TCP Throughput Calculator (Mathis Formula: Loss and Round-Trip Time)
The most one standard TCP connection can carry for a given round-trip time, segment size and packet loss rate — and the loss rate you would need for a target speed.
Results
The dashed line marks the value you entered.
What this tool does
A TCP connection that sees losses halves its speed each time and then creeps back up, so its average speed depends on loss and round-trip time, not on how fast the link is. With 100 ms of delay and 0.1 % loss, a 1 Gbit/s link gives one classic connection only about 4.5 Mbit/s. Halving the delay doubles the ceiling; cutting the loss by 100 multiplies it by 10. The formula is an upper estimate for steady random loss; CUBIC, BBR and parallel connections do better.
Formula
rate ≤ (MSS ÷ RTT) × C ÷ √p with C = √(3/2) ≈ 1.22 (ACK every segment) or √(3/4) ≈ 0.87 (delayed ACKs) (Mathis et al.)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
ms | Maximum segment size (MSS) | bytes |
rt | Round-trip time | ms |
lo | Packet loss rate | % |
ak | Receiver acknowledges | — |
tg | Throughput you want to reach | Mbit/s |
TH | Throughput ceiling of one connection | Mbit/s |
PP | Segments per second | /s |
WN | Average window in flight | kB |
NL | Loss rate that would allow that throughput | % |
Worked example
- Maximum segment size (MSS)1460 bytes
- Round-trip time50 ms
- Packet loss rate0.1 %
- Receiver acknowledges1
- Throughput you want to reach100 Mbit/s
- Throughput ceiling of one connection9.05 Mbit/s
- Segments per second775 /s
- Average window in flight56.5 kB
- Loss rate that would allow that throughput0.00082 %
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.