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UPS battery runtime

Enter load, inverter efficiency and battery bank to see how long the UPS holds up and how many Ah you need for the target backup time, with temperature and aging included.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Preliminary estimate
Load
Battery bank (lead-acid)

Bank voltage = number of 12 V batteries × 12 (6 cells of 2 V each). A string of sixteen 12 V batteries is 192 V and 96 cells.

Conditions and target
—Estimated run time
—

Run time versus load

Time to end voltage with the bank entered, new and at end of life (with the aging factor). The dot is the current load.

Tap the chart to see the values.

Required capacity per string versus run time

Ah of each battery for the current load, with temperature, end voltage and aging. The dashed line is the chosen battery.

Tap the chart to see the values.

The report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

P_battery = P_output ÷ η_inverter; I = P_battery ÷ (n_cells × V_avg), V_avg = (2.10 + V_end) ÷ 2 per cell
Peukert: t = H × [C_eff ÷ (I_string × H)]^k, with H = 20 h (C20) or 10 h (C10); C_eff = C × f_T × f_V ÷ f_aging
Temperature: f_T = 1 + λ (T − 25 °C), λ = 0.01/°C up to 1 h and 0.006/°C above 3 h; f_T ≤ 1
End voltage: f_V = 1 + 0.8 × (1.75 − V_end), limited to 0.85…1.12; required capacity: C = I × H × (t ÷ H)^(1/k) × f_aging ÷ (f_T × f_V)

Assumptions and limits

  • Lead-acid bank (VRLA or vented) at 2 V per cell, identical strings sharing current equally, and constant output power.
  • The end-voltage factor is a linear approximation of typical VRLA data-sheet curves; average discharge voltage is the mean of 2.10 V and the end voltage.
  • Peukert is reliable from about 30 min to 20 h. For discharges of a few minutes, proper sizing uses the maker’s constant-power tables (IEEE 1184 and IEEE 485).
  • Aging factor 1.25 (end of life at 80% capacity), per IEEE 485 and IEEE 1188. No design margin for load growth is included.

Standards and technical documents

  • IEEE 485: Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications
  • IEEE 1184: Guide for Batteries for Uninterruptible Power Supply Systems
  • IEEE 1188: Recommended Practice for Maintenance, Testing, and Replacement of Valve-Regulated Lead-Acid (VRLA) Batteries for Stationary Applications
  • IEC 60896-11 / IEC 60896-21: Stationary lead-acid batteries — vented types and valve-regulated types, methods of test
  • IEC 62040-3: Uninterruptible power systems (UPS) — Method of specifying the performance and test requirements
  • Linden, D.; Reddy, T. B.: Handbook of Batteries, McGraw-Hill

U.S. regulations

  • NFPA 70 (NEC), Article 480: storage batteries; Article 700/701/708 for emergency, standby and critical power
  • NFPA 111: Standard on Stored Electrical Energy Emergency and Standby Power Systems
  • NFPA 70E, Article 320: safety requirements related to batteries and battery rooms
  • OSHA 29 CFR 1910.305(j)(7) and 1910.178(g): storage batteries and charging areas

Frequently asked questions

How long will an 8 kW UPS run on sixteen 100 Ah batteries?

With 94% efficiency and a Peukert exponent of 1.15, about 93 minutes with new batteries and 72 minutes at end of life, at 77 °F and 1.75 V per cell.

Why not just divide battery Wh by the load?

Because Ah capacity is rated over 20 h. In a 1 h discharge, a 100 Ah C20 battery delivers only about 60 to 70 Ah. The Peukert exponent corrects for that.

How does cold affect runtime?

At 59 °F (15 °C), capacity drops about 10% on 1 h discharges. IEEE 485 sizes for the lowest expected room temperature.

Why use an aging factor of 1.25?

Batteries are replaced at 80% of rated capacity. Sizing with 1.25 keeps the required runtime until the last day before replacement.