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 ?

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??

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 :-)

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.

typo: Model S, not Tesla :-D

We need edit func!

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.

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.

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


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!

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