Electrical calculator

Battery Pack Sizing Calculator

Size battery capacity (Ah) from load and runtime targets, with optional series/parallel cell geometry. Inverse of Battery Runtime (watts load-side / amps battery-side).

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Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance

Input interpretation: Enter values to calculate.
Result: —
Assurance: Engineering
Declared partition coverage: PASS · 4/4 declared partitions (watts, amps, cells, invalid-domain) · Matrix
Known limitations: Planning estimate — not BMS / chemistry pack design
Core CVP does not include live graph, viewport, or pointer interaction.
Model: Required pack capacity (and optional nominal cell geometry) from runtime/load targets.
Scope: Constant load; ceil cell counts as nominal packing estimate; not Peukert or BMS design
Verification: Engine tested · Source checked · v1.2.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions: Calculation 1.2.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-12.round-xcal-iface
Verification revision: 2026-09-12.round-xcal-iface · 7/7 property · digest 1e3949ba3d8e
Legacy regression: 27/27 tests · Production surface contract 4/4
Trust layers: Verification VERIFIED · Production CURRENT · overall VERIFIED
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review: Internal · Pass · electrical-engineer
Named expert review: Not performed
CVP suite: 3/3 golden · 16/16 CVP boundary · 14/14 invalid · 7/7 property · 2/2 round-trip · 3/3 cross-interface · 2/2 cross-calculator · 4/4 CVP contract · Manifest
Sources: IEC 60050 — International Electrotechnical Vocabulary — Electric battery capacity and related quantities
Victron Energy — Battery capacity and Peukert exponent — SmartShunt / battery monitor documentation
CalculatorX Battery Runtime capability — Constant-load watts/amps model (1.2+) — internal method dependency
Sources
Methods: derived_from:electrical.battery_runtime@1.2.0 — inverse constant-load watts/amps model
Evidence: 3 legacy golden · 17 legacy boundary · legacy regression suite · 3/3 oracle-backed golden · 14/14 invalid · Artifact integrity PASS · CalculatorX electrical review
Semantic contract: PASS

Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Capacity (watts, load-side)Ah = (P × t) / (V × DoD × η)

Capacity (amps, battery-side)Ah = (I × t) / DoD

Approximate cell geometry (nominal)Ns = ceil(V/Vcell); Np = ceil(Ah/Ah_cell); V_pack = Ns·Vcell

iConstant-load idealization. Not Peukert or BMS design. Amps mode treats I as battery-side current — η does not enter. Cell Ns/Np are a nominal packing estimate only.

How to use

Enter required runtime and load

Hours plus load-side watts or battery-side amps.

Enter pack voltage and planning DoD/η

η applies in watts mode only.

Optional: cell V and Ah

Provide both for a nominal series/parallel packing estimate (ceil).

Example calculations

Common configurations with formula and result.

20 W · 6 h · 12 V

Ideal DoD=η=1

Ah = P·t/V

10 Ah · 120 Wh

Battery-side 2 A · 4 h · DoD 0.8

η ignored

Ah = (2·4)/0.8

10 Ah

4S4P cells (exact stack)

14.8 V · 29.6 W · 5 h · 3.7 V / 2.5 Ah cells

ceil geometry

Ns=4 · Np=4 · 16 cells

12 V target · 3.7 V cells

Non-integral series ratio

Ns=ceil(12/3.7)=4 → V_pack=14.8 V

warning PACK_VOLTAGE_DIFFERS_FROM_TARGET

Battery Pack Sizing calculator specification

Version 1.2.0 · Engine tested · Supplemental domain review · Internal · 2026-09-05

Calculation status

Engine tested 27/27 tests · Production surface contract 4/4
Supplemental domain review Internal · Pass · electrical-engineer · 2026-09-05
Named expert review Not performed
Calculation version 1.2.0

