---
id: equations-and-bounds
title: "Equations and Bounds"
status: established
source_sections: "Derived from context files and official specifications"
related_topics: [gb10-superchip, memory-and-storage, ai-workloads, connectivity]
key_equations: [flops-fp4, memory-bandwidth, model-memory-estimate, nvlink-c2c-bandwidth, storage-throughput]
key_terms: [tflops, pflop, bandwidth, throughput, fp4, fp8, fp16, fp32]
images: []
examples: [llm-memory-estimation.md]
open_questions:
  - "Sustained vs. peak TFLOPS under real workloads"
  - "Actual memory bandwidth under mixed CPU+GPU access patterns"
---

# Equations and Bounds

Reference for all quantitative specifications, formulas, and validation ranges for the Dell Pro Max GB10.

## 1. Compute Performance

### Peak TFLOPS by Precision

| Precision | Peak TFLOPS | Source   | Notes                              |
|-----------|-------------|----------|------------------------------------|
| FP4       | 1,000       | T0 Spec  | Headline figure, 1 PFLOP (w/ sparsity) |
| FP8       | ~500        | T3 Infer | Typical 2:1 ratio from FP4         |
| FP16      | ~250        | T3 Infer | Typical 4:1 ratio from FP4         |
| FP32      | ~125        | T3 Infer | Typical 8:1 ratio from FP4         |
| FP64      | ~0.675      | T2 Bench | HPL Linpack, Jeff Geerling          |

*Note: FP8/FP16/FP32 values are inferred from typical Blackwell architecture ratios. FP64 is benchmarked. FP4 headline includes sparsity.*

### GPU Cores
- **CUDA cores:** 6,144 (T0 Spec)
- **Tensor Cores:** 5th generation (count TBD)
- **RT Cores:** 4th generation (T0 Spec)
- **Copy engines:** 2 (T0 Spec)
- **NVENC:** 1 (T0 Spec)
- **NVDEC:** 1 (T0 Spec)

## 2. Memory

### Bandwidth
- **Memory bandwidth:** 273 GB/s (T0 Spec, LPDDR5X at 9,400 MT/s)
- **NVLink-C2C bandwidth:** 600 GB/s bidirectional (T0 Spec, CPU-GPU interconnect)

### Configuration
- **Interface:** 256-bit, 16 channels LPDDR5X 8533 (T0 Spec, NVIDIA DGX Spark User Guide)

### Capacity
- **Total unified memory:** 128 GB LPDDR5X (T0 Spec)
- **Usable for models:** ~109-115 GB (T3 Infer, after OS/framework/KV cache overhead)

## 3. Model Memory Estimation

### Formula: Memory Required for Model Weights

```
Memory (GB) = Parameters (billions) × Bytes_per_parameter
```

| Precision | Bytes/Param | Formula                           |
|-----------|-------------|-----------------------------------|
| FP4       | 0.5         | Params_B × 0.5                    |
| FP8/INT8  | 1.0         | Params_B × 1.0                    |
| FP16      | 2.0         | Params_B × 2.0                    |
| FP32      | 4.0         | Params_B × 4.0                    |

### Total Inference Memory (approximate)

```
Total Memory ≈ Model_Weights + KV_Cache + Activation_Memory + Framework_Overhead
```

Rule of thumb: budget **1.2-1.5x** the raw model weight size for total inference memory.

### Maximum Model Sizes (single unit, 128 GB)

| Precision | Max Params (raw)  | Max Params (practical, ~110 GB usable) |
|-----------|-------------------|----------------------------------------|
| FP4       | 256B              | ~200B                                  |
| FP8/INT8  | 128B              | ~100B                                  |
| FP16      | 64B               | ~55B                                   |
| FP32      | 32B               | ~27B                                   |

## 4. Networking Bounds

| Interface           | Spec Bandwidth     | Measured          | Direction       |
|---------------------|--------------------|-------------------|-----------------|
| NVLink-C2C          | 600 GB/s           | —                 | Bidirectional   |
| LPDDR5X memory      | 273 GB/s           | —                 | System memory   |
| QSFP (per port)     | 200 Gbps (25 GB/s) | ~106 Gbps single stream | Network   |
| QSFP (total)        | 400 Gbps (50 GB/s) | 200+ Gbps RDMA   | 2 ports combined|
| QSFP PCIe link      | x4 PCIe Gen 5      | —                 | Internal        |
| 10 GbE Ethernet     | 10 Gbps (1.25 GB/s)| —                 | Network         |
| USB-C (per port)    | 20 Gbps (2.5 GB/s) | —                 | I/O             |

*QSFP measured throughput from Jeff Geerling (T2 Benchmarked).*

## 5. Power Bounds

| Parameter               | Dell Pro Max | DGX Spark | Source      |
|-------------------------|-------------|-----------|-------------|
| PSU rating              | 280W        | 240W      | T0 Spec     |
| GPU TDP                 | 140W        | 140W      | T0 Spec     |
| Idle draw               | ~30W        | ~40-45W   | T2 Bench    |
| AI inference (LLM)      | 60-90W      | 60-90W    | T2 Bench    |
| CPU-only load           | 120-140W    | 120-130W  | T2 Bench    |
| CPU + GPU load          | ~200W       | ~200W     | T2 Bench    |

## 6. Environmental Bounds

| Parameter              | Dell (T0 Owner's Manual)           | DGX Spark (T0 User Guide)       |
|------------------------|------------------------------------|---------------------------------|
| Operating temperature  | 0°C to 35°C (32°F to 95°F)        | 5°C to 30°C (41°F to 86°F)     |
| Storage temperature    | -40°C to 65°C                      | —                               |
| Operating humidity     | 10% to 90% (non-condensing)        | 10% to 90% (non-condensing)    |
| Operating altitude     | -15.2 m to 3,048 m                 | Up to 3,000 m                  |
| Operating vibration    | 0.66 GRMS                          | —                               |
| Operating shock        | 110 G (2ms half-sine)              | —                               |
| Noise                  | < 40 dB at 1-1.5m (T2 Bench)      | —                               |

## 7. Physical Bounds

| Parameter     | Value         |
|---------------|---------------|
| Volume        | ~1.15 L       |
| Weight        | 1.31 kg       |
| Footprint     | 150 × 150 mm  |
| Height        | 51 mm         |

## 8. Validation Rules

When checking calculations:
- Model size estimates should not exceed 128 GB (single) or 256 GB (stacked)
- TFLOPS claims must specify precision — reject unqualified "1 PFLOP" statements
- Memory bandwidth (273 GB/s) is the system memory bus, NOT the NVLink-C2C (600 GB/s)
- Network bandwidth (QSFP) is in Gbps, not GB/s — divide by 8 for bytes