Relation between kWh and Ah ?

Relation between kWh and Ah ?

To my knowledge battery capacity is measured in Ah.
What is the relation between Ah and kWh ?
Do Tesla cars have kWh-indicators to measure the
charged energy ?

reitmanr | 8 November, 2012

Not sure how to best say this, but Ah is ampxhours at the given battery voltage and kWh is 1000 watts ( voltsxamps) x hours it can provide this power. Must be a better way to describe this. I bet a graph would help. Any ideas??

Jolinar | 8 November, 2012

Battery capacity si often measured by Ah (it can be calculated as number of ampers which I can take from battery multiplied by time how long I can take this current... current*time = A*hours = Ah), because usually all bateries have same (or similar) voltage, but in general it doesn't say anything about total energy stored in battery.

kWh (1000Wh) is unit to measure total energy stored in battery and it can be calculated as battery voltage multiplied by Ah (V*A*h = Wh). In general kWh is unit to measure energy used.

So if u have 2 batteries with same Ah, but different voltage, one with higher voltage has more energy (kWh) in it.

I hope it's clear now, electric cars need to store a lot of energy, but in compare to gasoline ones, they are more efficient in using it. Just for comparison: One gallon of gas contains 33.7kWh energy according to EPA :-)

Jolinar | 8 November, 2012

And yes, I think Tesla has kWh indicator to measure it.

hmm, that calculations of stored energy are a bit more complicated, because voltage of battery is different when it is fully charged and when it's empty, but I didn't want to make it chaotic.

Jolinar | 8 November, 2012

typo: Model S, not Tesla :-D

We need edit func!

evanstumpges | 8 November, 2012

In my opinion, the standard for measuring battery capacity should be Wh (Watt Hours) or kWh (Kilo-Watt Hours) instead of Ah (Amp Hours) since Wh is actually a measure of how much energy the battery contains. Knowing the Ah "capacity" of a battery is generally fairly useless you know that battery voltage as well.

Voltage is the link between Ah and Wh and the formula is as follows:
Wh=Ah*Vnom where Vnom is the nominal battery voltage

Seems very simple, but it becomes a bit more complicated when you consider that the instantaneous voltage of a battery does not stay constant as it is discharged. This is particularly problematic for Li-Ion batteries since their voltage curves are not very linear.

Measuring Vnom is more complicated than simply measuring Ah, hence why Ah is more commonly stated than Wh.

To measure Ah "capacity", all you have to do is connect a charged battery to a constant load (an LED for example) and measure the time it takes before the battery goes dead. Ah come from multiplying current (Amps) by time (hours). An LED draws a constant current, so there is no need for integration to get Ah capacity in this case.

Getting Wh does require integration, along with additional measurement instrumentation because you have to track the voltage and integrate it with respect to time to get Vnom. For example, you could connect a voltage reading device to a computer and record the battery voltage every second as the battery discharges through the same LED. Then you integrate voltage with respect to time to get Vnom and multiple that by Ah (as calculated before) to get Wh.

A Watt is a unit of power, which is equal to Voltage * Amperage. Energy is the power deliver over a certain duration of time, hence why you multiple time in hours.

Not sure if my description is more or less complex than you were looking for, but feel free to ask if anything is unclear.

noguwiba | 9 November, 2012

Thank you all for replies.
If Tesla EV´s really contain kWh indicators
with sufficient accuracy, it would be easy to
charge everywhere since the electric grid is
nearly everywhere in civilized regions of the earth,
not only at special stations.Big advantage in contrast to
gas filling stations and necessary to stay mobile.
For an account the energy difference before and after
charging can be measured within the EV.

Brian H | 9 November, 2012

Would you rather fill an ICE through a straw, garden hose, or fire hose?
110V; 240V; 880V.

Carl Barlev | 12 November, 2012


Nice analogy, but a little mis-leading as higher voltage doesn't necessarily mean you will be able to charge faster (in practice the opposite can be true).

I often use a water-analogy to help explain "electricity" to those with a non-electrical background, as you seem to have done here except that you've crossed the analogy by comparing voltage to flow-rate?

