UPS Battery Ah Formula (Free Guide — Runtime & Examples)
Introduction #
The sizing formula: Ah = (kW × 1000 × hours) / (V × DoD × η) — where V is nominal string voltage, DoD is usable depth of discharge (typically 0.5–0.8 for VRLA), and η is inverter/DC-path efficiency (typically 0.85–0.92).
When this guide fits: You need to translate target runtime minutes at a known kW load into battery Ah and string voltage for a static UPS (industrial or commercial).
When it does not fit: You still need the UPS frame in kVA (use UPS kVA Capacity Calculator or UPS sizing for factories), or you are sizing utility BESS / EV DC fast chargers — different codes and fault duties than classic UPS strings.
Not this page: Whole-system UPS kVA / redundancy selection. This page stops at Ah + string layout; confirm backup minutes afterward in the runtime calculator.
Sizing Formula and Worked Examples #
Core Formula #
Ah = (Load kW × 1000 × Runtime hours) ÷ (String voltage × DoD × Efficiency)
Equivalent energy form: Battery Wh = (Load W × Runtime hours) ÷ Efficiency, then Ah = Wh ÷ String voltage.
Example A — 48 V String #
2 kW load, 30 minutes, 48 V string, DoD 0.8, η 0.85:
Ah = (2 × 1000 × 0.5) / (48 × 0.8 × 0.85) = 1000 / 32.64 ≈ 30.6 Ah
Planning: round up to 35 Ah commercial block with aging margin. Cross-check minutes in the UPS Runtime Calculator.
Example B — 240 V String #
6 kW load, 30 minutes, 240 V string, DoD 0.8, η 0.92:
Ah = (6 × 1000 × 0.5) / (240 × 0.8 × 0.92) = 3000 / 176.64 ≈ 17.0 Ah
Higher string voltage reduces Ah for the same energy — but each series cell adds failure points. Confirm string topology with OEM before ordering.
Example C — Industrial 15-Minute Bridge #
18 kW load, 15 minutes, 192 V string, DoD 0.7, η 0.93:
Ah = (18 × 1000 × 0.25) / (192 × 0.7 × 0.93) = 4500 / 124.99 ≈ 36.0 Ah
Short high-power discharges hit C-rate limits — verify with vendor discharge tables, not just energy math.
Key Factors That Drive Battery Ah #
- Load power (kW) and power factor — determines kVA demand on the inverter
- Target runtime — longer backup = more Ah at the same voltage
- String voltage — higher V reduces Ah for the same energy (Wh = Ah × V)
- Depth of discharge (DoD) — VRLA often planned at 50–80% usable; shallow DoD extends cycle life
- UPS efficiency (η) — online 0.85–0.92; line-interactive 0.90–0.95; standby 0.95–0.98
- Battery type — VRLA, lithium-ion, NiCd have different energy density and aging profiles
- Temperature — every 10°C rise roughly halves VRLA calendar life; add Ah margin for hot rooms
Series and Parallel String Planning #
- Series blocks raise string voltage to match UPS DC bus (e.g. 20 × 12 V blocks = 240 V string).
- Parallel strings add Ah capacity and share discharge current — but each string must meet OEM C-rate limits independently.
- Do not mix old and new cells in the same string — resistance imbalance shortens effective runtime non-linearly.
- Lay out series/parallel blocks in the UPS Battery Calculator (string layout) after sizing Ah here.
Age and Temperature Derating #
VRLA Age Derating (Typical) #
| Year | Usable capacity (%) |
|---|---|
| 0–1 | ~100% |
| 2 | ~85–90% |
| 3 | ~70% |
| 4+ | Plan replacement |
Temperature Impact #
Use 20–25°C as the reference band. For every 10°C above 25°C, VRLA calendar life roughly halves. Add 10–20% Ah margin or reduce assumed runtime when the battery room runs hot. Confirm on OEM temperature derating curves.
