# How long will a 100Ah battery run an appliance that requires 400W?

This article explains in detail how you can determine the amount of time for which you can run a 400W appliance on a 100Ah battery (both lithium or lead-acid).

Before I get into it, there are a couple of variables that are relevant here and that you should be aware of:

• The hourly energy consumption of the 400W appliance in Watt-hours (Wh)
• The Usable Capacity of the 100Ah battery in Watt-hours.

Once you’ve determined these variables, you can use them to estimate how long a 100ah battery could run your 400W appliance through the following formula:

Runtime (hours) = (Usable Capacity of the battery (Wh) ÷ Hourly Energy Consumption of the appliance (Wh/hour)) x 0.85

Let’s get into it. ## How long will a 100ah battery run an appliance that requires 400w?

In general, and assuming the 400W appliance runs continuously, a 12V-100Ah Lead-Acid battery could run a 400W appliance for about an hour at a 50% depth of discharge. On the other hand, a 12V-100Ah Lithium battery could run a 400W appliance for 2 to 2 and a half hours at an 80% depth of discharge.

However, an important thing to keep in mind is that not all 400W appliances run continuously.

But, why is that important?

Well, what we’re really looking for is not how much power the appliance uses (which is what the 400 Watts rating is for), but how much energy the appliance consumes each hour.

Let me explain.

The Wattage (Watts) rating of an appliance indicates the rate at which it consumes energy (Watt-hours). And the relationship between Electrical Power and Energy Consumption can be expressed using the following formula:

Energy Consumption (Watt-hours) = Power Usage (Watts) x Runtime (hours)

Anything that has – more or less – the same output the entire time it is turned on, could be said to run continuously, and its energy consumption could easily be calculated by multiplying its power rating (in watts) by the amount of time for which it was left ON.

For example, a 50W light bulb that is left on for 3 hours, would have consumed 150 Wh at the end of those 3 hours:

Energy Consumption (Watt-hours) = Power Usage (Watts) x Runtime (hours)

Energy Consumption (Watt-hours) = 50 Watts x 3 hours

Energy Consumption (Watt-hours) = 150 Watt-hours

However, as mentioned above, not all appliances have the same output during their runtime.

For example, when appliances such as refrigerators or air conditioners are plugged in and left on, they automatically turn on and off in a way that maintains the set temperature.

This means that a 400W refrigerator or air conditioner will rarely (if not never) consume 400 Watt-hours of energy per hour.

The next section explains this

## How much energy does a 400W appliance consume each hour?

As mentioned above, if your 400W appliance is an appliance that has the same kind of output the entire time it is left ON (TV, lights, fans, etc…), it will consume 400Wh/hour (Watt-hours per hour).

Energy Consumption (Watt-hours) = Power Usage (Watts) x Runtime (hours)

Energy Consumption (Watt-hours) = 400 Watts x 1 hour

Energy Consumption (Watt-hours) = 400 Watt-hour

However, if it’s an appliance that automatically turns ON and OFF, a new variable is added to the equation: Duty Cycle.

This Duty Cycle represents the percentage (%) of time that the appliance is actually running when it’s left on. If you have a duty cycle estimate, you can use it to estimate the energy consumption of the 400W appliance:

Energy Consumption (Watt-hours) = Power Usage (Watts) x Runtime (hours) x Duty Cycle (%)

For example, consider a 5000 BTU air conditioner which is rated at 400 Watts of power.

When this air conditioner is first turned on, it will use 400W of power as long as it needs to reach the set temperature. When it does reach that set temperature, the air conditioner will then turn off, and only turn back on when the temperature exceeds a certain threshold.

The exact percentage of time for which our air conditioner is actually ON, or its Duty Cycle, depends on a few factors, such as the ambient temperature, the set temperature, and room square footage and insulation.

However, as a general rule of thumb, a 5000BTU air conditioner will typically only run for 45 minutes per hour. This translates to a duty cycle of 75% (0.75).

So, as a rule of thumb, the amount of energy that a 400W air conditioner consumes each hour is:

Energy Consumption (Watt-hours) = Power Usage (Watts) x Runtime (hours) x Duty Cycle (%)

Energy Consumption (Watt-hours) = 400 Watts x 1 hour x 75%

Energy Consumption (Watt-hours) = 400 Watts x 1 hour x 0.75

Energy Consumption (Watt-hours) = 300 Watt-hours

The same logic applies to refrigerators, except that refrigerators have much better insulation, and deal will smaller loads (fewer cubic feet to cool down).

In consequence, a refrigerator will typically only run for 20 minutes per hour. This translates to a duty cycle of 33% (0.33).

So, as a rule of thumb, the amount of energy that a 400W refrigerator consumes each hour is:

Energy Consumption (Watt-hours) = Power Usage (Watts) x Runtime (hours) x Duty Cycle (%)

Energy Consumption (Watt-hours) = 400 Watts x 1 hour x 33%

Energy Consumption (Watt-hours) = 400 Watts x 1 hour x 0.33

Energy Consumption (Watt-hours) = 133 Watt-hours

However, please keep in mind that these are just estimates. A better and more precise way to determine the energy consumption of these appliances is to actually measure it.

