How to use the muon survival fraction calculator
Find the fraction of fast muons that survive to reach the ground, using time dilation. Enter muon speed as fraction of light speed, distance travelled in the fields above; the muon survival fraction, lorentz factor are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “muon decay time dilation”, “cosmic ray muons survive”, “muon survival probability”, “calculate muon survival fraction”, “find muon survival fraction”.
Formula
Variables
- beta — Muon speed as fraction of light speed
- dist — Distance travelled (km)
Worked example
With muon speed as fraction of light speed = 0.99, distance travelled = 10 km, the calculator gives muon survival fraction ≈ 11.49315 %; lorentz factor ≈ 7.088812.
Frequently asked questions
What is the muon survival fraction calculator used for?
Find the fraction of fast muons that survive to reach the ground, using time dilation. It helps with questions such as “muon decay time dilation”, “cosmic ray muons survive”, “muon survival probability”.
What is the formula for the muon survival fraction calculation?
Muon survival fraction (%) = 100 × exp(-dist × 1000 × √(1-beta × beta) / (beta × CLIGHT × 2.197e-6)). Lorentz factor = 1 / √(1-beta × beta). Here beta is muon speed as fraction of light speed, dist is distance travelled (km).
What inputs do I need for the muon survival fraction calculator?
You need muon speed as fraction of light speed, distance travelled in km. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the muon survival fraction calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the muon survival fraction result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.