6 × params × tokens scaling law

LLM training time calculator

Training compute ≈ 6 × parameters × tokens. Divide by achieved GPU FLOPs and you get GPU-hours — plan your pretrain or fine-tune before booking a single node.

Training time — h

—6 × P × T ÷ (FP16 TFLOPS × 0.4 MFU × GPUs)

AD
Live comparison

Per-GPU training time

Single card, current model and token count

GPUFP16 TFLOPSSingle-card time
RTX 3060 25.5 —
RTX 4060 Ti 44 —
RTX 3090 142 —
RTX 4090 330 —
RTX 5090 419 —
A100 312 —
A100 312 —
H100 SXM 989 —
H200 989 —
B200 2250 —
AMD MI300X 1307 —
Dense FP16 tensor TFLOPS, vendor specs. MFU 0.4 — real clusters achieve 30-50%.
Quick reference

Chinchilla-optimal pretrains on H100

20 tokens per parameter

ModelTokens1 × H1001024 × H100
Llama 3.1 8B 160B 7.5 GPU-months 5.3 GPU-hours
Llama 3.1 70B 1400B 573.4 GPU-months 16.8 GPU-days
Llama 3.1 405B 8100B 19,195.5 GPU-months 18.7 GPU-months
Qwen 2.5 7B 140B 5.7 GPU-months 4 GPU-hours
Qwen 2.5 72B 1440B 606.7 GPU-months 17.8 GPU-days
Mistral 7B 140B 5.7 GPU-months 4 GPU-hours
Same factors as the calculator — one data source, no drift.
How the math works

Six FLOPs per parameter, per token.

Every training step runs the forward pass (about 2 FLOPs per parameter per token) and the backward pass (about 4), which is where the 6× rule comes from. Multiply parameters by tokens by six, divide by your cluster's achieved FLOPS — peak TFLOPS discounted by MFU — and the result is wall-clock GPU time before you spend a cent.

The rule scales linearly in every direction: double the data and time doubles, halve the model and time halves, and a 1024-GPU cluster finishes in 1/1024th the single-card time in the ideal case. Real clusters lose some of that to communication, which is exactly what MFU absorbs.

Good to know

Frequently asked questions

Where does the 6 × params × tokens rule come from?

Scaling-law literature (Kaplan 2020, Hoffmann/Chinchilla 2022) shows training compute is ≈ 6 FLOPs per parameter per token: 2 FLOPs for the forward pass and 4 for the backward. It is the standard estimate used across pretraining papers and GPU-hour forecasts.

Why 40% MFU?

MFU (model FLOPs utilization) is the share of a GPU's peak compute a real training run achieves. Large dense runs land at 30-50% on well-tuned clusters — we use 40% and state it, so you can scale the estimate for your own stack.

How many tokens should I train for?

Compute-optimal (Chinchilla) is roughly 20 tokens per parameter — 160B tokens for an 8B model. Modern frontier models deliberately overtrain far beyond this for better inference economics; multiply the token count accordingly and the time scales linearly.

More AI calculators

Keep computing