First choose "Find the battery size you need" or "How long a battery lasts". To find the size, enter the energy you want to use (kWh) directly, or add up the wattage (W) and hours of the devices you want to run. To find how long it lasts, enter the battery's rated capacity (kWh) and the total wattage (W) of the devices you use together. A blank depth of discharge or efficiency is treated as 90%.
The preset wattages are typical values. For devices that cycle on and off to hold a temperature, such as a refrigerator or air conditioner, the average wattage (often lower than the label) gives a more realistic result. Leave every field blank for devices you do not use.
Result and graph
On the left, choose "Find the battery size you need" or "How long a battery lasts", enter the energy, devices or battery values and press "Calculate". The battery size or runtime and a chart of the capacity breakdown will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formula
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter the energy you want to use (kWh), such as "10 kWh overnight", or add up the wattage (W) and hours of up to 5 devices you want to run in an outage. You get the rated battery capacity (kWh) you need, allowing for depth of discharge (DoD) and efficiency, and a typical product size (4 to 16 kWh)
- From the rated capacity (kWh) of a battery you have or are considering, find the energy you can really use (usable capacity) and how long it runs your devices together (hours and minutes)
- A bar chart splits the rated capacity into "usable", "lost to efficiency" and "held back by depth of discharge"
- Presets give typical wattages for devices people often run in an outage, such as a refrigerator, LED lights, TV, phone charging, microwave, window AC, CPAP machine and sump pump. You can change the numbers freely
- A plain-language explanation of rated vs. usable capacity, DoD, efficiency and power rating (kW), plus copy-and-paste formulas for Excel, Google Sheets and Python, are all on this page
The default depth of discharge and efficiency (90% and 90%) and the preset wattages are typical values; real values depend on the product, the device and how you use it, so replace them with the numbers on the spec sheet or label. Besides capacity (kWh), a battery has a power rating (kW), and the devices you run at the same time cannot add up to more than that. What a battery can power in an outage (the whole home or only some circuits) and its output limit also differ by product, so if backup power is your goal, always check with the installer or a licensed electrician. This calculation is an estimate for the conditions you enter, not a promise that you will have enough power. If you want the cost of running an appliance instead, use the "Electricity Cost Calculator".
What is this calculation used for?
How many kWh to keep the refrigerator, lights and phones going for one night
In a power outage, the first worries are the food in the refrigerator, the dark and staying in touch. Running a refrigerator (50 W average) for 24 hours, LED lights (40 W) for 6 hours, a TV (100 W) for 4 hours and phone charging (30 W) for 3 hours takes 1.2 + 0.24 + 0.4 + 0.09 = 1.93 kWh. With a battery at 90% DoD and 90% efficiency, the rated capacity needed is 1.93 ÷ 0.81 ≈ 2.38 kWh, so even a small 4 kWh class battery or a large portable power station would last one night.
But not every outage ends in one night. After hurricanes, winter storms or wildfire-related shutoffs, power can be out for days, and whether solar can recharge the battery in the daytime changes the size you need a lot. Deciding as a family how many days to plan for and which devices to do without is the starting point for choosing a size. If someone at home uses medical equipment such as a CPAP machine, include it first.
For using solar power at night, size the battery by your overnight use
Solar only produces in the daytime, so to cover your electricity after sunset yourself, you need to store the daytime surplus in a battery. What the battery must cover is roughly your overnight use (from sunset until the panels start producing the next morning). For example, if a home energy monitor or your utility's hourly data shows 10 kWh overnight, then at 90% DoD and 90% efficiency the rated capacity needed is 10 ÷ 0.81 ≈ 12.35 kWh, and a product of about 14 kWh is the guide.
On the other hand, a 10 kWh battery gives 10 × 0.81 = 8.1 kWh of usable energy, covering about 8 of the 10 kWh overnight, with the rest bought from the grid. Whether to choose a size that covers everything, or a smaller one and buy the rest, is a trade-off with cost (use the related solar payback calculator for the money side). With time-of-use rates, even a smaller battery can be worth it if it covers the expensive evening peak.
