# UPS Battery Runtime Calculator: Backup Time from Load and Batteries

> UPS runtime is how long a battery bank can carry a load after the mains fails. A linear estimate multiplies battery voltage, Ah and the number of batteries to get stored energy, reduces it for usable depth of discharge, ageing and inverter efficiency, and divides by the load in watts. Real runtime at high discharge rates is shorter, so battery discharge tables replace it.

## 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

| Assumption | Default | Basis |
| --- | --- | --- |
| Inverter efficiency | 90% | Battery-to-output efficiency of a typical online UPS on battery; check the datasheet at your load |
| Usable depth of discharge | 80% | The share of capacity used before the UPS's low-battery cut-off |
| Ageing and temperature derating | 80% | Capacity late in the battery's service life; a common end-of-life planning figure |

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.

| Step | Calculation | Result |
| --- | --- | --- |
| Nameplate energy | 12 V × 100 Ah × 8 × 1 | 9,600 Wh |
| Usable depth of discharge | 9,600 × 80% | 7,680 Wh |
| Ageing and temperature | 7,680 × 80% | 6,144 Wh |
| Inverter efficiency | 6,144 × 90% | 5,530 Wh |
| Runtime | 5,530 ÷ 3,000 W | 1.84 h, **111 minutes** |

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.

## Frequently asked questions

### How do I calculate UPS backup time?

Multiply the battery block voltage by its Ah rating and by the number of batteries to get stored watt-hours. Reduce that for the usable depth of discharge and for ageing, multiply by the inverter efficiency, and divide by the load in watts. The answer is in hours. It is a linear estimate; at high discharge rates the real figure is lower.

### Why is my real backup time shorter than the calculation?

Usually for three reasons. Batteries deliver less than their Ah rating when discharged quickly, because the rating is quoted at a slow rate. Capacity falls as batteries age and in warm rooms. And the load is often higher than assumed. The battery maker's constant-power discharge table, read at your load per battery, gives the realistic figure.

### Should I enter the load in watts or VA?

In watts, because watts are what the batteries supply. A UPS is often sold by its VA rating, but the load it carries is limited by its watt rating as well. If you only know the load in VA, multiply it by the load's power factor to get watts.

### Why can I not just add batteries in series to get more backup?

The number of batteries in series is fixed by the UPS's DC bus voltage, so it is not free to change. Backup time is extended by adding parallel strings, each with the same number of batteries in series, or by choosing batteries with a larger Ah rating. The UPS's charger must also be able to recharge the larger bank in a reasonable time.

### Should the UPS run the building until the DG starts or for hours?

That is a design decision about the load. A UPS that only bridges the gap until the generator takes over needs minutes of backup. One expected to run a server room without a generator needs far more batteries, space, ventilation and cooling. Most commercial buildings use a UPS for the critical load and a DG set for the rest.

## Sources

- [IEC 62040-3](https://webstore.iec.ch/en/) — UPS: method of specifying the performance and test requirements
- [IEC 60896-21](https://webstore.iec.ch/en/) — Stationary lead-acid batteries, valve-regulated types: methods of test
- [IEC 62485-2](https://webstore.iec.ch/en/) — Safety requirements for stationary battery installations

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Source: https://hagerstone.com/calculators/ups-runtime-calculator