Battery Chemistry Comparison #
| Chemistry | Typical life | Relative cost | Weight | Temperature tolerance |
|---|---|---|---|---|
| VRLA (AGM/Gel) | 3–5 years | Low | Heavy | Sensitive (20–25°C ideal) |
| Lithium-ion | 8–15 years | High | Light | Better high-temp tolerance |
| NiCd | 15–20 years | Very high | Heavy | Best for harsh environments |
Peukert Effect and C-Rate #
High discharge C-rate reduces usable Ah faster than nameplate arithmetic suggests — especially on older VRLA. Use vendor discharge tables at your cabinet temperature.
| C-rate (approx.) | Typical use | Planning note |
|---|---|---|
| 0.05–0.2C | Float / light discharge | Nameplate Ah closest to datasheet |
| 0.3–0.5C | UPS minutes-scale outage | Expect voltage sag earlier than "Wh / W" |
| >0.5C | Short high-power bursts | Requires vendor curves + inverter DC minimum headroom |
Scenario Table (Illustrative) #
| Load (kW) | PF | String V | Target runtime | Approx. Ah (DoD 0.8, η 0.90) |
|---|---|---|---|---|
| 2 | 0.8 | 48 | 30 min | ~29 Ah |
| 6 | 0.9 | 240 | 30 min | ~17 Ah |
| 18 | 0.95 | 192 | 15 min | ~33 Ah |
| 40 | 0.9 | 384 | 15 min | ~36 Ah |
| 120 | 0.95 | 480 | 30 min | ~174 Ah |
Always reconcile these screening numbers with manufacturer sizing software and local electrical codes.
DC Power Chain and Inverter Losses #
Runtime calculations must include UPS efficiency, battery cable drop, and end-of-discharge voltage. At high discharge rates, terminal voltage sags; the inverter may reach minimum DC input earlier than a simplistic Wh estimate predicts. When vendor curves are available, use constant-power load assumptions rather than flat efficiency guesses.
Common Sizing Pitfalls #
- Using nameplate capacity without derating for age or temperature.
- Mixing old and new batteries in the same string — resistance imbalance kills runtime.
- Ignoring power factor — runtime is bounded by both kW and kVA on the UPS frame.
- Poor airflow — heat kills VRLA quickly and accelerates lithium degradation.
- Treating spreadsheet Ah as exact — always verify with a load test.
Integration With Calculators #
Size Ah here, then continue through the UPS workflow:
- UPS Battery Calculator — quick Ah from kW and target minutes
- UPS Battery Calculator — string layout — series blocks and parallel strings for ordering
- UPS Runtime Calculator — verify backup minutes with Ah and strings entered
- kW to kVA Calculator — convert load kW to kVA with power factor
Browse UPS calculator hub for the full UPS tool set.
Related Articles #
- How to Calculate UPS Runtime
- UPS Battery Maintenance — maintenance schedules, impedance testing, and replacement triggers
- Lead Acid vs Lithium UPS Battery — chemistry comparison for UPS strings
- UPS Battery Maintenance — DoD, cycle life, impedance tests, and replace intervals
Next Steps #
- Run UPS Battery Calculator with your load kW and target minutes.
- Lay out series blocks and parallel strings in the UPS Battery Calculator (string layout).
- Cross-check backup minutes in the UPS Runtime Calculator at worst-case PF and end-of-life efficiency.
- For maintenance schedules and replacement triggers, see UPS Battery Maintenance.
How many Ah do I need for 30 minutes at 2 kW?
At 48 V with 0.8 DoD and 0.85 efficiency: Ah = (2000 × 0.5) / (48 × 0.8 × 0.85) ≈ 30.6 Ah before aging margin. Round up to the next commercial block size.
Does higher string voltage always reduce Ah?
Yes — for the same energy (Wh), higher voltage means fewer amp-hours. But higher voltage strings have more series cells, each a potential failure point. Match voltage to your UPS DC bus design.
Should I use kW or kVA for battery sizing?
Use the actual AC power the inverter must deliver — often bounded by both kW and kVA limits on the UPS frame. Low PF loads can hit kVA limits first.
What depth of discharge should I plan for?
VRLA UPS strings often plan 50–80% usable energy. Shallower DoD extends cycle life but requires more installed Ah. Align with your replacement policy and runtime contract.
Why does my UPS vendor software give a different Ah?
Vendors embed chemistry-specific discharge curves, temperature coefficients, and minimum cell voltages. Use this guide for directional planning, then finalize with OEM tools and stamped documentation.
Can I add battery capacity later?
Often yes, but mixing old and new jars in one string usually cuts effective life. Budget full-string replacement when expanding.
How does temperature affect UPS battery Ah sizing?
High ambient temperature accelerates VRLA aging and lowers usable capacity under load. Add 10–20% Ah margin when the battery room runs above 25°C. Confirm on OEM temperature derating curves.
Conclusion #
UPS battery sizing translates target runtime minutes into orderable Ah at a specific string voltage. Derate for age, temperature, and discharge rate; verify with vendor tools; then cross-check backup minutes in the UPS Runtime Calculator before procurement.