Can a battery keep the air conditioning on for pets during an outage?
In a summer outage, pets left at home or a fish tank can overheat. Running a window AC unit at an average of 500 W for 24 hours takes 500 × 24 ÷ 1000 = 12 kWh. At 90% DoD and 90% efficiency, the rated capacity needed is 12 ÷ 0.81 ≈ 14.81 kWh, which means the 16 kWh class, the top of this calculator's range for a single home battery.
So "air conditioning all day" is hard on a battery alone. You need to plan on recharging from solar in the daytime, or combine a fan (40 W, about 1 kWh for 24 hours) with a higher thermostat setting. Whether 240-volt central air or other large loads can run in an outage depends on the backup type (whole-home or partial-home) and the power rating, so check with the installer before you buy.
Knowing how long a "10 kWh battery" can run your devices
A battery with a rated capacity of 10 kWh at 90% DoD and 90% efficiency can deliver 10 × 0.81 = 8.1 kWh. With a refrigerator (50 W), LED lights (40 W), a TV (100 W) and a Wi-Fi router (10 W), 200 W in total, it lasts 8100 ÷ 200 = 40.5 hours, about 40 hours 30 minutes. Add a window AC at 500 W for 700 W in total, and it drops to 8100 ÷ 700 ≈ 11.6 hours; while a microwave (1000 W) runs, the total is 1700 W, and the battery drains by 1.7 kWh per hour.
As you can see, the runtime depends a lot on what you use at the same time. Deciding in advance which devices come first in an outage, and checking the battery's power rating (the limit on total wattage), keeps you from scrambling when the power goes out.
The same formulas work for a portable power station (rated in Wh)
Portable power stations for camping and emergencies list their capacity in Wh, such as "1000 Wh". 1000 Wh = 1 kWh, so enter "1" on this page. The capacity on a portable power station is the energy in the battery (rated capacity), and you can usually draw out about 80% to 90% of it after conversion losses. With 100% DoD and 85% efficiency, the usable energy is 1 × 0.85 = 0.85 kWh: an electric blanket (50 W) runs for 850 ÷ 50 = 17 hours, and a fan or a CPAP machine without its heated humidifier (about 40 W) for about 21 hours.
On the other hand, a high-power device such as an electric kettle (1200 W) may not run at all because of the power rating (for example, 600 W at most), even with enough capacity. When choosing a portable power station, the tip is to look at both the capacity (Wh) and the output (W).
Formula
Usable energy (usable capacity)
Standard notation
(the usual math form)
\(E_{u}\)
\(=\)
\(E_{r}\)
\(\times\)
\(D\)
\(\div\)
\(100\)
\(\times\)
\(\eta\)
\(\div\)
\(100\)
In words
(symbols replaced with words)
⑤
\(E_u\): usable energy (kWh)
\(=\)
①
\(E_r\): rated capacity (kWh)
\(\times\)
②
\(D\): depth of discharge (%)
\(\div\)
③
100 (percent to decimal)
\(\times\)
④
\(\eta\): efficiency (%)
\(\div\)
100 (percent to decimal)
The formula in words
①
Take the
\(E_r\): rated capacity (kWh)
②
multiply it by the
\(D\): depth of discharge (%)
③
divided by
100
(a decimal such as 0.9), then
④
multiply by the
\(\eta\): efficiency (%)
divided by 100,
⑤
and you get the
\(E_u\): usable energy (kWh)
Quick example
For a battery with a rated capacity of 10 kWh, a depth of discharge of 90% and an efficiency of 90%, the energy you can really use is
\(E_u\): usable energy (kWh)
\(=\)
rated capacity (10 kWh)
\(\times\)
depth of discharge (90%)
\(\div\)
100
\(\times\)
efficiency (90%)
\(\div\)
100
\(10 \times 0.9 \times 0.9 = 8.1\)
Key idea
The "10 kWh" on a spec sheet is the size of the battery itself (rated capacity), and not all of it reaches your devices. Draining a battery all the way shortens its life, so products set a limit such as "use down to 10%" (depth of discharge, DoD). On top of that, some energy turns into heat inside the battery and the inverter when it is drawn out (efficiency). What is left after both is the energy you can really use (usable capacity). In the example above, 8.1 kWh of the 10 kWh is usable, or 81%.
