Battery Runtime Calculator

Estimate battery runtime under a constant load from pack capacity, voltage, and load in watts (load-side power) or amps (battery-side current), with optional planning DoD and load-side efficiency. Optional standard uncertainties (u_*) compose an expanded interval on runtime via the Uncertainty Engine.

Status: Battery Runtime Basic v1.2.1 — Frozen model. Pin calculation_version: 1.2.1. Same constant-load formulas as 1.2.0; Agent schema now requires at least one u_* when uncertainty_k or confidence is set. Do not stack Peukert / temperature / duty-cycle / pack workspace into this page — those are separate capabilities.

Default example: 10 Ah · 12 V · 20 W · DoD 0.8 · η 0.9 → 4.32 h (usable 86.4 Wh).

Product position

Battery Runtime
├── Basic (this page, frozen 1.2.1)
│     Ah/mAh · V · W/A · DoD · η · first-order u_*
├── Temperature        → electrical.battery.runtime_temp
├── Pack sizing        → electrical.battery.pack_sizing
└── Future (separate)
      Peukert · Duty cycle · Manufacturer curves · Pack/System Workspace

Supported and not supported

Supported

• Constant watt (load-side) or amp (battery-side) load
• Capacity in Ah or mAh (mutually exclusive)
• Planning DoD and load-side efficiency fractions in (0, 1]
• Optional standard uncertainties on capacity, V, P/I, DoD, η with coverage k (default 2)
• API result { t_h, t_d, E_Wh, uncertainty? } via electrical.battery_runtime

Not supported

• Peukert / high C-rate capacity loss
• Temperature derating (see Battery Runtime with Temperature / electrical.battery.runtime_temp)
• Multi-step duty cycles or sleep currents
• BMS cutoff voltage modeling or pack sizing (see future pack tools)
• Monte Carlo / correlation / νeff UI on this page (use Uncertainty Propagate directly)

Agent / API notes

Capability id: electrical.battery_runtime · tool id: battery-runtime · pin calculation_version: 1.2.1.

Input schema is mode-discriminated (oneOf): watts requires P_W; amps requires I_A (battery-side discharge current; η ignored); capacity_Ah XOR capacity_mAh; uncertainty_k XOR confidence; uncertainty_k/confidence require at least one contributing u_*. Pin calculation_version: 1.2.1.

Canonical response inputs always echo capacity_Ah (mAh alias resolved); amps omits eta / P_W; watts omits I_A.

Stable error codes: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_MODE, CAPACITY_MUST_BE_POSITIVE, VOLTAGE_MUST_BE_POSITIVE, LOAD_MUST_BE_POSITIVE, FRACTION_OUT_OF_RANGE, VALUE_MUST_BE_NON_NEGATIVE, INVALID_INPUT.

When any u_* is set, the engine calls engineering.uncertainty.propagate (sensitivity) and attaches an UncertaintySummary ($ref /schemas/common/uncertainty-summary.json) { u_c, U, k, coverage, contributions, … } on t_h. Empty u_* preserves the nominal-only result.

Capability family & namespace

This Basic page is frozen at calculation_version 1.2.1. Related tools:

No breaking rename yet. When Agents and catalog consumers are ready, expose preferred ids with deprecated aliases pointing at the current public ids.

Future layers (separate pages/capabilities): Peukert, duty cycle, manufacturer curves, Pack Runtime Workspace — not stacked into this Basic page.

How the estimate works

Watts mode — P_W is delivered load-side power; η is load-side delivery efficiency:

E(Wh) = Q(Ah) × V × DoD × eta, tₕ = (E(Wh))/(P(W))

Amps mode — I_A is battery-side discharge current (converter loss already in the current); η does not enter runtime:

E(Wh) = Q(Ah) × V × DoD, tₕ = (Q(Ah) × DoD)/(I(battery))

Days are reported as t(d) = tₕ / 24.

Optional uncertainty

When you supply one or more standard uncertainties u(xᵢ), runtime is treated as tₕ = f(…) and combined with GUM sensitivity coefficients partial t/partial xᵢ. Expanded uncertainty uses coverage factor k (default 2):

u_c(t) = √(sumᵢ (cᵢ uᵢ)²), U = k u_c

Result UI shows tₕ ± U and contribution bars when any u_* is present.

Choosing DoD and efficiency

DoD and η are planning knobs, not chemistry models inferred by CalculatorX.

In amps mode, enter the measured battery current and leave η unused.