Muon Lifetime Calculator

Calculate muon time dilation and atmospheric survival probability

About Muon Time Dilation

Cosmic ray muons are created ~15 km above Earth's surface. With a lifetime of only 2.2 μs, they should decay in ~660 m. Yet many reach sea level - clear evidence of relativistic time dilation.

Key Values:

  • Rest mass: 105.66 MeV/c² (207 × electron mass)
  • Proper lifetime: 2.197 μs
  • Main decay: μ → e + νₑ + νμ (99.98%)

Formula:

  • P(survival) = exp(-L/(βcγτ₀))
  • γ = E/(mc²)
  • Mean decay length = βcγτ₀