The "efficiency" in this calculator is applied once to the rated capacity (the energy stored in the battery), to cover the losses when drawing it out. If you enter the "round-trip efficiency" from a spec sheet (the efficiency from charging to discharging, including charging losses), the estimate becomes a little conservative (on the safe side). If a product lists its "usable capacity", that value is this \(E_u\). DoD and efficiency differ by product, and the capacity itself slowly shrinks as the battery ages.
Rated capacity needed
Standard notation
(the usual math form)
\(E_{r}\)
\(=\)
\(E_{u}\)
\(\div\)
\((\)
\(D\)
\(\div\)
\(100\)
\(\times\)
\(\eta\)
\(\div\)
\(100\)
\()\)
In words
(symbols replaced with words)
④
\(E_r\): rated capacity needed (kWh)
\(=\)
①
\(E_u\): energy to use (kWh)
\(\div\)
\((\)
②
\(D\): depth of discharge (%)
\(\div\)
100
\(\times\)
③
\(\eta\): efficiency (%)
\(\div\)
100
\()\)
The formula in words
①
Take the
\(E_u\): energy to use (kWh)
and divide it by the product (the usable share) of the
②
\(D\): depth of discharge (%)
divided by 100 and the
③
\(\eta\): efficiency (%)
divided by 100,
④
and you get the
\(E_r\): rated capacity needed (kWh)
Quick example
To use 10 kWh overnight, a battery with a depth of discharge of 90% and an efficiency of 90% needs a rated capacity of
\(E_r\): rated capacity needed (kWh)
\(=\)
energy to use (10 kWh)
\(\div\)
\((\)
depth of discharge (90%)
\(\div\)
100
\(\times\)
efficiency (90%)
\(\div\)
100
\()\)
\(10 \div (0.9 \times 0.9) = 10 \div 0.81 \approx 12.35\)
Key idea
This is formula 1 rearranged to find the rated capacity. Divide the energy you want to use by the usable share (DoD as a decimal × efficiency as a decimal). The share is less than 1, so the rated capacity needed is always larger than the energy you want to use. In the example, using 10 kWh takes a rated capacity of about 12.35 kWh, so a product of about 14 kWh is the guide. (This calculator uses 4, 5, 6, 7, 8, 10, 12, 14 and 16 kWh as typical sizes and shows the smallest one that is at least the capacity needed. Real product capacities differ by maker, and larger needs are often met by stacking two or more batteries.)
Decide the energy to use from your overnight use (from sunset to the next morning) or the total for the devices you run in an outage. If you can see your hourly use in a home energy monitor or your utility's online account (many utilities with smart meters offer it), use that; if not, estimate it by adding up devices with formula 4.
Runtime
Standard notation
(the usual math form)
\(t\)
\(=\)
\(E_{u}\)
\(\times\)
\(1000\)
\(\div\)
\(P\)
In words
(symbols replaced with words)
④
\(t\): runtime (hours)
\(=\)
①
\(E_u\): usable energy (kWh)
\(\times\)
②
1000 (kWh to Wh)
\(\div\)
③
\(P\): total wattage of devices used together (W)
The formula in words
①
Take the
\(E_u\): usable energy (kWh)
②
multiply it by
1000
to turn it into watt-hours (Wh),
③
divide by the
\(P\): total wattage of devices used together (W)
④
and you get the
\(t\): runtime (hours)
Quick example
With 8.1 kWh of usable energy, running a refrigerator (50 W), LED lights (40 W), a TV (100 W) and a Wi-Fi router (10 W) together (200 W in total) lasts
\(t\): runtime (hours)
\(=\)
usable energy (8.1 kWh)
\(\times\)
1000
\(\div\)
total wattage (200 W)
\(8.1 \times 1000 \div 200 = 40.5\)
Key idea
Energy (Wh) is "power (W) × time (hours)", so turning it around, "energy ÷ power" is time. Do not forget to multiply by 1000 to turn kWh into Wh. In the example, the battery lasts 40.5 hours, or 40 hours 30 minutes (0.5 hours × 60 minutes = 30 minutes), about 1.7 days.
