# Lithium battery math, better than you may think

There’s a lot of talk about installing lithium batteries in boats, but the enthusiasm often comes to a crashing halt when boat owner hears the cost. I’ve just installed a Mastervolt lithium system in *Have Another Day* and I’m over the price shock. But as I work to understand the results of my upgrade I’m amazed by the benefits I hadn’t anticipated. Follow along with my math and see if you reach the same conclusions I do about the benefits of upgrading to a lithium house bank.

Deep cycle batteries are typically sold based on their voltage (v) and capacity measured in amp hours (Ah). For the sake of this article I’m going to compare an inexpensive flooded lead acid (FLA) battery and one of the most popular drop-in lithium iron phosphate (LiFePO4) batteries. I’ve selected a 100 Ah Duracell Group 31 12-volt deep cycle battery as the FLA exemplar. There are better batteries out there, but at $100 for a 100 Ah battery this is a value-leader. For comparison I’m going to use a BattleBorn 100 Ah 12-volt LiFePO4 battery that currently sells for $900.

I’m going to focus on cost not because it’s the only way to view the benefits, but because it’s probably the easiest way to understand what you’re getting. However, there are lots of other important benefits I touched on in part one of my Mastervolt install article, like faster charging allowing reduced generator runtime. Plus LiFePO4 batteries are lighter, smaller, sealed, better monitored, and have more safety systems than comparable FLA batteries.

To start, we’re going to look at the cost per amp hour of each battery. This math is pretty simple, the $100, 100 Ah Duracell is $1/amp hour. The $900, 100 Ah BattleBorn is $9/Ah. Right now the LiFePO4 battery is looking pretty darn expensive. However, I’ve been advised that it’s way more accurate to look at the cost per watt-hour (Wh) instead of the cost per amp hour, so let’s look at that instead.

In direct current (DC) calculating watts is very easy, it’s just volts times amps. So, a 12-volt 100-amp hour battery is a 1200 watt-hour battery. For the FLA battery the math will be $100 ÷ 1,200 = $0.083 / Wh and for the LiFePO4 it’s $900 ÷ 1200 = $0.75 / Wh. But, wait, that’s not a true comparison due to usable energy and nominal voltage factors, plus Peukert’s Law.”

## Usable energy

The life of a battery is affected by how much it is discharged. The less you discharge the battery, the more discharge-charge cycles it will survive. The general wisdom seems to be that it’s best not to discharge an FLA battery past 50 % depth-of-discharge (DOD) and a LiFePO4 battery past 80%.

So, now, let’s take our watt-hour numbers and compare again, but this time based on useable energy. For FLA we have 1,200 watt-hours but only half are usable, so it’s 1,200 Wh * 0.5 = 600 usable watt-hours. At a cost of $100 for 600 usable Wh, we are at 0.17 per Wh. For LiFePO4 we also have 1,200 watt-hours, but 80% of those are usable, so 1,200 Wh * 0.8 = 960 usable Wh. At $900 for 960 usable Wh each watt-hour costs $0.94. We’re down to only a little over five times the cost for LiFePo4. That’s still a huge difference, but stick with me, there’s more to consider.

## Nominal voltage

A 12-volt lead-acid battery is typically composed of six, 2-nominal-volt cells. Nominal voltage measures the typical voltage of a fully charged cell while being discharged with a load. So, the six cells combine to create a 12-nominal-volt battery. A 12-volt LiFePO4 battery is composed of four 3.3-nominal-volt cells meaning the battery actually has a 13.2 nominal voltage.

The difference in nominal voltage means that a 12-volt, 100-amp hour, LiFePO4 battery (13.2-nominal-volts) has 10-percent more watt-hours available than a 12-volt, 100-amp hour, flooded-lead-acid battery. Let’s take a look at the math behind this. For LiFePO4 we have a 13.2-volt battery with 100 amp hours of capacity. This yields: **13.2 v x 100 Ah= 1,320 watt-hours**. For FLA we have a 12-volt battery with 100-amp hours of capacity. This gives: **12 v x 100 Ah = 1,200 watt-hours**.

We can redo our math for the cost of usable watt-hours based on the new capacities. For FLA, nothing has changed so we remain at $0.17. For lithium the math is now 1,360 Wh * 0.8 = 1,088 usable watt-hours and $0.83 per usable watt-hour. We’re down below five times the cost, but we’re still not done.

