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