Use the usable energy here, not the rated capacity. Using the 10 kWh rated capacity as is, 10000 ÷ 200 = 50 hours, would overestimate the runtime. Also, besides capacity, a battery has a power rating (kW), the most it can deliver at one time. If the devices add up to more than that, they cannot run together even with charge left.
Adding up the energy of each device
Standard notation
(the usual math form)
\(E_{u}\)
\(=\)
\(\sum\)
\((\)
\(P_{i}\)
\(\times\)
\(t_{i}\)
\()\)
\(\div\)
\(1000\)
In words
(symbols replaced with words)
④
\(E_u\): energy to use (kWh)
\(=\)
\(\sum\)
\((\)
①
\(P_i\): wattage of device \(i\) (W)
\(\times\)
②
\(t_i\): hours of use of device \(i\)
\()\)
\(\div\)
③
1000 (Wh to kWh)
The formula in words
①
Take the
\(P_i\): wattage of device \(i\) (W)
②
multiply it by the
\(t_i\): hours of use of device \(i\)
to get the energy of each device (Wh), add them up for all devices (Σ),
③
divide by
1000
to turn it into kWh,
④
and you get the
\(E_u\): energy to use (kWh)
Quick example
For one night of an outage, running a refrigerator (50 W) for 24 hours, LED lights (40 W) for 6 hours, a TV (100 W) for 4 hours and phone charging (30 W) for 3 hours takes
\(E_u\): energy to use (kWh)
\(=\)
\((\)
50 W
\(\times\)
24 h
\(+\)
40 W
\(\times\)
6 h
\(+\)
100 W
\(\times\)
4 h
\(+\)
30 W
\(\times\)
3 h
\()\)
\(\div\)
1000
\((1200 + 240 + 400 + 90) \div 1000 = 1930 \div 1000 = 1.93\)
Key idea
\(\sum\) (sigma) is the symbol for "add them all up". Here it means adding "wattage × hours" for device 1, device 2, and so on. Find "W × hours = Wh" for each device, add them, and finally divide by 1000 to get kWh. Putting the 1.93 kWh from the example into formula 2 gives a rated capacity of 1.93 ÷ 0.81 ≈ 2.38 kWh, so even a small 4 kWh class battery could cover one night.
Use the wattage on the label or spec sheet. But for devices that cycle on and off to hold a temperature, such as a refrigerator or air conditioner, the average wattage gives a more realistic result than the label value (which is close to the maximum). On the other hand, devices that draw a lot of power for a short time, such as a microwave or an electric kettle, use little energy but can easily hit the power rating (the most the battery can deliver at once). Motors such as a sump pump or well pump also draw a surge of power when they start.
The energy a battery can really deliver (usable capacity) is "rated capacity × DoD as a decimal × efficiency as a decimal", which is 20% to 30% less than the rated capacity on the spec sheet (about 19% less at 90% DoD and 90% efficiency). The rated capacity you need is the reverse, "energy to use ÷ (DoD as a decimal × efficiency as a decimal)", and the runtime is "usable energy (Wh) ÷ total wattage of devices used together (W)". Remember that, apart from capacity, a battery also has a power rating (kW) limit.