## Peukert’s Law

The capacity rating of a battery is typically given assuming a 20-hour discharge cycle; meaning, that a 100-amp hour battery will be discharged at 5 amps per hour for 20 hours. But, for lead-acid batteries, the faster you discharge the battery, the less capacity is available. Peukert’s component is a measure of the reduction in capacity resulting from larger loads. Mastervolt says their LiFePO4 batteries aren’t impacted by faster discharging and will maintain their rated capacity (scroll to the section on Peukert’s Law in the linked article).

As you can see in the chart above, discharging FLA batteries above their 20-hour rate can significantly decrease the amount of actual power they can deliver. For example, a 100 Ah FLA battery discharged at 25 amps (five times its 20-hour rate) will only deliver 71.3 amp hours.

Up to now, all of our cost comparisons have been based on the 20-hour rate of 5 amps. But, instead, let’s compare at a discharge rate of 20 amps. At 20 amps of discharge, the previously 100 amp hour battery actually provides 74.75 amp hours. At 12-volts, that’s 897 Wh, but we only want to discharge the battery to 50-percent, so we have 449 useable Wh. $100 ÷ 449 Wh = $0.22 per usable watt-hour for FLA. LiFePO4’s cost doesn’t change since they’re not impacted by the rate of discharge.

Now we’re at $0.22 per usable Wh for FLA and $0.83 for LiFePO4. These numbers can vary a lot. If you look at the comparison at 10 amps per hour the cost for lead-acid declines to $0.19, on the other hand, if consumption increases to 40 amps the cost increases to $0.26.

## Voltage stability

Another big difference between lead-acid and lithium batteries is the behavior of the batteries under larger loads. Lead-acid batteries’ voltage drops significantly under heavy loads. On the other hand, LiFePO4 voltage barely moves. The chart above shows a period of huge draws from the oven onboard *Have Another Day* and the nearly perfect stability of the voltage under the load. This was an unintentional test that I’ll detail in the second installment about my refit, but it also provided a great test of how the batteries perform under big loads. If I put this same load on my prior FLA battery bank the inverter would have shut down due to low voltage moments after the load started.

Even under moderate loads, voltage stability can affect capacity. That’s because an electrical load that’s being serviced by lower voltage will draw additional amperage. If you have a 100-watt load, at 12 volts it will require 8.3 amps of current, but if the voltage should sag half a volt, you will now need 8.7 amps for the same load. This additional current means the battery will be depleted sooner.

I don’t have good measurements of voltage sag and I don’t suspect it will change our cost per watt-hour significantly. But, I can tell you that not having the voltage sag under big loads sure feels better. It doesn’t seem like the whole DC power system is struggling under the load.

## Battery life versus cost

The last way to compare the two battery technologies is by comparing how much energy they can deliver over their life. Battle Born says their batteries have a life of 3,000 – 5,000 cycles. The chart above suggests around 400 cycles for the flooded lead acid. Duracell offers a one-year warranty on their batteries but doesn’t publish a rated spec.

If we assume the Battle Born battery will last 3,000 cycles and deliver 1,088 watt-hours per cycle that gives us a total of 3,264,000 watt-hours or 3,264 kilowatt-hours (kWh). At 400 cycles for the Duracell and 449 watt-hours per cycle, we have 179,600 watt-hours or 179 kWh. This is when we see a big change in the cost comparison. These numbers mean that over their life the FLA battery costs $0.55 per kWh and the LiFePO4 costs $0.27 per kWh.

## Final thoughts

The cost per kilowatt-hour is a lot lower for LiFePO4, but I suspect that many lithium battery owners will never cycle them that often and are also unlikely them down to 80-percent DOD each time. With that in mind, the cost per kWh of LiFePO4 batteries is more likely to be comparable with FLA.

But let me be clear, if the costs of the two technologies are even close I think that LiFePO4 is a huge upgrade well worth your investment. It may take years for that investment to pay off, but during those years you will enjoy the many lithium benefits like faster charging, better voltage stability, more advanced safety systems, and reduced weight and size. For me, all these benefits and similar total costs make this upgrade a no-brainer.

