UPS & Battery Backup Runtime Calculator

A UPS or a battery backup has one job in a power cut, and the question that matters is how long it can keep doing it. Enter the load in watts and the batteries as their labels describe them to get the runtime, the share of rated capacity available at that load, and the energy that reaches your equipment. A table repeats the estimate from a quarter of your load to twice it.

The usual shortcut divides watt-hours by watts, perhaps allowing for inverter losses. For a lead-acid UPS that overstates the runtime badly, because a battery drained in minutes gives up only part of the capacity printed on it. At the default settings the shortcut gives 35 minutes where this page gives 14. The difference is Peukert's law.

How the estimate works

The calculation runs in three steps. First comes the battery energy: the voltage times the amp-hours of each battery, times the number of batteries, or a watt-hour figure entered directly. Wiring makes no difference to the total. Two 12 V 9 Ah batteries hold 216 Wh whether they are connected in series or in parallel.

Second is the power the batteries must supply. The inverter loses some energy turning battery power into mains power, so the batteries supply more than the equipment uses:

P = load ÷ efficiency

Third is the correction for discharge rate. A lead-acid battery's amp-hour rating holds only at the current that would empty it in its rated time, usually 20 hours. Drain it faster and less of that capacity is available:

share = (E ÷ (P × H))^{k − 1}

runtime = depth × share × E ÷ P

Here E is the battery energy in watt-hours, H the rated discharge time in hours, k the Peukert exponent and depth the share of capacity you allow the battery to use. The ratio E ÷ (P × H) equals the rated current divided by the actual current, so the battery voltage cancels out and only energy and power matter. When the load is light enough for the ratio to reach 1, the share stops at 100 percent rather than crediting the battery with more than its rating.

A worked example

Take the defaults: two 12 V 9 Ah lead-acid batteries running a 300 W load through an inverter that is 80 percent efficient. The batteries hold 2 × 12 × 9 = 216 Wh and must supply 300 ÷ 0.8 = 375 W. Over the 20-hour rating that rate of draw would need 7,500 Wh, so the ratio is 216 ÷ 7,500 = 0.0288. With the lead-acid exponent of 1.25 the share is 0.0288^0.25 = 0.412, or 41 percent. The runtime is 0.412 × 216 ÷ 375 = 0.237 hours, which is 14 minutes, and 71.19 Wh reaches the equipment.

Dividing 216 Wh by 300 W gives 43 minutes, and allowing for the inverter still gives 35. The gap comes from the current: at 375 W the batteries supply nearly 35 times the current their 20-hour rating assumes. Halve the load to 150 W and the estimate rises to 34 minutes. That is 2.38 times as long rather than twice, because 2 raised to the power 1.25 is 2.38.

Peukert's law

In 1897 Wilhelm Peukert published an empirical rule in the Elektrotechnische Zeitschrift describing how the capacity of lead-acid batteries falls as the discharge current rises. Written with a battery's rated capacity C over its rated time H, it gives the time to empty at a current I:

t = H × (C ÷ (I × H))^k

An ideal battery would have an exponent of exactly 1. Real lead-acid batteries sit above it. Victron Energy, whose battery monitors apply the correction, sets 1.25 as the default and calls it "an acceptable average value for most lead acid batteries". Its example is a battery rated at 100 Ah over 20 hours, which "may only give C2 = 56Ah" when emptied in two hours. Its manuals tell owners whose datasheet gives no exponent to set 1.25 for lead-acid and 1.01 for lithium, and those are the two presets here.

The rule is a fit to measurements, not a law of physics. Victron calls the exponent "no more than a rough approximation of reality". A 2006 review in the Journal of Power Sources by Dennis Doerffel and Suleiman Abu Sharkh found that it predicts remaining capacity accurately only when the current and the temperature stay constant. A UPS carrying steady equipment indoors comes close to those conditions. A load that cycles on and off, or a cold room, does not.

From Planté's cell to the UPS

The battery in most UPS units descends from the lead-acid cell that Gaston Planté designed in 1859. In 1860 he presented a series of nine connected cells to the French Academy of Sciences. UPS batteries such as CSB's HR1234W are sealed and valve-regulated, with the acid held in an absorbent glass mat, but the chemistry is the same.

Uninterruptible supplies came much later, and they began as machines. Fuji Electric's history of its own UPS work records a prototype completed in 1954 that stored energy in a flywheel, a heavy disk spinning at high speed. In 1966 the company delivered a 250 kVA unit to Nakayama Racecourse to supply the totalisator that calculated betting odds. In 1969 it developed a 200 kVA constant-voltage, constant-frequency supply built around a thyristor inverter, delivered to Fujitsu's Kawasaki plant to power computers.

Finding your numbers

Battery labels give the voltage and the amp-hours, usually rated over 20 hours. Yuasa's NP7-12, for instance, is rated at 7 Ah over 20 hours to 1.75 V per cell. Some batteries are rated in watts instead. CSB rates its HR1234W, which it designs for high-rate UPS use, at 34.3 W per cell for 15 minutes. If your battery or power station lists watt-hours, switch the capacity entry to watt-hours.

