B | calculated eV | Calculation | cosmic rays | observed eV |

B | 1.7 × 10 | M | the first knee | 3 × 10 |

The midpoint between B | 2 × 10 | Equation (6) | the first ankle | 2 × 10 |

F | 2.35 × 10 | M | the second knee | 3 × 10 |

The midpoint between F | 2.8 × 10 | Equation (6) | the second ankle | 3 × 10 |

B | 3.2 × 10 | M | the toe | 4 × 10 |

F | 4.4 × 10 | M | beyond the GZK limit (5 × 10 | not observed |

B | 1.13 × 10 | M | Plank mass for gravity | 1.22 × 10 |