Source: https://guthlabs.ai/docs/instruments/battery-capacity-c-rate-runtime-calculator/mechanism/

instrument mechanism / verified-clean

# Battery Capacity / C-Rate / Runtime Calculator mechanism

The inspectable method record for Battery Capacity / C-Rate / Runtime Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The two stated arithmetic formulas are valid only under the Ah/A ideal-battery assumptions. The specification is incomplete because it advertises Ah/Wh capacity, current/power load, and derated capacity without defining the required Wh/W formula, voltage conversion, derating model, or constraints.

- t = Capacity(Ah) / I(A) is correct for an ideal battery when capacity is in ampere-hours and load is a constant current in amperes.

- I_max = C-rate × Capacity(Ah) is correct for nominal maximum discharge current when C-rate is dimensionless and capacity is in ampere-hours.

- The declared capacity input may be Ah or Wh, but the runtime formula only supports Ah; Wh requires t = Energy(Wh) / Power(W), or conversion using nominal voltage.

- The declared load input may be current or power, but no voltage input or power-based runtime formula is provided for power loads.

- The declared output derated capacity has no formula or defined inputs; it cannot be computed from the supplied formulas.

- The exact ambiguity requiring review is whether runtime inputs are capacity/current in Ah/A or energy/power in Wh/W, and how nominal voltage should be supplied for conversion between them.

## Units and conventions

- Capacity is in Ah for the supplied runtime and C-rate formulas.

- Load is a constant current in A; runtime is returned in hours.

- C-rate is dimensionless, expressed as a multiple of the rated capacity per hour; for example, 1C × 100Ah = 100A.

- For Wh/W operation, runtime would be in hours only after using t = Wh/W; converting power to current requires voltage in volts.

- The formulas are ideal estimates and do not include Peukert behavior, voltage sag, cutoff voltage, temperature, aging, or discharge-rate-dependent capacity.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "capacity_Ah": 100,
    "load_current_A": 5,
    "c_rate": 0.5
  },
  "expected_outputs": {
    "runtime_hours": 20,
    "max_discharge_current_A": 50
  },
  "working": "Runtime: t = Capacity / current = 100 Ah / 5 A = 20 h. Maximum current: I_max = C-rate × Capacity = 0.5 × 100 Ah = 50 A."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

A zero load current creates a division-by-zero runtime result, and the specification does not define whether to reject it or report unlimited idealized runtime. Negative-current sign handling is also unspecified, producing either a misleading negative runtime or a charging-state interpretation. No derated-capacity formula or true piecewise branch is supplied.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/battery-capacity-c-rate-runtime-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/battery-capacity-c-rate-runtime-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/battery-capacity-c-rate-runtime-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`