Voltage = water pressure = height of the dam or water tank
Current = flow-rate of water

In a simple circuit, a higher voltage will drive a higher current and fill your battery faster, but in practice we can and do see the opposite.

1. The "strength" of the power grid can and does vary a lot depending on where you are and what protection is installed (among other factors).... a 110 V connection at one location may be capable of supplying more power than a 240 V connection at another location.

2. Chargers have a power rating that tells you the maximum power the charger can deliver... some 110 V chargers have a higher power rating than other 240 V chargers.

I wonder if anybody with a non-electrical background can follow what I've written - that's the real test!

jstack6 | 16 August, 2015

Simply put, Amp Hours are a measure of electric current and Kilowatt Hours are a measure of electric power.

Here's some formulas and comparisons=

Power in Watts = Current in Amps x Voltage

Consider the following…

A battery rated for 100 amp hours will provide 5 amps for 20 hours.

If we have a 12 volt battery, we multiply 100 by 12 and determine that the battery will provide 1200 watt hours.

To apply the metric ‘kilo’ prefix, we divide the result by 1000 and determine that the battery can supply the 1.2 KW hours.

There is something to keep in mind. The Amp Hour rating is a 20 Hour rating, therefore it is necessary to treat any kilowatt conversion you make as a 20 hour rating as well.

In the case of our 1200 Watt Hour conversion, we need to understand that what is really being said is that the battery will provide 60 Watt Hours for 20 Hours.

Timo | 17 August, 2015

60 Watts for 20 hours. 1200Wh doesn't change, that's the energy.

johnse | 17 August, 2015

Actually the 20 hour term has nothing to do with watt-hours, but rather the efficiency of the battery chemistry and design. A perfect battery would supply the full rated energy no matter what current was being drawn from the battery.

In the real world, though, some batteries (such as Lead Acid) are inefficient when drawing at high loads.

In the 12V 100Ah example, you can reasonably draw 5 amps from the battery for 20 hours. This does not prelude you from drawing 100 amps. ICE cars often draw several hundred amps from their battery when starting the car. This is the value commonly known as "cold cranking amps." However, the lose their stored energy much more quickly at such high loads. The perfect 12V 1200Wh battery could supply 1000A for 1/10 hour, or 6 minutes. In reality, if you tried cranking a car's starter for that long you'd run out of energy very quickly.

When comparing batteries and how they can reasonably be used, we use a rate designated C. 1C means that you are charging or discharging a battery such that you use 100% of the rated power in 1 hour. Thus, in the battery we're using for an example, the 1C rate would be 100A or 1200W.

Lead Acid batteries begin to lose efficiency at anything above 0.05C--the 20 hour rate.

One horsepower is 748W. When the P90D is running in Ludicrous mode it might be delivering 700hp. That translates to 523.6kW... That's a discharge rate of approximately 5.8C, meaning it can only sustain that power output (assuming a perfect battery) for about 10 minutes.

Lithium Ion batteries are typically rated to be able to charge and discharge around 2C rate. Tesla and Panasonic have improved their batteries to do better than that, but even at 2C, they are 40x better than Lead Acid.

Mike83 | 18 August, 2015

@jstack6 and

Great explanations. I have a question if anyone knows.
There is an Electric bus in Monterrey that charges wireless.
In addition we got an induction range that requires metal in the pan to work. Are these methods related?
How does that work and does this expose one to radiation?

johnse | 19 August, 2015

The two are related, phenomena. They work on low frequency electromagnetic fields. Radiation is a word that covers many things, some not even remotely similar.

The Electric Bus: Induction charging is really the same as a transformer.

First a little bit of Electromagnetic theory... Any time you pass current through a wire, an electromagnetic field builds up around that wire. If you imagine wrapping your right hand around the wire with your thumb pointing in the direction current is flowing, your fingers will show the direction of the field. If you have an alternating current (AC) it will build the field in one direction, then the field collapses as the current drops to zero, and then builds in the opposite direction. This changing field is the basis for many of the things we take for granted in our modern world: motors, radio, our beloved Teslas :)

If you wind the wire into a coil, the circular magnetic fields align with all of the lines inside the coil pointing down the center of the coil, and all the lines outside pointing the opposite direction on outside. You may have seen school experiments where you wind wire around a nail and hook it up to a battery. The nail turns into an electromagnet.

