the universe has a finite age (about 13.8 billion years), so we only see light from a limited distance, and expansion redshifts distant light.
How to use the Olbers’ Paradox Calculator
- Star density (stars per cubic light-year)
- Average star luminosity (L☉)
- Observable depth R
- Shell thickness Δr
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the average number density of stars, their average luminosity and the depth of the universe you can see (light travel distance).
Inputs explained
| Field | What to enter |
|---|---|
| Star density (stars per cubic light-year) | A number |
| Average star luminosity (L☉) | A number |
| Observable depth R | Units: ly, Gly, pc |
| Shell thickness Δr | Units: ly, pc |
What each result means
- Flux from one shell = [n (SI)]×[Average star luminosity (L☉)]×3.828e26×[Shell thickness Δr]
- Total flux from stars out to R (no blocking) = [n (SI)]×[Average star luminosity (L☉)]×3.828e26×[Observable depth R]
- Compared with sunlight at Earth (1,361 W/m²) = [Total flux from stars out to R (no blocking)]÷1361×100
- Depth at which the sky would be as bright as the Sun’s surface = 6.3e7÷([n (SI)]×[Average star luminosity (L☉)]×3.828e26)÷9.4607304725808e15
Example values
How the main result changes when Star density changes and everything else stays at the example values above:
| Star density (stars per cubic light-year) | Total flux from stars out to R (no blocking) (W/m²) |
|---|---|
| 0.002 | 59.0203 |
| 0.003 | 88.5305 |
| 0.004 | 118.0407 |
| 0.005 | 147.5508 |
| 0.006 | 177.061 |
| 0.008 | 236.0813 |
Formula
Flux from a shell of thickness Δr: F = n·L·Δr (independent of distance) · Total to radius R: F = n·L·R
Worked example
Inputs — Star density (stars per cubic light-year): 0.004; Average star luminosity (L☉): 0.5; Observable depth R: 13,800,000,000 ly; Shell thickness Δr: 1 ly.
Results — Flux from one shell = 8.5537e-9 W/m²; Total flux from stars out to R (no blocking) = 118.04067 W/m²; Compared with sunlight at Earth (1,361 W/m²) = 8.67308 %; Depth at which the sky would be as bright as the Sun's surface = 7.3653e15 ly.
Key terms
- Olbers' paradox
- The darkness of the night sky contradicts an infinite, static universe.
Frequently asked questions
Why doesn't distance dim the shells?
Each shell is fainter by 1/r² but contains r² more stars.
What really solves the paradox?
The finite age of the universe and the redshift of distant light.
Would we be blinded in an infinite universe?
Yes – the whole sky would be as bright as a star's surface.
Who stated the paradox?
Heinrich Olbers in 1823 (earlier Kepler and Halley).