This can be done using electricity monitors such as the Kill-A-Watt meter. These monitors are plugged between the appliance and the outlet and are able to give accurate energy measurements.

For example, as the video above shows, you can plug the Kill-A-Watt meter into the outlet, and plug the appliance into the meter. After an hour of runtime, you can then push the purple button that says KWH to see the energy consumption of your appliance during that hour.

In any case, once you’ve determined the amount of energy that your 400W appliance consumes each hour, the next step is to determine the usable capacity of your 100Ah battery.

## How much usable capacity does your 100Ah battery provide?

Batteries are rated in Amp-hours (Ah) and Volts (V), and both of these ratings influence the amount of energy (in Watt-hours or Wh) that a battery can store:

Rated Energy Capacity in Watt-hours (Wh) = Rated Charge Capacity in Amp-hours (Ah) x Rated Voltage in Volts (V)

For example, a 12V-100Ah battery can store 1200 Wh of energy. Or, if the battery is rated at 24V-100Ah, it can store 2400 Wh of energy.

However, not all types of batteries are equipped to deliver 100% of their rated capacity. While some types of batteries can afford to fully discharge, making their rated capacity fully usable, other types can only discharge to 50% of their rated capacity.

This brings us to what we call the Depth of Discharge.

Battery manufacturers usually provide a recommended Depth of Discharge (or DOD) for their batteries. This recommended DOD represents the percentage of a battery’s capacity that can be repeatedly used without causing permanent damage to the battery.

For example, if a battery has a rated capacity of 1200Wh, and has a recommended DOD of 50%, it could be said that the battery has a Usable Capacity of 600Wh (50% of 1200Wh):

Usable Capacity (Wh) = Rated Capacity (Wh) x Depth Of Discharge (%)

Usable Capacity (Wh) = 1200 Wh x 50%

Usable Capacity (Wh) = 600 Wh

Exceeding this recommended DOD will cause the battery to lose its storage capacity faster, and therefore have a shorter lifespan.

In general, battery types (or chemistries) could be divided into 2 groups:

• Lead Acid batteries: these batteries will generally have a recommended Depth of Discharge of 50%, at which they can provide 500 to 1000 charge/discharge cycles (depending on the battery).
• Lithium Batteries: these batteries will generally have a recommended Depth of Discharge of 80%, at which they can provide 3000 to 5000 charge/discharge cycles (depending on the battery)

In other words, if you have a 12V-100Ah Lead-Acid battery, its usable capacity is actually only 600 Watt-hours. If you have a 12V-100Ah Lithium battery, its usable capacity is around 960 Watt-hours.

In any case, once you’ve determined the usable capacity of your 100Ah battery, the next and last step is to calculate the amount of time for which it should be able to run your 400W appliance.

However, since 400 watts is a relatively big load for a single 12V-100Ah, for Lead-Acid batteries, there is another factor that could influence this amount of runtime that we’re looking for.

But first, let’s start with the case of a 12V-100Ah lithium battery.

## How long will a 100Ah lithium battery run an appliance that requires 400W?

Assuming it runs continuously, a 12V-100Ah lithium battery could run a 400W appliance for 2 to 2 and half hours at an 80% DOD. If the 400W appliance runs intermittently, such as a fridge or an air conditioner, a 12V-100Ah lithium battery could run the 400w appliance for up to 10 hours, depending on its hourly energy consumption.

This runtime can be calculated using the formula:

Runtime (hours) = (Usable Capacity of the battery (Wh) ÷ Hourly Energy Consumption of the appliance (Wh/hour)) x 0.85

Please note that the 0.85 coefficient represents the efficiency of the inverter. (average inverter efficiency is 85%)

To understand this better, let’s look at a couple of examples:

Example 1:

For this example, we’ll assume that we’re trying to run a 400W grow light on a 12V-100Ah Lithium Iron Phosphate (LiFePO4) battery.

An optimal depth of discharge for these kinds of batteries is 80%, so our usable battery capacity is 960Wh (12V x 100Ah x 0.8).

Since our appliance is basically a 400W light bulb, it will continuously draw 400 watts of power. This means that our appliance is going to consume 400 Watt-hours per hour (400Wh/hour).

Using our formula, we can now determine the amount of runtime that we should be able to get out of the battery:

Runtime (hours) = (Usable Capacity of the battery (Wh) ÷ Hourly Energy Consumption of the appliance (Wh/hour)) x 0.85

Runtime (hours) = (960 Wh ÷ 400 Wh/hour) x 0.85

Runtime (hours) = (2.4 hours) x 0.85

Runtime (hours) = 2.04 hours

According to these calculations, our 12V-100Ah lithium battery should be able to run the 400W appliance for 2 hours.

Example 2:

For this 2nd example, we’ll assume that we’re trying to run a 400W refrigerator on a 12V-100Wh LiFePO4 battery.