Symbols and terms
Symbols
| \(E_r\) | E sub r | The rated battery capacity (kWh), the capacity on the spec sheet. \(E\) is for energy, and the small \(r\) is for rated. |
| \(E_u\) | E sub u | The energy you can really use (usable capacity, kWh). The small \(u\) is for usable. When finding the capacity needed, it means the energy you want to use. |
| \(D\) | D | The depth of discharge (%), how much of the rated capacity is used. From "Depth of Discharge", also written DoD. |
| \(\eta\) | eta | The efficiency (%), the share of the stored energy that reaches your devices. The Greek letter eta is the usual symbol for efficiency in physics and engineering. |
| \(t\) | t | The runtime (hours). From the first letter of "time". |
| \(P\) | P | The total wattage of the devices used together (W). From the first letter of "power". |
| \(P_i,\ t_i\) | P sub i, t sub i | The wattage (W) and hours of use of device \(i\) (the 1st, 2nd, and so on). The small \(i\) is the position number, from "index". |
| \(\sum\) | sigma | The symbol for "add them all up", the Greek letter sigma (S for sum). Here it means adding the energy of device 1, device 2, and so on. |
| 100, 1000 | one hundred, one thousand | Constants for converting units. 100 turns a percent into a decimal (such as 0.9), and 1000 converts between kWh and Wh (k = kilo = 1,000 times). |
Terms
| rated capacity | The amount of energy the maker says the battery can store (kWh), also called nominal or total capacity. It is the size of the battery itself, and not all of it can be used by your devices. |
| usable capacity | The part of the rated capacity that actually reaches your devices (kWh), the rated capacity times DoD and efficiency as decimals. Some spec sheets list it. When comparing batteries, comparing usable capacity is closer to real life than comparing rated capacity. |
| depth of discharge (DoD) | How much of the rated capacity is used (%). Draining a lithium-ion battery all the way shortens its life, so products limit the range they use, such as "down to 10%". A DoD of 90% means 10% of the rated capacity is always kept in reserve. |
| efficiency | The share (%) of the stored energy that is not lost on the way to your devices. Some turns into heat in the battery and the inverter during discharge. This calculator applies these losses once to the rated capacity as the "efficiency". 85% to 95% is common for home batteries. |
| round-trip efficiency | The share (%) of energy that is not lost over the whole trip from charging to discharging. The efficiency on a spec sheet is often this round-trip value, which includes charging losses. Entering it in this calculator's "Efficiency" field also takes off the charging loss, so the estimate becomes a little conservative (on the safe side). |
| power rating | The most power a battery can deliver at one time (kW), also called continuous output. If capacity (kWh) is the size of a water tank, the power rating (kW) is the width of the faucet. A battery rated at 5 kW cannot run devices that add up to more than 5,000 W at once, even with charge left. Some products limit output further during an outage. |
| power | How fast electricity is used, in watts (W) or kilowatts (kW). A power rating and a device's wattage are power. It is related to energy (Wh, kWh) by "energy = power × time". |
| energy | The total amount of electricity used, in watt-hours (Wh) or kilowatt-hours (kWh). Energy = power × time, so 1 kWh is 1,000 W used for 1 hour. The capacity of a home battery or a portable power station (Wh) is energy. |
| watt-hour (Wh) | A unit of energy, 1 W used for 1 hour. It is used for the capacity of portable power stations and power banks. 1000 Wh = 1 kWh, so divide by 1000 to get kWh for this page. |
| state of charge (SOC) | How much charge is left in the battery right now (%), the same as the battery level on a phone. With a DoD of 90%, the battery stops discharging when the SOC reaches 10%. |
| whole-home backup | A battery setup that can power the whole home in an outage (some can also run 240-volt loads such as central air or an electric range). When choosing for outages, check that the devices you want to run are covered. |
| partial-home backup | A battery setup that powers only chosen circuits in an outage (such as the refrigerator outlet and some lights), usually through a separate essential-loads panel. When choosing for outages, check that the devices you want to run are on those circuits. |
| inverter | The device that converts between the battery's DC power and the home's AC power. Every solar or battery system has one, and some energy is lost in the conversion (one of the losses in the efficiency). |
| capacity fade | The slow loss of storage capacity as a battery is charged and discharged again and again (one full charge and discharge is one cycle). After about 10 years, capacity can drop by 20% to 30%, so if you plan to use a battery for a long time, choosing a little extra capacity is one approach. |
| solar self-consumption | Using your own solar power at home instead of sending it to the grid. Storing extra daytime power in a battery and using it after sunset raises self-consumption. The battery size for this is set mostly by your overnight use. With time-of-use rates, the battery can also cover the expensive evening hours. |
| home energy monitor | A device or system that records electricity use hour by hour for the whole home or for each circuit, so you can see your overnight use. Many utilities with smart meters also show hourly use in your online account. Without either, estimate the overnight share from the monthly kWh on your bill. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
If you get stuck, going back over these topics is the quickest way forward.
