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Battery Runtime Calculator

Work out how long a battery will actually run a load, with Peukert losses, depth of discharge and temperature applied — not just capacity divided by current.

How to use this calculator

  1. 1Enter the whole bank’s capacity, not one battery, unless you are sizing a single battery.
  2. 2Check the hour rate the capacity was quoted at. A 100 Ah battery at the 100-hour rate is a smaller battery than a 100 Ah one at the 20-hour rate.
  3. 3Enter the load in watts at the socket if it runs through an inverter — the calculator adds the conversion loss for you.
  4. 4Read the runtime-against-load table rather than only the headline. It shows where Peukert starts to hurt, which is the point at which lead-acid stops being the right chemistry.

How the calculation works

Battery amps = load watts ÷ inverter efficiency ÷ system voltage Effective capacity = nameplate Ah x temperature factor Peukert: t = H x (C ÷ (I x H))^k Capacity delivered = t x I Usable runtime = t x depth of discharge
H
The hour rate the capacity was measured at, almost always 20. A 100 Ah battery at the 20-hour rate means 5 A for 20 hours
C
Rated capacity in amp-hours, after any temperature correction
I
Actual discharge current drawn from the battery, including inverter losses for AC loads
k
The Peukert exponent: about 1.25 for flooded lead-acid, 1.15 for AGM, 1.03 for LiFePO4. At k = 1 there is no penalty at all

Peukert’s law describes a diffusion limit, not a loss. At high current the acid near the plate surface is consumed faster than fresh acid can diffuse in, so the reaction stops while material remains unreacted. Rest the battery and some capacity returns — which is why a lead-acid battery that seemed flat will run a small load again an hour later.

The exponent is a property of the specific battery, not just its chemistry. Manufacturers who publish capacity at several discharge rates make it calculable; those who publish only a 20-hour figure leave you with the chemistry default.

Beware capacity quoted at a 100-hour rate, common on some marine and leisure batteries. It produces a larger headline number for the same physical battery, and comparing a 100-hour figure against a 20-hour one overstates it by roughly 15–20%.

Worked example

A 300 W load through an inverter, on a 100 Ah flooded lead-acid battery

  1. 1.The inverter turns 300 W at the socket into 333 W from the battery at 90% efficiency.
  2. 2.At 12 V that is 27.8 A of discharge current.
  3. 3.Temperature is the 77°F rating point, so effective capacity stays 100 Ah.
  4. 4.Peukert: t = 20 x (100 ÷ (27.8 x 20))^1.25 = 20 x (0.180)^1.25 = 20 x 0.1173 = 2.35 hours to completely flat.
  5. 5.Capacity actually delivered: 2.35 x 27.8 = 65.2 Ah of the 100 — a 35% Peukert loss.
  6. 6.At the 50% depth of discharge limit, usable runtime is 1.17 hours.
  7. 7.The simple answer of 100 x 50% ÷ 27.8 = 1.80 hours overstates it by more than half an hour.

Result: 1.2 hours

What Peukert actually described

In 1897 the German scientist Wilhelm Peukert published an observation about lead-acid batteries that still governs how they are specified: the faster you discharge one, the less total capacity it gives you. Not less power, less *energy*. A battery that delivers 100 amp-hours over twenty hours might deliver only sixty-five over two.

The mechanism is diffusion. In a lead-acid cell, the reaction happens at the surface of the plates and consumes sulphuric acid from the electrolyte immediately adjacent to them. At a gentle discharge, fresh acid diffuses in from the bulk electrolyte as fast as it is used. At a heavy discharge it cannot keep up: the acid at the plate surface is depleted, cell voltage collapses to the cutoff, and the discharge ends while a substantial amount of active material sits unreacted deeper in the plate.

This is why the energy is not really lost. Rest a lead-acid battery that has just gone flat under heavy load and acid diffuses back into the depleted zone; an hour later it will run a small load again. Anyone who has restarted a car after waiting a few minutes has used this directly.

The exponent k captures how badly a particular battery suffers. At k = 1 there is no penalty at all. Flooded lead-acid sits around 1.25, AGM around 1.15 because its glass-mat construction holds electrolyte closer to the plates, and lithium iron phosphate near 1.03 — close enough to 1 that the effect is usually ignored entirely.

Why this decides the chemistry for inverter loads

Peukert is the reason lead-acid and lithium behave so differently under an inverter, and it compounds with the depth-of-discharge difference to produce a gap far wider than the nameplate suggests.

Take a 100 amp-hour battery and a 1,000 watt load — a microwave, a kettle, a small induction hob. Through a 90% inverter at 12 volts that is about 93 amps of discharge current, or nearly a 1C rate.

Flooded lead-acid at k = 1.25 delivers perhaps 45 of its 100 amp-hours at that current, and only half of that is usable before the 50% limit. Real runtime: around fifteen minutes. Lithium iron phosphate at k = 1.03 delivers about 95 amp-hours, 80% of which is usable, giving around fifty minutes — more than three times as long from the same nameplate.

This is why van and RV builders moved to lithium far faster than the price difference alone would explain. It is not simply that lithium is better; it is that the specific loads modern off-grid systems run — inverters driving kitchen appliances — are exactly the loads Peukert punishes hardest.

The other two deductions

Peukert is the one people have not heard of. Two more familiar ones apply at the same time, and all three multiply.

