Formula Derivation

CEH™ (Compute Energy Hour) is defined as the kilowatt-hours of energy consumed per unit of compute output, normalized for facility overhead. The formula is derived from first principles of power consumption and throughput measurement.

// Step 1: Compute total draw (kW) for a hardware configuration
Power_kW = ( TDP_W × Units × Util% × PUE ) ÷ 1,000

// Step 2: Compute output rate (output units per hour)
Output_per_hour = COU_rate × Units × 3,600

// Step 3: CEH™ rate = energy per output unit
CEH™ = Power_kW ÷ Output_per_hour

// Derived: cost and carbon dimensions
CEH™ Cost = CEH™ × $/kWh (any energy source)
CEH™ Carbon = CEH™ × kg CO₂/kWh (grid or facility mix)

The result — CEH™ — is dimensionless in its normalized form: kWh of energy consumed per output unit produced. It is a pure efficiency ratio. The cost and carbon dimensions are derived by multiplying the efficiency ratio by the respective input (energy rate or carbon intensity). This design ensures the core efficiency measure is independent of energy price and source.

Variable Definitions

VariableDefinitionSource / Method
TDP_W Thermal Design Power per accelerator unit, in watts. Represents rated maximum draw under sustained load. Vendor datasheet. Measured draw may be used where independently verified and documented.
Units Count of accelerator units (GPUs, TPUs) in the reference configuration. CEH™ Index v1.0 uses 8-unit nodes. Configuration declaration. Must match throughput measurement configuration exactly.
Util% Average utilization rate of the compute hardware (0.0–1.0). Represents fraction of time hardware is active at rated throughput. Operational measurement (preferred) or contractual utilization commitment. Must be disclosed.
PUE Power Usage Effectiveness — total facility power draw divided by IT equipment draw. Captures cooling, power conversion, and overhead. ASHRAE standard measurement or facility disclosure. PUE 1.2 applied uniformly in CEH™ Index v1.0 baselines.
COU_rate Compute Output Units per second per accelerator unit. Workload-class dependent (see COU Definitions). Third-party benchmark (MLPerf, CUDO, Koyeb, Spheron) or operator-disclosed measurement with methodology. Must specify batch size, model class, and framework.
$/kWh Energy rate applied to compute CEH™ Cost. Source-agnostic — applies identically to grid, BTM, nuclear, or any blend. Operator disclosure (type only — not the specific rate — for certification purposes). Benchmark uses $0.085/kWh (US grid avg) and $0.035/kWh (BTM source-agnostic range).
kg CO₂/kWh Carbon intensity of the energy supply, in kilograms of CO₂ equivalent per kWh. EPA eGRID 2024 (regional grid mix), PPA disclosure, or operator-declared for non-grid sources. CEH™ Index v1.0 uses 0.386 kg CO₂/kWh (US average, eGRID 2024).

Compute Output Unit (COU) Definitions

The Compute Output Unit (COU) is the workload-specific unit of output that defines the denominator in the CEH™ formula. COU selection is workload-portable: CEH™ rates are comparable across hardware within a workload class. Cross-class comparisons require normalized COU translation.

Workload Class COU Measurement Basis Normalization Notes
LLM Inference Tokens / hour Output tokens/sec measured at specified batch size and model class. vLLM or equivalent. CEH™ Index v1.0: Llama-class models, batch size 8. Specify model class in disclosure.
Model Training TFLOPS / hour Sustained floating-point ops/sec at FP16/BF16 mixed precision. Normalize by model parameter count for cross-configuration comparison.
Rendering / VFX Frames / hour GPU rasterization + ray tracing pipeline. Studio-grade reference scene required. Frame complexity factor (FCF) must be declared. CEH™ grade thresholds scale to FCF.
HPC / Simulation Iterations / hour Simulation steps per second. Domain-specific measurement protocol. Requires per-study COU normalization. Cross-study comparisons require declared normalization factor.
Additional workload classes (video encoding, RAG retrieval, embedding generation) are under consideration for v2.0. COU definitions for new workload classes require community review prior to index inclusion.

Grade Scale Rationale

The S → F grade scale is calibrated to the LLM inference workload class (CEH™ Index v1.0). Thresholds were set to reflect the practical distribution of hardware efficiency across currently available commercial configurations, with S reserved for hardware achieving best-class efficiency at the time of publication.

Grade CEH™ Rate (kWh/token) Calibration Basis Operator Implication
S< 2.0 × 10⁻¹⁰Best-class Blackwell-generation hardware at publication dateDeploy as primary inference hardware
A2.0 – 4.0 × 10⁻¹⁰Current-generation flagship hardware (H200, TPU v4)Cost-competitive at scale; preferred configuration
B4.0 – 8.0 × 10⁻¹⁰Previous-generation compute hardware (H100, L40S)Viable for mixed workloads; monitor utilization
C8.0 – 15.0 × 10⁻¹⁰Legacy accelerators (A100, older-gen consumer)Suitable for low-priority or burst workloads
D15.0 – 30.0 × 10⁻¹⁰Older-generation hardware approaching end of productive lifeAvoid for sustained production; energy cost excessive
F> 30.0 × 10⁻¹⁰Legacy hardware or non-accelerated configurationsRetire or limit to legacy / compatibility use only

Grade thresholds for training (TFLOPS), rendering (frames), and HPC (iterations) are defined proportionally to the efficiency distribution of reference hardware in each workload class. These equivalent thresholds are published in the full methodology specification document (CEH™ Whitepaper v1.0, available at /resources).

