Battery Runtime Calculator

Estimate how long a battery, portable power station or UPS will run a load, using capacity, usable depth of discharge, inverter efficiency and an optional Peukert correction for lead-acid batteries.

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Ah
Wh
V
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W
h
Results will appear here once you enter your values.

The runtime formula, with a worked example

For a steady load the energy method is all you need: runtime (h) = battery Wh x usable depth of discharge x inverter efficiency / load W. Battery watt-hours are amp-hours times nominal voltage.

Example: a 100 Ah, 12 V LiFePO4 battery stores 100 x 12 = 1,200 Wh. At 90% usable depth of discharge that is 1,080 Wh. Running a 100 W AC load through a 90% efficient inverter gives 1,080 x 0.90 / 100 = 9.72 hours, or about 9 h 43 min. Run the same 100 W as a DC load (no inverter) and the answer rises to 10.8 hours.

Portable power stations usually quote capacity in Wh already (for example 1,024 Wh on a 51.2 V LiFePO4 pack). Their built-in inverters typically deliver 80-90% of stored energy at the AC outlets, so a 300 W load on a 1,024 Wh station at 85% efficiency lasts roughly 1,024 x 0.85 / 300 = 2.9 hours.

Peukert's law for lead-acid and UPS batteries

Lead-acid capacity is rated at a slow discharge, usually 20 hours (C/20). Pull current faster and you get fewer amp-hours out. Peukert's law models this: t = H x (C / (I x H))^k, where H is the rated hours, C the rated Ah, I the discharge current in amps and k the Peukert exponent. The calculator finds I from the load: I = W / (V x efficiency), then multiplies by your depth of discharge.

Example: a 100 Ah battery rated at 20 h, discharged at 10 A with k = 1.2, runs 20 x (100 / 200)^1.2 = 8.7 hours, not the 10 hours the simple Ah / A division suggests. A small 12 V 9 Ah UPS battery feeding a 60 W computer load through an 85% inverter draws about 5.9 A, over ten times its C/20 rate of 0.45 A, so Peukert cuts the linear estimate substantially.

Typical exponents: about 1.05 for lithium, 1.1-1.25 for AGM and gel, 1.2-1.4 for flooded. Use the value on the manufacturer's data sheet when one is given.

Choosing depth of discharge and efficiency

  • Lead-acid (AGM or flooded): plan on 50% depth of discharge. Deeper cycles are possible but shorten cycle life sharply.
  • LiFePO4: 80-100% is normal; the battery management system cuts off before damage.
  • NMC lithium-ion: about 80-90%.
  • Power stations: the advertised Wh is the pack rating; use 100% DoD and let the inverter efficiency (80-90%) account for losses.
  • Inverters: pure sine wave units run 85-94% at mid load but are less efficient at very light loads, and they draw an idle current of 10-30 W on larger units. Add that idle draw to your load when running small devices overnight.

Common mistakes

  • Using peak or surge watts. Runtime depends on average power. A refrigerator rated 150 W that cycles on about a third of the time averages near 50-60 W.
  • Mixing Ah at different voltages. 100 Ah at 12 V (1,200 Wh) is half the energy of 100 Ah at 24 V (2,400 Wh). Compare in watt-hours.
  • Ignoring temperature and age. Lead-acid loses roughly 20% of capacity near freezing, and every battery loses capacity as it ages. Size with a margin of 20-25%.
  • Applying Peukert to lithium as if it were lead-acid. Lithium exponents are close to 1, so the correction is small.

Frequently Asked Questions

Common questions about the Battery Runtime Calculator

A 12 V 100 Ah battery holds 1,200 Wh. With a LiFePO4 battery at 90% depth of discharge and a 90% efficient inverter, it runs a 100 W AC load about 9.7 hours. A lead-acid battery limited to 50% depth of discharge runs the same load about 5.4 hours before Peukert losses.

Sources & References

Batteries, charge controllers and inverters for off-grid systems

DOE guidance on battery depth of discharge, capacity and inverter selection for stand-alone systems.
→Source: U.S. Department of Energy

Battery capacity and Peukert exponent

Manufacturer explanation of Peukert's law, rated discharge time and typical exponents for lead-acid and lithium batteries.
→Source: Victron Energy

Peukert's law

Formula t = H (C / (I H))^k and worked examples of capacity loss at high discharge rates.
→Source: Wikipedia

Energy storage and batteries: SAND2013-5131 DOE/EPRI Electricity Storage Handbook

Technical reference on battery chemistries, depth of discharge and round-trip efficiency.
→Source: Sandia National Laboratories

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