📐 Mathematical Formula & Derivation
VRAM_{total} = (P \times B_{quant}) + (2 \times L \times H \times C \times B_{batch} \times 2\text{ bytes}) + \text{CUDA}_{overhead} 🔬 Engineering Methodology & Benchmark Analysis
Deploying Large Language Models (LLMs) in production or on local workstations requires accounting for three distinct memory layers: static model weights, dynamic Key-Value (KV) attention cache, and CUDA context activation buffers.
Many engineers make the mistake of multiplying parameter count by quantization bytes alone (e.g., 70B × 0.5 bytes = 35 GB). However, at 32k+ context lengths and multi-user concurrency, the KV-cache easily expands by 8 GB to 40+ GB, triggering Out-Of-Memory (OOM) crashes on 48GB dual-GPU setups.
Our formula incorporates Grouped-Query Attention (GQA) scaling heuristics alongside a mandatory 1.6 GB + 8% CUDA activation safety margin so your hardware sizing remains rock-solid under load.
🛠️ Step-by-Step Engineering Calculation Guide
- Model Parameter Count (Billions): Configure "Model Parameter Count (Billions)" (default benchmark: 70) or select an industry preset.
- Quantization Precision (Bits per Weight): Configure "Quantization Precision (Bits per Weight)" (default benchmark: 4.5) or select an industry preset.
- Context Window Length (Tokens): Configure "Context Window Length (Tokens)" (default benchmark: 16384) or select an industry preset.
- Concurrent Batch Size (Active Streams): Configure "Concurrent Batch Size (Active Streams)" (default benchmark: 4) or select an industry preset.