Battery Life Calculator — Runtime from Capacity, Load, Depth of Discharge and Peukert Exponent

Background.

How long a battery lasts is one division and three corrections. The division is capacity over load. The corrections are how much of the battery you are actually willing to use, what the electronics between the battery and the load throw away, and how much a battery derates when you discharge it quickly. Skip all three and you get a number that is right in principle and optimistic in practice, sometimes by half.

The base calculation is simple enough to do in your head. A 12 V battery rated 100 ampere-hours holds 100 × 12 = 1200 watt-hours. A 100 W load draws 100 ÷ 12 = 8.33 amps from it. Dividing 100 ampere-hours by 8.33 amps gives 12 hours, and dividing 1200 watt-hours by 100 watts gives the same 12 hours, which is a useful check that the two routes agree. Everything else on this page moves that 12 hours downward for a specific, nameable reason.

Depth of discharge is the first. Every battery has a rating and a rather different figure for how much of that rating the manufacturer wants you to take out on a normal cycle, because discharging deeply costs cycle life. This page defaults to 100 percent, which is the full theoretical figure, and it deliberately does not fill in a recommended value for you. That number belongs to your battery's datasheet, not to a calculator, and the trade-off between depth and longevity is the manufacturer's to specify.

System efficiency is the second. If the load runs straight off the battery there is nothing to lose. Put an inverter in the path and it takes its cut: the battery has to supply the load's power divided by the inverter's efficiency, so the current goes up and the runtime comes down in proportion. The calculator reports the battery current separately from the load's power so you can see the difference the converter makes.

The Peukert exponent is the third, and it is the one most calculators leave out. Lead-acid capacity is not a fixed quantity: the faster you take the charge out, the less of it you get. Peukert's law describes that with a single exponent, and this page implements it in the form Victron Energy publishes in its battery-monitor documentation. An exponent of 1.00 means an ideal battery whose capacity does not care about the discharge rate — Victron's own wording is that such a battery "has a fixed capacity regardless of the size of the discharge current". Victron defaults its monitors to 1.25 as an average for lead-acid. This page defaults to 1.00 instead, because 1.25 is an average someone else measured and your battery has its own number, but the 1.25 figure is quoted with attribution both in the field hint and beside the result so you know where to start looking.

There is a neat property worth knowing about the Peukert form: at exactly the current the capacity was rated at, every exponent gives the same answer. A 100 Ah battery rated over 20 hours is being discharged at 5 A at that rating, and at 5 A the calculator returns 20 hours whether the exponent is 1.00 or 1.6. The derating only appears when you discharge faster than the rating assumed, which is precisely when it matters.

The result is an estimate for planning, not a guarantee, and the page says so beside the number rather than in a footnote. It assumes a constant load, so use an average rather than a peak. It does not model self-discharge, ageing, cold weather or the exact point at which a low-voltage cut-off decides to disconnect — and inverters and battery-management systems trip on voltage, which often happens earlier than an ampere-hour count suggests. Size in some spare capacity for anything that matters.

What is battery life calculator?

Battery life in this sense means runtime: the time a charged battery can supply a given load before it reaches the discharge limit you set. It is a different question from cycle life, which is how many charge-discharge cycles a battery survives before its capacity falls below a threshold, and different again from calendar life.

Runtime is capacity divided by load, once both are expressed in compatible units. Capacity comes in two flavours — charge in ampere-hours and energy in watt-hours — linked by the nominal voltage, so a 100 Ah 12 V battery is also a 1200 Wh battery. A load comes in watts or in amps, linked by the same voltage. Dividing ampere-hours by amps and dividing watt-hours by watts give the same answer, which is why either pair of units works.

Three modifiers stand between the ideal division and reality. Depth of discharge sets what fraction of the rating is in play. System efficiency accounts for conversion losses between the battery and the load, raising the current the battery has to supply. And the Peukert exponent captures the fact that a battery's effective capacity falls as the discharge current rises — pronounced in lead-acid, much weaker in lithium chemistries.

The C-rate is a convenient way to describe how hard a battery is being worked: it is the discharge current divided by the rated capacity in ampere-hours. A 100 Ah battery at 5 A is at 0.05 C, an overnight trickle. The same battery at 100 A is at 1 C, emptying its rating in about an hour, and that is the regime where rate effects, heating and voltage sag all become significant.

How to use this calculator.

1. 01Enter the battery's rated capacity and choose whether that figure is in mAh, Ah, Wh or kWh.
2. 02Enter its nominal voltage. This is needed whichever capacity unit you used, because it links charge to energy and converts a wattage load into a current.
3. 03Enter the load and choose watts, amps or milliamps. Use the average load over the period you care about, not the peak.
4. 04Set the depth of discharge to whatever your battery's datasheet supports, or leave it at 100 % for the theoretical maximum.
5. 05Set the system efficiency: 100 % for a load wired straight to the battery, lower for an inverter or converter in between.
6. 06Set the Peukert exponent from your battery's datasheet. Leave it at 1.00 for the ideal, no-derating case; lead-acid batteries at fast discharges need more.
7. 07If the exponent is above 1, check the rated discharge time — 20 hours for a C20 rating. It has no effect at an exponent of 1.00.
8. 08Read the runtime, then add margin. Nothing on this page models cold weather, ageing or where a low-voltage cut-off will actually trip.

The formula.