Lastly, please let me know if you see any logical or mathematic errors in what I’ve outlined. I believe I’ve correctly applied all the considerations but I certainly may have made a wrong turn somewhere.

Good analysis and you haven’t even assigned a value to the greater charging efficiency you get from LiFePo being able to accept higher charge current above 70-80% SOC.

All that said, there are some downsides and tradeoffs with lithium:

1. More complexity and ways to fail. Lots of internal connections, internal electronics, and external electronics if there’s a proper Battery Management System

2. Lithium doesn’t like to charge below freezing and doesn’t like to float at 100% SOC

3. “Wild West” claims from manufacturers (e.g. I would assume 2000 charge cycles)

4. To get the most life and performance out of Lithium, you really need a good BMS, not a “drop in”

5. Your charging system very likely needs upgrades (e.g. alt cooling and disconnect protection)

6. Max current limitations with smaller banks having fewer batteries

7. Possible (though unlikely) catastrophic failure modes involving fire and smoke

Don’t get me wrong, I love my lithiums but I there’s still plenty of hype out there and people need to understand that they aren’t a panacea, just a different set of tradeoffs.

STP, you’re right that I glossed over the big benefit of charging efficiency. Even without the financial benefits, the quality of life benefits of not running the generator for a couple of hours to up in a few percent is really nice.

I think your list of tradeoffs is pretty spot on though I think several of them can be mitigated through clever design. In fact, I think Mastervolt has done that with their BMS and external disconnect relays. But, I’m about 10 cycles into a lifespan that should last hundreds of times that, so it’s far too early for me to speak to reliability.

As for the considerations to the rest of the system, you’re absolutely correct that charging and distribution need to be addressed at the same time you’re changing your batteries.

-Ben S.

Hi Ben. Great article. Since you asked, here are a couple of errata (I acknowledge you know this already and were being concise in the name of clarity):

1. To get to the 20-hour rate, you are discharging simply at “five amps,” not “five amps per hour.” Discharging at five amps for a period of one hour is five amp-hours. You could say “five amp-hours per hour” but that’s the same as “five amps” — the hours cancel out.

2. Generally speaking, lowering the voltage does not increase amps, but decreases them. Specifically, entirely resistive loads such as incandescent lights, many LED lights, and “universal” or DC motors all use less current at lower voltage, and thus consume less power. In fact, the power is a square relationship: if you cut voltage in half, power consumption will drop to one quarter. This is why lights look so dim with even a small drop in voltage. There are some exceptions: AC induction motors, and devices with smart controllers or regulated power supplies, such as variable-voltage LEDs, will increase their current consumption to attempt to draw the same amount of power when the voltage is lower. So resistive devices using battery power directly will actually consume a little more power (and draw a little more current) on the higher voltage of lithiums than on lead-acid. Lights will be a touch brighter, small dc motors will run a hair faster, and anything marginal to begin with might “burn out” a tad sooner on lithium. One way to mitigate this is to use a DC-to-DC converter to supply regulated 12vdc power to DC loads.

When I did my own analysis, I came up with similar numbers to yours for cost-per-kWh delivered over the life of the battery. But the real-world numbers get better when charging from a generator, because lithiums charge at a nearly constant rate from empty to full, whereas the “acceptance rate” of lead-acid drops rapidly as the batteries get more full. This means that you will be running a lightly loaded and thus inefficient generator periodically to deliver the “topping charge” to the lead-acid batteries. So for those of us charging from a generator, the cost of those kWh going into the batteries is lower for lithium than for lead-acid. This tips the scales even further in favor of lithium.

The biggest advantage for me, though, is no longer having to worry about ruining a lead-acid bank through over-discharge or chronic under-charging, both problems I’ve had to combat in the past. We replaced 750 aH (at 24v nominal) of AGM with just 315 aH of LiFePO4. Very happy (so far) that we made the switch, for all the reasons you mentioned.

very interesting analysis… and confess i had missed the “power” aspect in comparisons, but your totally correct..

however it may be even better? than your description, given that it will actually be about “area under the curve”.

yes the LiFePo4 start at higher voltage (good) … but im thinking they have a “flatter” curve (as compared to FLA discharge voltage curve).

and hence the “power” delivered may be even higher … eg its about the “shape” of the discharge curve, and if i recall my theory from waaaaayyy back, i believe its about area under the curve.