Read the load in watts from the UPS display or a plug-in power meter. A UPS carries two ratings, volt-amperes for apparent power and watts for real power. Schneider Electric's White Paper 17 puts it plainly: "Battery run time is dictated by the watt load on the UPS." Real power is the VA figure multiplied by the power factor, so multiply by the power factor if VA is all you have. Enter the same wattage in the electricity cost calculator to see what the equipment costs to run from the mains.

The 80 percent efficiency default follows advice from the battery maker EnerSys to assume 0.80 when the real figure is unknown and the UPS carries at least 40 percent of its rated load. Your UPS datasheet may give a better number.

Depth of discharge is the share of capacity you are willing to use. A UPS runs its batteries down to its own cutoff, so the default is 100 percent. For a battery bank you want to last, Victron's monitors default to a 50 percent discharge floor for lead-acid and recommend a lower one for lithium, so enter 50 here for lead-acid. If your datasheet lists capacity at two discharge rates, you can work out your own exponent from the times and currents and enter it as a custom value:

k = log(t₂ ÷ t₁) ÷ log(I₁ ÷ I₂)

How far to trust the estimate

The estimate is a starting point, not a guarantee. Yuasa lists its NP7-12 at 150.9 W for 10 minutes to 9.6 V at 20 °C. Entered here as one 12 V 7 Ah lead-acid battery at 150.9 W with 100 percent efficiency, the calculator gives 14 minutes. A custom exponent of 1.34 brings it to Yuasa's 10. Victron warns of exactly this: "In case of very high currents, the battery will give even less capacity than predicted by a fixed exponent." UPS runtimes are measured in minutes, which means very high currents, so treat short results as optimistic and use an exponent from your own datasheet when you can.

Temperature and age push in the same direction. EnerSys advises extra headroom where batteries get near or below freezing, and more for ageing. Fluke notes that most manufacturers recommend replacing a battery once its capacity falls below 80 percent of its rating. Yuasa and CSB both quote a design life of up to five years for these batteries, so to see roughly what an older battery has left, enter 80 percent of its rated amp-hours.

Past a year the calculator stops counting and says so. By then self-discharge, which Yuasa puts at about 3 percent a month at 20 °C, matters more than the load.

Runtimes here are estimates from a simplified battery model, not a figure from any battery or UPS maker. Test the real runtime before relying on a UPS for medical, safety or other critical equipment. See the site disclaimer.

Frequently asked questions

How long will a UPS run on battery?

It depends mostly on the load. Two 12 V 9 Ah lead-acid batteries running 300 W through an inverter that is 80 percent efficient last about 14 minutes. At 150 W the same batteries last about 34 minutes, more than twice as long, because a lead-acid battery gives up more of its capacity when it is drained slowly. Enter your own load and the figures on your battery label to see yours.

Why is the runtime shorter than watt-hours divided by watts?

Because a lead-acid battery's amp-hour rating assumes a slow 20-hour discharge. Two 12 V 9 Ah batteries hold 216 Wh, and 216 × 0.8 ÷ 300 W suggests 35 minutes. At 300 W, though, they supply nearly 35 times the current their rating assumes, and Peukert's law with an exponent of 1.25 leaves 41 percent of the rated capacity, so the estimate is 14 minutes.

Does doubling the batteries double the runtime?

For lead-acid batteries at UPS loads it does better than double. Each battery then supplies half the current and gives up more of its rated capacity, so four 12 V 9 Ah batteries run a 300 W load for about 34 minutes against 14 minutes for two, 2.38 times as long. With lithium batteries, whose exponent is close to 1, the gain is almost exactly double.

Should I enter VA or watts?

Watts. A UPS is rated in volt-amperes, the apparent power, and in watts, the real power. Schneider Electric's White Paper 17 explains that battery run time is dictated by the watt load, and that real power is the VA figure multiplied by the power factor. If you only know the VA your equipment draws, multiply it by its power factor; the paper cites a PC Magazine study that found 0.65 for typical desktop computers.

What Peukert exponent should I use?

The one on your battery's datasheet, if it gives one. Otherwise Victron Energy's battery monitor manuals advise 1.25 for lead-acid and 1.01 for lithium, the two presets here. If the datasheet lists capacity at two discharge rates, you can work it out: divide the logarithm of the ratio of the two discharge times by the logarithm of the inverse ratio of the two currents, and enter the result as a custom exponent.

Sources

1. Battery capacity and Peukert exponent (SmartShunt manual), Victron Energy
2. All features and settings (SmartShunt manual), Victron Energy
3. Yuasa NP7-12 Technical Data Sheet, Yuasa, via RS Components, 2026
4. HR1234W Datasheet, CSB Battery
5. Runtime and Right Sizing a UPS, EnerSys
6. Gaston Planté, Engineering and Technology History Wiki
7. History of Uninterruptible Power Supplies (UPS), Part I, Fuji Electric