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition: Invert the constant-load battery runtime model: watts Ah = (P·t)/(V·DoD·η); amps Ah = (I_battery·t)/DoD. Optional cell V and Ah yield nominal Ns/Np via ceil (packing estimate only).
What it calculates: Required pack capacity (and optional nominal cell geometry) from runtime/load targets.
Inputs: mode watts (P_W load-side) | amps (I_A battery-side); t_h > 0; V > 0
Optional dod, eta in (0,1]; eta unused in amps mode
Optional V_cell + capacity_cell_Ah together
Outputs: capacity_Ah
E_Wh
n_s?
n_p?
n_cells?
V_pack?
warnings?
…
Formula: watts: Ah=(P·t)/(V·DoD·η); amps: Ah=(I·t)/DoD; Ns=ceil(V/Vcell); Np=ceil(Ah/Ah_cell) — nominal packing only
Assumptions: Constant load; ceil cell counts as nominal packing estimate; not Peukert or BMS design
Amps mode I_A is battery-side; η does not enter Ah
V is target/system nominal voltage; V_pack = Ns·V_cell may differ
Units: h, V, W or A, Ah
Boundary conditions: Only one of V_cell/capacity_cell_Ah → NEEDS_TWO_INPUTS
Bad mode → INVALID_MODE; dod/eta out of range → FRACTION_OUT_OF_RANGE
t/V/P/I ≤ 0 → VALUE_MUST_BE_POSITIVE / VOLTAGE_MUST_BE_POSITIVE / LOAD_MUST_BE_POSITIVE
V_pack ≠ V → warning PACK_VOLTAGE_DIFFERS_FROM_TARGET
Example: 20 W · 6 h · 12 V → 10 Ah
Validation cases: 4 published on this page · 27/27 tests · Production surface contract 4/4 · View evidence
P=20, t=6, V=12 → Ah=10, E=120
I=2, t=4, DoD=0.8, eta=0.9 (amps) → Ah=10 (η ignored)
cells 3.7V 2.5Ah @ 14.8V 29.6W 5h → Ns=4, Np=4
P=20, t=6, V=12, V_cell=3.7, capacity_cell_Ah=2.5 → Ns=4, V_pack=14.8, warning PACK_VOLTAGE_DIFFERS_FROM_TARGET
Methods: derived_from:electrical.battery_runtime@1.2.0 — inverse constant-load watts/amps model
Sources: IEC 60050 — International Electrotechnical Vocabulary — Electric battery capacity and related quantities
Supports: Ah capacity and Wh energy relationship E ≈ Q·V for nominal estimates
Victron Energy — Battery capacity and Peukert exponent — SmartShunt / battery monitor documentation
Supports: Ideal Ah ≈ I·t under constant current; Peukert and rate effects as reasons this tool stays first-order (Not Peukert)
CalculatorX Battery Runtime capability — Constant-load watts/amps model (1.2+) — internal method dependency
Supports: Inverse capacity sizing; shared watts/amps semantics with electrical.battery_runtime
Last reviewed: 2026-09-05
Reviewed by: CalculatorX electrical review (electrical-engineer)
Calculation version: 1.2.0

Background

Interpretation and common distinctions.

Size pack capacity from runtime and load — the inverse of Battery Runtime — with optional series/parallel cell counts.

Default: 20 W · 6 h · 12 V → 10 Ah (120 Wh).

Agent / API notes

Capability id: electrical.battery.pack_sizing · tool id: battery-pack-sizing · pin calculation_version: 1.2.0.

Input Schema: mode-discriminated oneOf (watts / amps) — inverse of BatteryRuntimeBaseInput (t_h instead of capacity). Optional V_cell + capacity_cell_Ah must both be present or both omitted.

Aligned with Battery Runtime 1.2+: watts = load-side power (+ η); amps = battery-side current (η ignored).

Other calculators in this family: Battery Runtime Calculator, Battery Runtime with Temperature, Linear Battery Aging Calculator . Explore all Battery & Energy Storage.

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Frequently asked questions

Key distinctions behind the calculation.

How is this related to Battery Runtime?

Runtime solves t from Ah; pack sizing solves Ah from t — the same constant-load energy model inverted (Battery Runtime 1.2+ watts/amps semantics).

Must I enter cell data?

No. Omit both V_cell and capacity_cell_Ah for Ah/Wh only. Provide both together for a nominal Ns/Np packing estimate.

Is Ns = ceil(V/Vcell) a real pack design formula?

No. It is a nominal series packing estimate only. Real packs must satisfy cell min/max voltage, system operating range, BMS limits, and chemistry — not just ceil(V_target/V_cell_nom). When V_pack ≠ V_target the API emits PACK_VOLTAGE_DIFFERS_FROM_TARGET.

Does η apply in amps mode?

No. Amps mode uses battery-side current; η is ignored (same as Battery Runtime).