Olber's Paradox Calculator

Olbers' Paradox is the seemingly simple question: if the universe is infinite, static, and uniformly filled with stars, why is the night sky dark? In such a universe, every line of sight would eventually hit a star's surface, making the sky as bright as the surface of an average star. The fact that the night sky is dark tells us something fundamental about the universe.

There are two key reasons. First, the universe has a finite age (~13.8 billion years), meaning light from very distant stars simply hasn't had time to reach us yet. Second, the universe is expanding — light from distant galaxies is redshifted, pushing it out of the visible spectrum and reducing its energy, which dramatically lowers the total flux we observe.

The calculator uses F = (n × L × L☉ × R) / pc², where n is star density (stars/pc³), L is average luminosity in solar units, R is the universe radius in parsecs, and pc is the parsec in meters. This integrates the contribution of all stars within the observable sphere, showing how flux scales linearly with both density and radius in an infinite model.

Current observations suggest the observable universe has a finite radius of about 46 billion light-years, but whether the universe as a whole is infinite remains unknown. The resolution of Olbers' Paradox does not require the universe to be finite in size — the finite age of the universe and cosmic expansion are sufficient to explain the dark night sky.

Light flux scales directly with star density. Doubling the number of stars per cubic parsec doubles the expected flux. The Milky Way has an average density of roughly 0.004 to 0.14 stars per cubic parsec depending on the region. Try increasing density in the calculator to see how rapidly the theoretical sky brightness grows.

In a uniform static universe, adding a spherical shell of stars at greater distance contributes a constant amount of flux regardless of how far away it is — because the greater number of stars in a larger shell exactly compensates for their greater distance (flux ∝ 1/r² while shell volume ∝ r²). This means each additional shell adds the same flux, so total flux grows linearly with radius — the core of the paradox.

Inputs use parsecs (pc) for distance and solar luminosities (L☉) for brightness. One parsec equals approximately 3.086 × 10¹⁶ meters, or about 3.26 light-years. One solar luminosity equals 3.828 × 10²⁶ watts. The observable universe spans roughly 9.26 billion parsecs.

Beyond philosophical curiosity, this calculator lets students, educators, and astronomy enthusiasts experiment with cosmological parameters to understand how star density, luminosity, and the size of the observable universe all contribute to the night sky's brightness. It makes abstract astrophysics tangible by producing real flux numbers you can compare to sunlight or starlight.