.. thinking out aloud .. and off to check my theory some more, interested in others thoughts if Im on the correct track..

.. correcting myself,

area under a voltage-time discharge curve .. at constant current will be energy delivered ..

however as you correctly note … devices typically want “power” and hence will increase their current draw as voltage reduces..

so a more correct comparison between the two is about “energy delivered” ….

I went through this analysis last year for (6) batteries on my WhisperJet and I ended up in the middle with this version of the common 100ah AGM battery:

https://www.mightymaxbattery.com/shop/12v-sla-batteries/12v-100ah-sla-battery/

$174.99, free shipping, and I wasn’t charged sales tax (10% in WA) so that was a net cost. Biggest factor over the FLA is the cycles / DOD:

1200 @ 50% DOD

500 @ 80% DOD

All good stuff Ben, however a good external BMS with cell resister top balancing monitors on individual cells and temperature sensing by the charger provides the greatest flexibility. Sean is correct in that users need to understand the differences e.g. don’t like to be left on float or stored at 100% SOC or their capacity is reduced. Also can not have SOC indicated by voltage, they like to be store at approx. 60 % SOC and customized charging profiles as all LFP04 batteries are not the same. I favor individual cells in a series parallel bank. That provides an alternative if single cell fails. You can then isolate it with just a reduction in capacity. After I experienced the reduction in capacity having them on float for an extended time, I isolated them from the charger leaving them discharged to 70% soc if laying say over the winter. I provided power to the ship’s 12

volt systems(pumps, toilet, etc) by a small separate charger acting as a power supply. As you know they can be so quickly recharged by shore, generator/alternators that isn’t much of a problem. They still last and return greater watts vrs LA batteries that you are still ahead economically even if they lose some capacity. If equipped with solar, it acts to cycle them at night so reduces the chance of reduction in SOC storage at 100%soc.

Nice write up and comparison. I’m in the process of battery replacement after good 10+ years of service from my AGMs. In trying to justify a Lifepo upgrade I’m coming up with a large (self) install cost.

New inverter/charger, seperate the charge and load buses, LVC/HVC, solar controllers,…….

The total cost when you then add in the actual lithium batteries to the support equipment is hard to justify versus the cost of alternatives that are much closer to drop in.

It would be interesting to see the total cost of ownership math which includes all the new controllers etc. needed. (This is the reason we did not switch to LiFePo with out latest batteries a couple of years ago (a switch probably makes more sense now).

It would be interesting to see how the math works out for Ben’s boat when you include all the costs to change to LieFePo, the fuel usage charging etc. VS the cost if you’d stayed with Flooded. After how many years/months does it make more sense to switch. Obviously it will depend greatly on power usage etc.

I’m working on the second installment of the main Mastervolt upgrade series. In that piece I’m going to break down the component costs. I haven’t yet captured fuel cost differences and I’m not sure I’ll be able to do that very well. At some point it feels like I could probably bend the numbers to say whatever I want if I make enough assumptions.

-Ben S.

FWIW, I also included Firefly Oasis G31 in my evaluation. I am _very_ comfortable with AGMs over almost 2 decades of use and I really wanted to talk myself into one of these newer technologies – but I couldn’t justify it. I have had LiFePo4 in my EPCarry for a couple of seasons and love it. One more consideration – what if advances in batteries make LiFePo (or even a subsequent technology) significantly cheaper in – say – 5 years?

We made the switch to LiFePo4 on the Katie B. Couldn’t be happier. We went with Big Battery due to their on/off switch, modular construction, built in BMS, 300 amp fuse, 10 year warranty, & Anderson connectors. We travel 3-4 months of the year by RV. On the boat & RV we have a connector for each 170 Ah battery, with equal length 2/0 marine wires, leading to our main buss bar. They just plug in like grapes, so in 30 minutes I can move my battery bank from boat to RV (47 lbs. each). One battery always stays in the boat or RV. So far 680 Ah is more than enough for us. Not affiliated with Big Battery, just was impressed with the logic & the You Tube teardown by Will Prose.