Just as you can create a magnetic field around wire by passing current through the wire, you can also induce a current flow in wire if you push the wire through a magnetic field. This is how generators work. A current will also be induced if it is the field moving past the wire.

Therefore, if you take two coils and place one next to another, you form a transformer. One coil has AC voltage applied to it. As the AC voltage oscillates positive and negative, a magnetic field builds up first in one direction, then in the other. This coil is called the Primary coil. The other coil, the Secondary, is set up so that the magnetic field of the first will pass through the wires of the Secondary as the Primary field oscillates. This induces current in the second coil.

Transformers are extremely common. If you open any wall wart for your portable electronics, you will find a small transformer inside. The ratio of the number of turns (literally the number of times you wind the wire in the coil) in the primary and secondary coils determines the voltage available in the secondary. For example, if there were 1000 turns in the primary, and 100 turns in the secondary, the voltage available on the secondary would be 1/10 the voltage. So if you apply 120 volts AC to the primary, you get out 12V from the secondary. The current available works exactly the opposite, but is determined by the load on the Secondary. If you draw 10 amps from the secondary, which means you are drawing 120 watts, you will be pulling only 1 amp from the primary supply--also 120 watts. This is all assuming perfect transfer with no losses. This is, of course, not the case, so the power in will be slightly greater than the power out, but you get the idea.

Just as you can step down voltage, you can also step the voltage up. If you turn that transformer around and apply 120V to the 100 turn side (making it the primary), you will get 1200V out of the 1000 turn side.

The transformers used in such power supplies are typically wound around a common core, and the wires of the coils are interlaced. This provides a very tight coupling and increases efficiency.
There are a number of modern electric toothbrushes which charge by placing them in a stand. The stand has the primary coil of a transformer, and the toothbrush has the other.

The bus charges in the same manner, just with a lot more power. The spacing between the primary and secondary coils presents some difficulties in getting the efficiency up--but I know there's someone on the board who has been saying that they've been able to get above 90% efficiency.

As for "radiation", I'm not well versed in "EM pollution", but I don't think it's really anything to be concerned with.

Your stove:
This works on the same general principles as the transformer. However, instead of coils of wire, you have a sheet of metal in the pan. When the coil in your stove creates the oscillating magnetic field, the magnetic lines of force move through the pan. As with any conductor, this will cause current to be induced. However, since you don't have strands of wire to direct the current flow, you get what are known as eddy currents. These currents are very low voltage but high current (you effectively have a single turn on the secondary, so you are stepping the voltage down by hundreds or thousands-to-one, but also stepping the current up by a similar ratio). These eddy currents heat the metal in the same way that if you feel the cord of a charging car, you will find the cord gets warm.

By using appropriate metals in the pan, this form of induction heating can be very efficient. Induction heating is also used in foundries to melt metals.

Again, radiation...not so much.

EM radiation:

EM pollution (most of it is unsubstantiated fear-mongering, in my opinion):

Timo | 19 August, 2015

Shortened version: EMF is not EMR.

Mike83 | 19 August, 2015

I thank you very much johnse. The clarity of your explanation is excellent and helps refresh my long ago understanding of electricity and magnetism.
We have put in Solar and have all electric now including a heat pump water heater. No more gas in the house. We are waiting to get the Tesla PowerWall to hook up to our PV system inverter.
Electricity is amazing and learning more is fascinating.

johnse | 19 August, 2015

It's amazing how much explaining it helps dredge up details I learned 40 years ago :) Thanks for your kind words.

Mike83 | 20 August, 2015

Your welcome. The value of growing older is the accumulation of knowledge. It comes down to experience which for me makes life a very amazing journey. I am grateful for many things but having an open mind to learn is one very good advantage.
Have a great day.

bluebeemer42 | 20 August, 2015


I am a registered professional electrical engineer, and used be on the IEEE 1188 technical review committee (Valve Regulated Lead Acid batteries (VRLA)). Your electrical system posts are some of the best I have ever seen on a public, non-engineering forum. You are a valuable asset to this forum. Bravo!