UPS Battery Runtime Calculator: Backup Time from Load and Batteries

What it calculates

The calculator estimates how long a UPS battery bank will carry a given load after the mains fails, in minutes and hours. It also works the problem backwards: for the backup time you need, it gives the number of parallel battery strings required.

Along the way it shows the DC bus voltage of the bank, the nameplate and usable battery energy, and the current each string has to supply. That last figure matters because it tells you how far the simple linear estimate is likely to overstate the real runtime.

It is meant for checking a quoted UPS, comparing battery options and setting expectations before a UPS supplier or electrical engineer sizes the bank properly.

Inputs

Load on the UPS is the real power in watts that the UPS supplies during an outage. Measure it at the UPS if you can, or add up the nameplate ratings of the connected equipment. If you only have VA, multiply by the load's power factor.

Backup time you need drives the reverse calculation of strings.

Battery block voltage is the nominal voltage of one battery, usually 12 V for the sealed lead-acid batteries common in UPS banks.

Battery capacity is the Ah rating from the battery label or datasheet.

Batteries in series per string is set by the UPS's DC bus voltage, which its datasheet gives. Eight 12 V batteries make a 96 V bus, for example.

Parallel strings is the number of identical strings connected side by side.

The assumptions panel holds the inverter efficiency, the usable depth of discharge and the ageing and temperature derating.

Method

1. Stored energy (Wh) = block voltage × Ah × batteries in series × strings.
2. Usable energy (Wh) = stored energy × usable depth of discharge × derating.
3. Runtime (h) = usable energy × inverter efficiency ÷ load in watts. Multiply by 60 for minutes.
4. Strings needed = load × target hours ÷ (block voltage × Ah × batteries in series × depth of discharge × derating × efficiency), rounded up to a whole string.
5. DC bus voltage = block voltage × batteries in series.
6. Battery current per string = load ÷ efficiency ÷ DC bus voltage ÷ strings. Dividing it by the Ah rating gives the discharge rate as a multiple of capacity, written as C.

Assumptions

The derating is the assumption people most often leave out. A new battery bank may deliver close to its rating, but the bank has to give the backup you need near the end of its service life too, and lead-acid capacity falls faster in warm rooms. Sizing on a new battery means the backup time quietly shrinks year after year.

Limitations

• It is linear, so it ignores Peukert's effect. A battery delivers less energy when it is discharged quickly than when it is discharged slowly, and the Ah figure on the label is usually quoted at a slow rate (often 10 or 20 hours). At the discharge rates typical of a UPS, real runtime is shorter than this calculation. The calculator flags this when the current is above 0.1C. The battery maker's constant-power discharge table, read at the watts per battery and the end voltage of your UPS, replaces this estimate.
• It assumes a steady load. Real loads vary; size on the load you expect at the moment the mains fails, not the average over a day.
• It treats all strings as identical and healthy. One weak battery in a string limits the whole string.
• It does not check the charger. A larger bank takes longer to recharge, and the UPS charger rating limits how quickly backup time is restored after an outage.
• It does not cover lithium-ion. Lithium-ion batteries have different usable depth of discharge, efficiency and ageing behaviour; use the supplier's figures.

Worked example

A 3,000 W load on a UPS with a 96 V battery bank: one string of eight 12 V, 100 Ah batteries, with the default 90% efficiency, 80% usable depth of discharge and 80% derating.

For a target of 30 minutes, the strings needed are 3,000 × 0.5 h ÷ (12 × 100 × 8 × 80% × 80% × 90%), which is 0.27, rounded up to 1 string. The DC bus is 12 V × 8 = 96 V.

The battery current is 3,000 ÷ 90% ÷ 96 V, about 34.7 A per string, or 0.35C on a 100 Ah battery. That is several times faster than the rate a 100 Ah rating is normally quoted at, so the calculator shows its warning: expect the real runtime from the battery maker's discharge table to be noticeably less than 111 minutes.

Raise the target to 120 minutes and the calculation gives 1.09 strings, so 2 strings of eight batteries. On the linear method, two strings would run the load for about 221 minutes; halving the current per string also brings the discharge rate down, so the gap between the linear estimate and the discharge table narrows.

How engineers use it

A UPS designer starts from the critical load and the backup time the business needs, usually decided alongside the generator: minutes to bridge a DG start, or longer where there is no generator or the critical load must ride through a generator failure. The battery is then sized from the manufacturer's constant-power discharge data at the UPS's end-of-discharge voltage, with ageing and temperature allowances, rather than from Ah.

The engineer also checks what the battery room needs: floor loading, ventilation for any gas released during charging, temperature control, access for maintenance, and DC cabling and protection. Safety requirements for stationary battery installations are set out in IEC 62485-2. UPS performance itself is specified and tested to IEC 62040-3.

When a professional design must replace it

Use the calculator to check whether a quoted bank is in the right range and to compare battery options. Replace it with sizing by the UPS supplier or a qualified electrical engineer, using the battery maker's discharge tables, before batteries are ordered, whenever the backup time is critical to the business, and whenever the bank needs its own room or significant floor space. The engineer confirms the battery selection, the charger, ventilation and protection for the actual installation.