This time, we’ll assume our lithium battery is a high-end battery, which will still last over 8 years even at 100% Depth Of Discharge. Since we can use 100% of the battery’s capacity, in this case, our usable capacity is 1200 Watt-hours (12V x 100Ah).

As mentioned above, refrigerators don’t run 100% of the time and typically have a duty cycle of 30% to 40%. For simplicity, we’ll just assume a worst-case scenario and say the refrigerator has a 50% duty cycle.

In this case, the hourly energy consumption of the fridge is 200 Watt-hours per hour (200Wh/hour):

Energy Consumption (Watt-hours) = Power Usage (Watts) x Runtime (hours) x Duty Cycle (%)

Energy Consumption (Watt-hours) = 400 Watts x 1 hour x 50%

Energy Consumption (Watt-hours) = 400 Watts x 1 hour x 0.5

Energy Consumption (Watt-hours) = 200 Watt-hours

Using our formula, we can now determine the amount of runtime that we should be able to get out of the battery:

Runtime (hours) = (Usable Capacity of the battery (Wh) ÷ Hourly Energy Consumption of the appliance (Wh/hour)) x 0.85

Runtime (hours) = (1200 Wh ÷ 200 Wh/hour) x 0.85

Runtime (hours) = (6 hours) x 0.85

Runtime (hours) = 5.1 hours

Based on our assumptions, the 12V-100Ah lithium battery should be able to run the refrigerator for – at least – 5 hours.

## How long will a 100Ah Lead-Acid battery run an appliance that requires 400W?

When it comes to lead-acid batteries, their capacity ratings can be a little misleading. For example, when it says 12V-100Ah on a lead-acid battery case, somewhere on that case, it will probably also say something like 20HR or 10HR (hours).

This means that this capacity rating (12V-100AH) is only true if you discharge the battery over 10 or 20 hours (depending on the battery) This is due to the fact that the rate at which you discharge a lead-acid battery (also called C-rate) will have an effect on the capacity of the battery. This effect that the discharge rate has on the capacity of a battery is referred to as the Peukert Effect.

In other words, the faster you discharge a lead-acid battery, the lower its overall energy capacity is going to be.

Since most Lead-acid batteries are rated at a 0.05C discharge rate (discharged over 20 hours), and our appliance uses 400 Watts of power (around 33 Amps of current at 12 volts); the battery is going to discharge at a 0.33C discharge rate and in consequence, will lose a big chunk of its capacity.

The exact percentages of capacity a battery loses at different discharge rates (C-rates) are going to depend on the internal resistance of the battery itself.

However, for the sake of simplicity, we’ll assume that our battery is going to lose 30% of its efficiency. This means that our new Rated Capacity (@ 0.33 C-rate) is 70% of the Rated Capacity at 0.05 C-rate, which is 1200 Watt-hours (12V x 100Ah):

Rated Capacity @ 0.33C-rate (Wh) = Rated Capacity @ 0.05C-rate (Wh) x 70%

Rated Capacity @ 0.33C-rate (Wh) = 1200 Wh x 0.7

Rated Capacity @ 0.33C-rate (Wh) = 840 Wh

Also, keep in mind that this is Rated Capacity, and assuming a recommended Depth of Discharge of 50%, the new Usable Capacity of our 12V-100Ah Lead-Acid battery is:

Usable Capacity (Wh) = Rated Capacity (Wh) x Depth Of Discharge (%)

Usable Capacity (Wh) = 840 Wh x 50%

Usable Capacity (Wh) = 840 Wh x 0.5

Usable Capacity (Wh) = 420 Wh

So, after taking the recommended DOD of the battery and its discharge rate into consideration, we’re left with 420 Watt-hours of usable capacity.

Let’s use the same examples from the section above to see how much runtime we should be able to get out of our battery.

Example 1:

In this example, our 400W appliance uses 400 Watt-hours of energy per hour. Using our formula, the runtime can be calculated as such:

Runtime (hours) = (Usable Capacity of the battery (Wh) ÷ Hourly Energy Consumption of the appliance (Wh/hour)) x 0.85

Runtime (hours) = (420 Wh ÷ 400 Wh/hour) x 0.85

Runtime (hours) = (1.05 hours) x 0.85

Runtime (hours) = 0.89 hours

In this particular case, our 12V-100Ah Lead-Acid battery should be able to run our 400W appliance for about 55 minutes.

Example 2:

In the 2nd example, our 400W fridge uses 200 Watt-hours of energy per hour. Using our formula, the runtime can be calculated as such:

Runtime (hours) = (Usable Capacity of the battery (Wh) ÷ Hourly Energy Consumption of the appliance (Wh/hour)) x 0.85

Runtime (hours) = (420 Wh ÷ 200 Wh/hour) x 0.85

Runtime (hours) = (2.1 hours) x 0.85

Runtime (hours) = 1.78 hours

In this particular case, our 12V-100Ah Lead-Acid battery should be able to run our 400W fridge for about an hour and 50 minutes. 