| Percents (Grades 6–7) |
|
| Multiplying and dividing decimals (Grades 5–6) |
|
| Converting units (Grades 4–8) |
|
| Power and energy (middle school physical science) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the usable energy (usable capacity)
| Rated capacity (kWh) | 10 |
| Depth of discharge (%) | 90 |
| Efficiency (%) | 90 |
| Usable energy (kWh) | =B1*B2/100*B3/100 |
Table to find the rated capacity needed
| Energy to use (kWh) | 10 |
| Depth of discharge (%) | 90 |
| Efficiency (%) | 90 |
| Rated capacity needed (kWh) | =B1/(B2/100*B3/100) |
Table to find the runtime
| Usable energy (kWh) | 8.1 |
| Total wattage of devices used together (W) | 200 |
| Runtime (hours) | =B1*1000/B2 |
Table to add up the energy of each device
| Refrigerator wattage (W) | 50 |
| Refrigerator hours of use | 24 |
| LED lights wattage (W) | 40 |
| LED lights hours of use | 6 |
| TV wattage (W) | 100 |
| TV hours of use | 4 |
| Phone charging wattage (W) | 30 |
| Phone charging hours of use | 3 |
| Energy to use (kWh) | =(B1*B2+B3*B4+B5*B6+B7*B8)/1000 |
After pasting, the upper cells in column B are your inputs and the green formula cells are calculated automatically.
The first table is a 10 kWh battery at 90% DoD and 90% efficiency, and B4 shows 8.1 (kWh). The second table is for using 10 kWh overnight, and B4 shows about 12.35 (kWh). The third table is 8.1 kWh of usable energy with 200 W in total, and B3 shows 40.5 (hours). The fourth table is one night of an outage with a refrigerator, LED lights, a TV and phone charging, and B9 shows 1.93 (kWh). To add more devices, add rows and add pairs such as "+B9*B10" to the last formula.
The first table is a 10 kWh battery at 90% DoD and 90% efficiency, and B4 shows 8.1 (kWh). The second table is for using 10 kWh overnight, and B4 shows about 12.35 (kWh). The third table is 8.1 kWh of usable energy with 200 W in total, and B3 shows 40.5 (hours). The fourth table is one night of an outage with a refrigerator, LED lights, a TV and phone charging, and B9 shows 1.93 (kWh). To add more devices, add rows and add pairs such as "+B9*B10" to the last formula.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the usable energy (usable capacity)
| Rated capacity (kWh) | 10 |
| Depth of discharge (%) | 90 |
| Efficiency (%) | 90 |
| Usable energy (kWh) | =B1*B2/100*B3/100 |
Table to find the rated capacity needed
| Energy to use (kWh) | 10 |
| Depth of discharge (%) | 90 |
| Efficiency (%) | 90 |
| Rated capacity needed (kWh) | =B1/(B2/100*B3/100) |
Table to find the runtime
| Usable energy (kWh) | 8.1 |
| Total wattage of devices used together (W) | 200 |
| Runtime (hours) | =B1*1000/B2 |
Table to add up the energy of each device
| Refrigerator wattage (W) | 50 |
| Refrigerator hours of use | 24 |
| LED lights wattage (W) | 40 |
| LED lights hours of use | 6 |
| TV wattage (W) | 100 |
| TV hours of use | 4 |
| Phone charging wattage (W) | 30 |
| Phone charging hours of use | 3 |
| Energy to use (kWh) | =(B1*B2+B3*B4+B5*B6+B7*B8)/1000 |
These formulas use only multiplication and division, so the same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace column B with your own battery and device numbers. To add up devices, you do not need a function such as SUMPRODUCT; adding pairs of multiplications as in the formula above is enough.