Start by putting the capacity and the load into compatible units. The nominal voltage is what links them. Title 49 of the US Code of Federal Regulations, section 171.8, defines the watt-hour rating of a lithium ion battery as the rated capacity in ampere-hours multiplied by the nominal voltage, which gives Wh = Ah × V and, inverted, Ah = Wh ÷ V. A load given in watts becomes a current through OpenStax University Physics Volume 2, section 9.5, Equation 9.12, "P = IV", so I = P ÷ V; a load given in amps is already a current and its power is I × V.

Anything between the battery and the load has to be paid for. If the conversion chain is η efficient, the battery must supply I_battery = I_load ÷ η. The calculator reports both figures, so a 100 W load behind an 85 percent efficient inverter shows a load power of 100 W and a battery current about 18 percent higher than the naive figure.

The discharge itself uses Peukert's law. Victron Energy's SmartShunt manual states it as "Cp = In x t" — Peukert's capacity equals the current raised to the exponent, multiplied by the time. Pinning that constant from the battery's own rating makes it usable: a battery rated C ampere-hours over H hours is being discharged at C ÷ H amps at that rating, so Cp = (C ÷ H)ⁿ × H. Dividing by the actual current raised to the same exponent gives the runtime form used here, t = H × (C ÷ (I × H))ⁿ.

Two properties of that expression are worth checking, and both are tests on this calculator. First, at n = 1 it collapses exactly to t = C ÷ I, the ideal battery — which is how the same manual describes it: "An ideal (theoretical) battery has a Peukert exponent of 1.00 and has a fixed capacity regardless of the size of the discharge current." Second, when the discharge current equals the rated current C ÷ H, the bracket is exactly 1, and 1 raised to any power is 1, so every exponent returns exactly H hours. The derating exists only away from the rated point, growing as the discharge gets faster.

Depth of discharge scales the time linearly. At a constant current the fraction of capacity removed is proportional to elapsed time, so stopping at 50 percent takes exactly half as long as running to empty. That is why the depth of discharge multiplies the runtime rather than entering the Peukert expression.

Working the default case through: a 12 V, 100 Ah battery holds 1200 Wh. A 100 W load draws 100 ÷ 12 = 8.3333333333 A, and at 100 percent efficiency that is also the battery current — a rate of 0.0833333333 C. With the exponent at 1.00 the runtime is 100 ÷ 8.3333333333 = 12 hours exactly, which the energy route confirms at 1200 ÷ 100 = 12 hours. Raise the exponent to Victron's lead-acid average of 1.25 and the same load runs 20 × (100 ÷ (8.3333333333 × 20))^1.25 = 20 × 0.6^1.25 = 10.5613408415 hours, so the Peukert correction costs about 1 hour 26 minutes. Halve the depth of discharge and the ideal figure becomes 6 hours; drop the efficiency to 85 percent and it becomes 10.2 hours; do both and it is 5.4 hours.

No chemistry-specific constant is baked into this page. The Peukert exponent and the depth of discharge are editable inputs defaulting to their neutral values, and Victron's 1.25 appears only as an attributed starting point, never as an assumption the result rests on.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Victron Energy B.V., SmartShunt product manual, section "Battery capacity and Peukert exponent". Primary manufacturer documentation for the Peukert form implemented here. Retrieved text: the formula "Cp = In x t"; "An ideal (theoretical) battery has a Peukert exponent of 1.00 and has a fixed capacity regardless of the size of the discharge current"; and "The default setting in the battery monitor for the Peukert exponent is 1.25. This is an acceptable average value for most lead acid batteries." The 1.25 figure is quoted with attribution and is NOT this page's default, which is 1.00. Access: open. Retrieved 2026-07-29.
2. [2]US Government Publishing Office / US Department of Transportation, Code of Federal Regulations, 2024 edition, Title 49 § 171.8 (definitions). Statutory source for the charge-to-energy conversion: "Watt-hour (Wh) means a unit of energy equivalent to one watt (1 W) of work acting for one hour (1 h) of time. The Watt-hour rating of a lithium ion cell or battery is determined by multiplying the rated capacity of a cell or battery in ampere-hours, by its nominal voltage." Access: open. Retrieved 2026-07-29.
3. [3]OpenStax (Rice University), University Physics Volume 2, §9.5 "Electrical Energy and Power". Primary source for turning a wattage load into a current and for the energy-time relation. Equation 9.12 gives "P = IV"; the section states "E = Pt" for power delivered at a constant rate and that "The energy unit on electric bills is the kilowatt-hour (kW·h), consistent with the relationship E = Pt", with "1 kW·h = 3.6 × 10⁶ J". Access: open. Retrieved 2026-07-29.
4. [4]W. Peukert, "Über die Abhängigkeit der Kapazität von der Entladestromstärke bei Bleiakkumulatoren", Elektrotechnische Zeitschrift, volume 20 (1897), pages 20–21. The original statement of the law this page's rate correction implements. ACCESS: PRINT — a 129-year-old German print journal, cited bibliographically for attribution only and deliberately shipped without a URL rather than with a link that would look dead. No value on this page is taken from it; the working form comes from the Victron documentation above, which was retrieved and verified.
5. [5]NIST, Special Publication 811, "Guide for the Use of the International System of Units (SI)", 2008 edition (DOI 10.6028/NIST.SP.811e2008). Used only for unit symbols and typography — A, V, W, Wh, h — not for any battery relation. NIST's own landing page notes that SP 811 "has not yet been updated to reflect the changes in the SI that came into effect on May 20, 2019"; none of those changes affect the symbols used here. Access: open. Retrieved 2026-07-29.