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Napkin Math, Cost & Capacity / 23
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What does one training token cost?

Dollars per FLOP from the GPU price and the MFU, times 6N: a 70B training token costs about three quarters of a microdollar, and the whole 15T-token run follows in one multiplication. The chain, the comparison to an inference token, and why the training token is cheaper.

Updated Sep 2026 · Grounded in real AI infrastructure interview loops and written to a senior-engineer editorial bar, with every number worked and every diagram hand-built.

Dollars per FLOP from the GPU price and the MFU, times 6N: a 70B training token costs about three quarters of a microdollar, and the whole 15T-token run follows in one multiplication. The chain, the comparison to an inference token, and why the training token is cheaper.

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The concepts behind this question

Ranked by how closely each one overlaps this question's topic, so the first card is the thing to read if the answer above moved too fast.

Core
🧮 Napkin Math & CapacitySign in
GPU-Hours and Time to TrainThe fleet equation turns a training run's FLOPs into a schedule: time = 6ND divided by (GPUs times peak FLOPS times MFU). Every term is a stated assumption, and the interviewer grades the assumptions rather than the digits: which peak, which MFU, and what happens to the answer when MFU falls from 40% to 30%. This page works three runs end to end (an 8B, a 70B and a 405B), inverts the equation for the GPU count a deadline needs, and shows the sensitivity that separates a considered estimate from a lucky one.
Advanced
🧮 Napkin Math & Capacity🔒 Premium
Cost per Million TokensThe unit every serving decision cashes out in. It is one formula: the fleet's dollars per second divided by the tokens per second it sustains, scaled to a million, with utilization in the denominator because idle replicas still cost money. This page derives it from a GPU price and a throughput estimate, works it at three batch sizes to show why batching is the main lever, separates prefill from decode pricing, and shows how the same fleet's cost per token moves by 5x between a quiet hour and a busy one.
Foundational
🧮 Napkin Math & Capacity
Training FLOPs: 6NDThe compute needed to train a language model is six floating-point operations per parameter per token: two for the forward pass and four for the backward. Multiply by the parameter count and the token count and you have the whole run's compute, which is the number every fleet-sizing, time-to-train and cost question starts from. This page derives the 6, states the attention correction and when it matters, and shows where the 2N of inference comes from, so the reader can rebuild the formula rather than recall it.
Core
🕸️ Distributed TrainingSign in
MFU and HFUModel FLOPs utilization is the fraction of a GPU's peak that goes into the model's own forward and backward math, computed from 6ND and the step time; hardware FLOPs utilization also counts recomputation. Production LLM training lands at 35 to 45% MFU, and knowing where the other 55% goes is the job.
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FEDITOR'S NOTE

The interviewer wants the candidate to build a dollars-per-FLOP figure with MFU inside it, then multiply by 6N, then check the run total against a known GPU-hour figure. The surprise to surface is that a training token costs less than an output token at inference.

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