  • Depth of discharge — lead-acid cycle life collapses below about 50% state of charge, so half the nameplate is off limits if you want the rated cycles. LiFePO4 tolerates 80% or more with cycle lives measured in thousands.
  • Temperature — capacity is rated at 77°F and lead-acid loses roughly 0.6% per degree below it — a fifth of the battery at 40°F. This applies before Peukert, compounding with it.
  • Age — not modelled here, but real. A lead-acid battery at the end of its rated life delivers perhaps 80% of its original capacity, and the decline accelerates.
  • Inverter overhead — the conversion loss is obvious, but the idle draw is not. A large inverter switched on with nothing plugged in can consume 20 to 40 watts continuously, which on a small bank is a significant background load.

What the C-rate tells you

Discharge current is often expressed as a C-rate: the current as a fraction of the battery’s capacity number. A 100 amp-hour battery discharged at 20 amps is at C/5; at 100 amps it is at 1C.

The convention matters because battery specifications are written in it. Capacity is quoted at C/20 for most deep-cycle batteries — the twenty-hour rate — and a battery’s continuous discharge rating, the maximum its construction and its battery management system will allow, is usually given as a C-rate too.

Rough guidance: lead-acid is comfortable up to about C/5 and increasingly unhappy beyond it, with Peukert losses climbing and plate stress rising. LiFePO4 typically handles 1C continuously and many cells accept more, though the BMS will enforce whatever the manufacturer specified by simply disconnecting when exceeded — an abrupt failure mode that surprises people the first time it happens mid-cook.

One thing to watch when comparing batteries: a capacity quoted at the 100-hour rate rather than the 20-hour rate produces a bigger number for the same physical battery, typically by 15 to 20%. Some leisure and marine batteries are specified this way, and comparing across the two conventions without noticing is a straightforward way to buy less battery than you thought.

Measuring instead of calculating

Every figure on this page is a model, and there is a piece of hardware that replaces it with a measurement: a shunt-based battery monitor.

A shunt is a precision resistor placed in the battery’s negative cable, through which every amp in and out of the bank must pass. The monitor measures the tiny voltage across it and integrates current over time, giving a true count of amp-hours consumed and returned. Good ones apply a Peukert correction internally, and learn the bank’s actual capacity as it ages.

This matters more than any calculation, because it converts the whole question from estimation to observation. It tells you what the fridge really costs per day, whether the inverter is drawing more at idle than you assumed, and how much capacity the bank has lost over three years — none of which any model can know about your specific system.

Voltage alone is a poor substitute. A lead-acid battery’s resting voltage does indicate state of charge reasonably well, but only after several hours at rest with no load or charge, which is almost never the case in a working system. Lithium iron phosphate is worse still: its discharge curve is so flat that voltage says almost nothing about state of charge across the middle 80% of its range. On an LFP system, a shunt monitor is not a refinement, it is the only way to know.

What this assumes, and where it stops

Assumptions

  • Peukert’s law is applied in its standard form, t = H x (C ÷ (I x H))^k, at constant current.
  • The temperature factor is applied to nameplate capacity before the Peukert calculation.
  • Depth of discharge is applied to the resulting runtime as a flat proportion.
  • The load is constant. Real loads cycle, and an intermittent load of the same average current will run longer than this predicts, because the battery recovers between draws.
  • The battery is new and at its rated capacity. Ageing is not modelled.

Limitations

  • Peukert’s law is an empirical fit, not physics. It describes lead-acid behaviour well over ordinary discharge rates and less well at extremes.
  • A constant-current model does not represent an intermittent load well. A fridge that cycles gets partial recovery between compressor runs, so real runtime exceeds this figure.
  • The Peukert exponent is a property of the specific battery. Chemistry defaults here are typical, and a datasheet giving capacity at two discharge rates lets you calculate the real one.
  • Inverter idle consumption is not modelled separately and can be 20 to 40 W continuously on a large unit.
  • Battery management systems impose their own continuous and peak discharge limits, and will disconnect rather than degrade gracefully when those are exceeded.

Common questions

How long will a 100Ah battery run a 300W load?

On LiFePO4, about 2.6 hours to the 80% depth limit. On flooded lead-acid, about 1.2 hours to the 50% limit — less than half, from the same nameplate. The gap comes from depth of discharge and from Peukert losses, which cost lead-acid roughly a third of its capacity at that discharge rate.

What is Peukert’s law?

The observation that a lead-acid battery delivers less total capacity the faster it is discharged, because acid cannot diffuse into the plates quickly enough to sustain a heavy reaction. It is expressed as t = H × (C ÷ (I × H))^k, where k is around 1.25 for flooded lead-acid and near 1.0 for lithium iron phosphate, which barely suffers from it.

Why does my battery not last as long as the simple calculation says?

Three reasons compound. Depth of discharge means only half a lead-acid battery is usable. Peukert losses remove more capacity the harder you draw. And temperature costs about 0.6% per degree below 77°F. Together these routinely make real runtime half of what capacity divided by current suggests.

Is a 100Ah lithium battery really equal to 200Ah of lead-acid?

For most real loads, yes or better. Lithium gives 80% usable against 50%, loses almost nothing to Peukert where lead-acid loses 20 to 40% at inverter-sized currents, and holds capacity better in the cold. At heavy loads the effective ratio can exceed three to one, which is why the price comparison per nameplate amp-hour is misleading.

How do I know my battery’s Peukert exponent?

From a datasheet that gives capacity at two different discharge rates — the exponent follows from the ratio. If only the 20-hour figure is published, use the chemistry default: about 1.25 flooded, 1.15 AGM, 1.03 LiFePO4. Many shunt-based battery monitors let you enter it and apply the correction in real time.

Sources

Formula and content last reviewed on .

Results are estimates for information only, not professional advice.

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