While BattleBorn batteries is a great benchmark it should be noted that off the shelf drop-in solutions is not the only game in town. I’ve put together my own 200Ah Lifepo4 battery with external BMS for just over $500. The discharge numbers are mind blowing. In my tests I easily run 21A load for 8-9 hours!

One thing I wish I would think more about ahead of time is how I would charge it. Things get tricky and costly. I started looking at high output alternators but even with the cost aside, I really dont want to be pushing 140-180A (thats a lot of energy!) through the wires on my sailboat. I would have to get 3/0AWG wire and even then I would worry about resistance/heat at connections. Brands like Balmar would set me back another $1500-1800 for all.

Instead I am perfectly happy with only 30-40A(max) out of my alternator at full RPM but the issue now is my 60A Hitachi/Yanmar alternator might burn itself trying to do it for long periods of time. At this moment I dont have a solution for this one…yet. Still researching….

Wanted to add one thing that’s not immediately obvious to some people. Lithium battery cannot be used to start an engine. it cannot deliver the hundreds of CCA (cold cranking amps) the engine needs.

Val, they may be true of some lithium batteries but certainly not all. Good example here:

https://panbo.com/weego-crankenstein-serious-jumpstart-pack-with-24v-capabilities/

But lithium doesn’t make much sense for fixed starting batteries because you’d be paying a lot for features starting batteries don’t generally use or need. Also, engine alternators need to be protected from possible damage if a lithium battery management system suddenly shuts the batteries down while they’re being charged.

From Joseph Pica:

“…Lithium battery cannot be used to start an engine….”

I had no problem at all with starting my two 4jh4 Yanmar Diesels from my 740 amp hr LFp04 bank. They will provide ample amps to start a diesel and certainly did so for me. Think of the popular compact lithium jump packs they are currently selling.

Ben, very true. I only meant lifepo4 can’t start an engine. For example, Lithium titanate LTO would be great for it at their 10C discharge rate.

LiFePo most certainly can start an engine, as long as the bank is configured appropriately. My house bank consists of three 143Ah/12V modules in parallel and each is rated for 1C continuous output, so the bank can deliver over 400A continuously. That’s more than enough to start my Yanmar 4JH3-HTE even under difficult circumstances.

I don’t have a separate starting bank and protect my alternator with a circuit that kills the field on a warning from the BMS, backed up by a failsafe dump diode.

I believe the overall Ah of your battery bank is clouding the confusion. Lifepo4 batteries should not be charged or discharged at higher rate than 1C. LTO chemistry, on the other hand, can do 10C.

And, yes, as stated by others, given 400ah bank 1c would be 400a but this is hardly the “norm” because a) placement relatively close to the engine all that 400ah bank or a really big wire gauge. B) BMS that’s rated for 400a

Val,

I don’t think that’s the case. Mastervolt rates the MLi 12/5500 that I have installed in my boat at 1,800 amps for 10 seconds and 500 amps of continuous load. 1,800 amps is 4.5C and 500 is 1.25. https://www.mastervolt.com/products/li-ion/mli-ultra-12-5500/.

Plus, the MLi 12/2750 with half the capacity is still rated for 500 amps of continuous discharge and 1,800 amps peak (https://www.mastervolt.com/products/li-ion/mli-ultra-12-2750/). I’m wondering if that’s a misprint, but even the 90 amp hour MLi-E 12/1200 is rated for 200 amps of continuous discharge and 380 amps for 30 seconds (https://www.mastervolt.com/products/li-ion/mli-e-12-1200/).

-Ben S.

The marketing material looks very interesting. Thank you for sharing it.

I’ve been reading information off of this site among other sources but perhaps chemistry and technology improves with time.

https://batteryuniversity.com/index.php/learn/article/types_of_lithium_ion

I don’t know how you define “norm” but a 300-400Ah bank isn’t that unusual on cruising boats in the US.

Placement of the bank relative to the engine is immaterial if you use an appropriate wire gauge. In my case, the run from the batteries to the engine is over 2m but it’s not a problem with 2/0 wire, which isn’t exceedingly big.

As for the BMS, it doesn’t handle the large currents directly, it only monitors cells and provides balancing charge. My BMS is rated only for the string voltage and the number of batteries: 1000VDC or 65 batteries in any XSXP configuration, whichever is less. The BMS does control a contactor that sees all the current, but it’s rated for 500A continuous.