TCP Retransmission Calculator
Apply the Mathis equation to see the throughput ceiling packet loss imposes on a single TCP stream.
About TCP Retransmission Calculator
The Mathis equation comes from averaging the AIMD sawtooth: a loss event halves the congestion window and it then grows one segment per RTT, so the mean window — and therefore throughput — scales with the inverse square root of the loss rate. Goodput subtracts the retransmitted share from the offered rate. Loss hurts far more than intuition suggests: going from 0.01% to 1% loss cuts a single stream's ceiling tenfold, which is why a 'barely lossy' WAN link kills bulk transfers.
Formulas
TCP Retransmission
throughput ≈ MSS ÷ (RTT × √p), where p is the loss probability.
- MSS
- Maximum segment size in bits
- RTT
- Round-trip time in seconds
- p
- Packet loss probability (loss % ÷ 100)
Goodput after loss
goodput = segments/s × MSS × 8 × (1 − p)
- p
- Loss probability
- MSS
- Payload bytes per segment
Worked example
With the default values below, TCP Retransmission Calculator returns Mathis Throughput Ceiling of 9.23. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Maximum segment sizeaccepts 88–9,000 bytes
- 1,460 bytes
- Round-trip timeminimum 0.1 ms
- 40 ms
- Packet loss rateaccepts 0–50 %
- 0.1 %
- Segments sent per secondminimum 0 segments/s
- 20,000 segments/s
Results
- Mathis Throughput Ceiling
- 9.23 Mbit/s
- Retransmitted Segments
- 20.0 segments/s
- Effective Goodput
- 233.37 Mbit/s
- Retransmission Overhead
- 0.100%
Step by step
- 1Values used
- 2TCP Retransmission
- 3Goodput after loss
- 4Mathis Throughput Ceiling= 9.23 Mbit/s
- 5Retransmitted Segments= 20.0 segments/s
- 6Effective Goodput= 233.37 Mbit/s
- 7Retransmission Overhead= 0.100
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is TCP Retransmission calculated?
throughput ≈ MSS ÷ (RTT × √p), where p is the loss probability. The Mathis equation comes from averaging the AIMD sawtooth: a loss event halves the congestion window and it then grows one segment per RTT, so the mean window — and therefore throughput — scales with the inverse square root of the loss rate. Goodput subtracts the retransmitted share from the offered rate.
Why does TCP Retransmission matter?
Loss hurts far more than intuition suggests: going from 0.01% to 1% loss cuts a single stream's ceiling tenfold, which is why a 'barely lossy' WAN link kills bulk transfers.
What values do I need to enter?
This calculator takes 4 inputs: Maximum segment size, Round-trip time, Packet loss rate, Segments sent per second. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.
Does the Mathis equation apply to modern congestion control?
It models loss-based Reno/CUBIC behaviour, so treat it as the pessimistic bound. BBR and other rate-based algorithms are far less loss-sensitive and can exceed this figure on links with non-congestive loss.