The Time-To-Live (TTL) is not "calculated" in the mathematical sense. Rather, it's a pre-set value that decrements by one each time a packet passes through a router.
Here's a breakdown:
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Initial TTL Value: When a packet is created, it's assigned an initial TTL value. This value varies depending on the operating system and network configuration. Common default values are 64, 128, or 255.
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Decrementing at Each Hop: As the packet travels across the network, each router it encounters decrements the TTL value by one. This process is crucial for preventing packets from endlessly circulating the network due to routing loops.
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TTL Reaching Zero: When the TTL value reaches zero, the router that receives the packet does not forward it. Instead, it drops the packet.
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ICMP Time Exceeded Message: The router that drops the packet typically sends an Internet Control Message Protocol (ICMP) "Time Exceeded" message back to the source of the packet. This message indicates that the packet's TTL expired.
In summary, TTL isn't calculated dynamically during transit; it's a countdown timer that starts with a pre-defined value and counts down to zero as the packet traverses the network. The decrementing process at each router determines how long a packet can "live" before being discarded.