How the break-even model works
Self-hosting and cloud API are two cost structures. Local = fixed cost F + marginal m×volume: F is hardware price amortized monthly plus hosting/ops; m is electricity per million tokens (from power, price and throughput). Cloud API = blended price c × volume — pure usage, zero fixed.
Where the two lines cross is the break-even M\* = F ÷ (c − m): above it local wins, below it cloud API wins. The other constraint is single-box capacity M_max = throughput × utilization × seconds per month — one box can only emit so many tokens a month; beyond that you add hardware and fixed cost multiplies.
One card: price $2,000, 24-month depreciation, $30/mo fixed → fixed F ≈ $113. With a blended cloud price of $2/M tokens and local marginal $0.1/M tokens — break-even ≈ 113 ÷ (2 − 0.1) ≈ 59 M tokens/mo.
So below ~59M tokens a month, cloud API is actually cheaper.
Throughput (TPS) dominates the result and depends on model size, quantization, batch and concurrency — measure it on your real deployment. To calibrate the cloud price first, see the Token Cost Calculator or LLM price comparison.