Design Rationale

Why energy-agnostic?
A standard that conflates energy efficiency with energy source is not measuring efficiency — it is measuring source preference. CEH™ is designed to measure how efficiently a unit of energy (regardless of origin) is converted into compute output. This design allows the same standard to apply across grid-connected, BTM, nuclear, and renewable configurations without making an implicit policy judgment about which source is preferable.
Why include PUE in the formula?
PUE (Power Usage Effectiveness) captures facility overhead — cooling, power conversion, lighting, and support systems — that directly affects the energy cost of compute output but is not captured by hardware TDP alone. A configuration running in a PUE 1.5 facility consumes 50% more energy per token than the same hardware in a PUE 1.0 facility. Excluding PUE would make CEH™ a hardware benchmark, not an infrastructure benchmark.
Why separate CEH™ Cost and CEH™ Carbon from CEH™ Rate?
The core efficiency ratio (kWh/output unit) is stable and comparable across configurations. The cost and carbon dimensions vary based on operator-specific inputs (energy rate, carbon intensity) that change over time and differ by geography. Keeping them as derived dimensions prevents operators with expensive grid contracts from appearing less efficient than operators with cheap BTM power when measuring hardware efficiency.
Why a letter grade scale rather than a continuous index?
Grade scales communicate threshold-based risk more clearly than continuous indices for procurement decisions. A continuous 0–100 score implies precision that the underlying data does not support. The S → F model follows established practice in analogous standards (energy appliance ratings, building efficiency ratings) and maps directly to operator decision categories: deploy / monitor / phase out.

Data Sources

CEH™ Index v1.0 throughput figures are sourced from published third-party benchmarks. Oak Ridge Management does not operate all benchmarked configurations directly. Independent replication is invited and constitutes a contribution to the standard.

  • MLPerf v5.1Industry-standard ML inference and training benchmark. Primary source for H100, H200, A100 throughput figures.
  • CUDO ComputePublished cloud GPU benchmark data. Source for consumer and workstation GPU inference figures.
  • KoyebCloud inference platform benchmark disclosures. Supplementary throughput data (2025–26).
  • SpheronDecentralized compute benchmark data. Supplementary throughput and utilization data (2025–26).
  • EPA eGRID 2024US electricity grid carbon intensity by region. CEH™ Index v1.0 uses US national average: 0.386 kg CO₂/kWh.
  • IEA Energy & AI Report (Apr 2025)Global AI energy demand projections. Referenced in thesis documentation.
  • FERC Dec 2025 OrderColocation rule reform for behind-the-meter compute. Regulatory basis for BTM configuration analysis.
  • LevelTen PPA Price Index Q1 2026Power purchase agreement pricing data. Referenced for BTM rate benchmark range.
  • Vendor datasheetsTDP figures sourced from NVIDIA, AMD, and Google published hardware specifications as of benchmark date.

Replication Protocol

Independent replication of the CEH™ Index is explicitly invited. The following protocol defines how to reproduce any row in CEH™ Index v1.0.

  • Obtain hardware TDP from the vendor datasheet current at the replication date. Note any variance from the v1.0 source.
  • Configure an 8-GPU node matching the specified hardware. Apply PUE 1.2 or disclose your measured facility PUE.
  • Run the specified workload: LLM inference, Llama-class model (7B–70B), batch size 8, vLLM or equivalent inference framework.
  • Measure output tokens per second for a minimum 30-minute sustained run at the declared utilization rate.
  • Apply the CEH™ formula: (TDP × 8 × util × PUE) / 1000 / (tps × 8 × 3600).
  • Apply the grade scale thresholds to determine the CEH™ grade.
  • Publish results with: hardware version, firmware version, model class, batch size, framework version, measurement duration, and any deviation from v1.0 configuration.

Replications that produce materially different results (greater than ±15% CEH™ rate deviation from v1.0 figures) should be submitted to Oak Ridge Management for review. Confirmed corrections will be incorporated in the next versioned update with attribution to the replicating institution.

Version Archive

v1.0
Initial publication. LLM Inference (Tokens) workload class. 10 hardware configurations. Grade scale S → F calibrated to Blackwell-through-CPU-baseline distribution. Energy-agnostic formula with BTM and Carbon derived dimensions.
April 21, 2026
CURRENT
v2.0
Planned: Training (TFLOPS), Rendering (Frames), HPC (Iterations) workload class additions. Expanded hardware configurations. arXiv preprint co-submission. Community review period.
TBD

Citation

Formal Citation · CEH™ v1.0
Cobb, D. (2026). CEH™: A Proposed Standard Unit of Measurement for Compute Energy Intensity. DGE&I / Oak Ridge Management. First published April 21, 2026. arXiv: [pending submission]. Available at: oakridgemanagement.net/standard/methodology
CEH™ (Compute Energy Hour) is a trademark of Oak Ridge Management. v1.0 first published April 21, 2026. The methodology is open and may be cited, replicated, and co-published with attribution. The CEH™ name and mark require a license for use in commercial certification contexts. Contact: oakridgemanagement.net/contact