# Revisiting What an Amp-Hour Means for Cordless Power Tool Batteries, and Other Tidbits

I wrote most of this in an email to a reader, but realized a post would be an even better idea.

I posted about Amp-hours a while back, here. But here’s a revisit:

Amp-Hour Analogy

Consider a fixed container that can hold 5 gallons of water. You can attach a large spigot or a small one to fill drinking cups with. Either way, you get 5 gallons of water out of the container until you have to refill it.

But now consider that the spigot size matters. That container might hold 5 gallons of water, but attach a very large spigot and you might not fill as many cups of water as if you had used a small spigot.

With batteries, each cell has a measurable maximum capacity, measured in amp-hours. Amps are units for current flow. A battery cell with 1.0 amp-hour capacity can supply 1.0 amps of current for 1 hour.

If for the same cell, a more power-hungry tool is connected, and it draws 2.0 amps of current, the battery can supply 2.0 amps of current for 1/2 hour.

Attach an even larger motor, and it can supply say 10.0 amps of current for 1/10 an hour, or 6 minutes.

Let’s say there’s an even larger motor, still, and it draws 20.0 amps of power. In theory, we could expect 1/20th of an hour of runtime, or 3 minutes.

Internal Resistance, or What Blocks the Spigot

But in reality, there are other forces at play. Have you ever felt a wire, motor, or battery that was warm or even hot to the touch?

As with water flowing through a pipe, current flowing through a wire can lead to energy losses. Akin to friction, resistance will convert some electrical energy into heat.

(Heat and noise are two signals that there is energy loss.)

Battery cells have something called internal resistance. Think of internal resistance as built-up in a spigot that restricts flow.

A battery’s rated charge capacity will decrease based on environmental and application factors.

In an over-taxed battery cell, you would likely see higher cell temperatures, faster voltage drops, and reduced runtime due to greater energy losses and higher internal resistance.

So while a battery’s amp-hour spec is in theory a constant rating, it is dependent on other factors.

Size, Capabilities, and Capacity

Now let’s consider different battery cell sizes. You have a smaller cell, such as 18650, with 3.0Ah rating, and a larger cell, such as 21700, with the same 3.0Ah rating. Assuming they are both modern high performance cells, the 21700 cell will be rated at being able to supply more current.

Why? Manufacturers push batteries to their limits and from that they can specify safe operating parameters for their cells.

A weight lifter can bench press 200 pounds and complete 6 reps. How do they know that? Testing.

Consider 2 battery packs, both compact, one built with the smaller battery cell and the other built with the larger cell. Connect the same tool, say a low-powered LED flashlight. You might see comparable runtime from both tools. Then connect a heavy duty tool, such as a reciprocating saw that’s being used to cut through a tough block of material.

The tools will draw high current from both battery packs. The smaller one, with lower continuous current rating, won’t be able to power the tool for long before it overheats. Or, if it doesn’t overheat, it might at least still lose more energy to internal resistance, and get hotter. Battery packs are designed to cool their cells, but there is a maximum thermal dissipation rate. If they can’t cool cells fast enough, temperature sensors will shut things down beyond a certain temperature, to avoid damage to the cells or battery pack.

More Muscle, Less Fatigue

Now consider a 2.0Ah compact battery pack and a 4.0Ah high capacity battery pack. The compact pack is built with 5 cells connected in series, while the higher capacity battery pack is built with 10 cells connected in series and parallel.

What happens if you have 2 weight lifters, with each able to lift 200 pounds? They can lift a 400 pound boulder together. Some brands program their tools to draw a little more power from higher capacity battery packs, because they can.

But let’s say you have a 200 pound boulder. One weight lifter can lift it, but the boulder is at the limit of what they can handle, leading to some huffing and puffing. Two weight lifters will make easier work of it, because they’re only working half as hard as their max output.

A similar analogy can be applied to individual battery cells. An 18650 cell that is rated to deliver a maximum continuous current of 15A will run hotter than a 21700 cell of the same capacity that is rated to deliver a maximum of 30A of continuous current.

Specific Examples

Here are battery discharge characteristic graphs for two batteries – Samsung IRN18650-30Q, and Panasonic NCR20700A. These graphs ignore battery pack design considerations and only look at individual cells.

This Samsung INR cell, with 3.0Ah charge capacity rating, has a max continuous discharge current of 15A.

It’ll reach 60°C after fully discharged at 10A. At 15A, it’ll reach 60°C after only 1.3Ah of discharge, and 80°C after full discharge. At 20A, it’ll reach 60°C after 0.95Ah, and 100°C after full discharge. There’s no operating temperature range rating that I can find.

This Panasonic 21700 cell, with 3.1Ah capacity, has a max continuous discharge rating of 30A.

At 10A, the Panasonic cell will fully discharge and reach ~42°C. With a 20A discharge rate, it’ll reach ~60°C when fully discharged.

The larger cell will run cooler and longer at higher current discharge rates.

When More Isn’t Better

While some brands used 18650-sized 3.0Ah cells in 6.0Ah battery packs, stepping up from 2.5Ah cells to 3.0Ah cells results in a significant drop in continuous current ratings. When I asked one product manager about 6.0Ah packs, they told me that they tested a competitor’s pack, and saw that their 6.0Ah packs were providing less runtime than 5.0Ah battery packs in demanding applications.

Cell Size and Cooling Considerations

Smaller Li-ion cells have reached a technology ceiling. Larger cells can achieve higher performance ratings, but there might be a limit on energy density since larger cells have less efficient cooling.

Surface area of a cylinder is 2πrh + 2πr^2, and the volume is πr^2*h.

Consider an 18650 battery cell, as a perfect cylinder with 9 mm radius and 65 mm height. Its surface area would be 4.2 cm^2, and its volume 16.5 cm^3.

Consider a 21700 battery cell as a perfect cylinder with 10.5 mm radius and 70 mm height. It surface area would be 5.3 cm^2, and its volume 24.2 cm^3.

Going from an 18650 cell to 21700 results in a 47% increase in internal volume, but only 26% increase in surface area.

Thus, when you hear people talking about reduced cooling efficiency of larger battery cells, that’s what they’re referring to. Battery packs are not fixed designed, and so brands can work on pack designs that make up for this.

BUT, as shown in the above plots, larger cells run cooler than smaller ones, at least in those two specific examples. The Panasonic 21700 3.0Ah battery is clearly a better choice than the Samsung 18650 3.0Ah battery in demanding applications. 2.0Ah or 2.5Ah battery cells in 18650 size factor might even be better choices too.

Measuring Ah

Lastly, I can measure amp-hours of any given 12V Max, 18V, or 20V Max battery pack. I have the equipment to do so – it doesn’t take much. An electronic load provides a steady load to a battery pack and measures how long it takes before the battery pack reaches its operating voltage cut-off point. From all that you get an amp-hour measurement.

Or, measure the power draw from something like an LED worklight, and time low long it will be powered by a selected battery pack.

Measuring amp-hour rating for batteries under heavy demand? That’s a different story. The necessary lab equipment sells for $4,000 to $5,000 (and up), and that’s not including what would be needed to create a safe testing environment.

The bottom line is this: a battery’s amp-hours are based on manufacturer’s ratings, real-world conditions, and usage behaviors.

Questions?