How to calculate it in Python
rated_kwh = 10 # rated battery capacity (kWh)
dod_percent = 90 # depth of discharge, DoD (%)
efficiency_percent = 90 # efficiency (%)
# usable energy (usable capacity) = rated capacity x DoD x efficiency
usable_kwh = rated_kwh * dod_percent / 100 * efficiency_percent / 100
print(f"Usable energy: {usable_kwh:.2f} kWh")
# Devices to run in an outage: (name, wattage W, hours of use)
appliances = [
("Refrigerator", 50, 24),
("LED lights", 40, 6),
("TV", 100, 4),
("Phone charging", 30, 3),
]
needed_kwh = sum(watts * hours for _, watts, hours in appliances) / 1000
print(f"Energy to use: {needed_kwh:.2f} kWh")
# rated capacity needed = energy to use / (DoD x efficiency)
required_kwh = needed_kwh / (dod_percent / 100 * efficiency_percent / 100)
print(f"Rated capacity needed: {required_kwh:.2f} kWh")
# runtime = usable energy (Wh) / total wattage of devices used together (W)
total_watts = sum(watts for _, watts, _ in appliances)
hours = usable_kwh * 1000 / total_watts
print(f"Running {total_watts} W together lasts {hours:.1f} hours (about {int(hours)} h {round((hours - int(hours)) * 60)} min)")
Runs with the standard library only. Change the rated capacity, DoD and efficiency at the top and each row of appliances (name, wattage, hours of use) to your own values and run it. Add rows to include more than 5 devices.
How to write it in LaTeX and other math languages (copy and paste)
Usable energy (usable capacity)
E_u = E_r × D ÷ 100 × η ÷ 100
E_u = E_r \times \frac{D}{100} \times \frac{\eta}{100}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>E</mi><mi>u</mi></msub>
<mo>=</mo>
<msub><mi>E</mi><mi>r</mi></msub>
<mo>×</mo>
<mfrac><mi>D</mi><mn>100</mn></mfrac>
<mo>×</mo>
<mfrac><mi>η</mi><mn>100</mn></mfrac>
</mrow>
</math>
E_u = E_r * D/100 * eta/100
usable = rated*dod/100*efficiency/100
E_u := E_r*dod/100*eta/100;
E_u = E_r*D/100*eta/100;
E_u = E_r×D/100×η/100
Rated capacity needed
E_r = E_u ÷ (D ÷ 100 × η ÷ 100)
E_r = \frac{E_u}{\dfrac{D}{100} \times \dfrac{\eta}{100}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>E</mi><mi>r</mi></msub>
<mo>=</mo>
<mfrac>
<msub><mi>E</mi><mi>u</mi></msub>
<mrow>
<mfrac><mi>D</mi><mn>100</mn></mfrac>
<mo>×</mo>
<mfrac><mi>η</mi><mn>100</mn></mfrac>
</mrow>
</mfrac>
</mrow>
</math>
E_r = E_u / (D/100 * eta/100)
rated = usable/(dod/100*efficiency/100)
E_r := E_u/(dod/100*eta/100);
E_r = E_u/(D/100*eta/100);
E_r = E_u/(D/100×η/100)
Runtime
t = E_u × 1000 ÷ P
t = \frac{E_u \times 1000}{P}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>t</mi>
<mo>=</mo>
<mfrac>
<mrow><msub><mi>E</mi><mi>u</mi></msub><mo>×</mo><mn>1000</mn></mrow>
<mi>P</mi>
</mfrac>
</mrow>
</math>
t = E_u * 1000 / P
hours = usable*1000/power
t := E_u*1000/P;
t = E_u*1000/P;
t = E_u×1000/P
Adding up the energy of each device
E_u = Σ(P_i × t_i) ÷ 1000
E_u = \frac{\sum_{i} P_i \, t_i}{1000}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>E</mi><mi>u</mi></msub>
<mo>=</mo>
<mfrac>
<mrow>
<munder><mo>∑</mo><mi>i</mi></munder>
<msub><mi>P</mi><mi>i</mi></msub>
<msub><mi>t</mi><mi>i</mi></msub>
</mrow>
<mn>1000</mn>
</mfrac>
</mrow>
</math>
E_u = (sum_i P_i t_i) / 1000
usable = Total[power*hours]/1000
E_u := add(P[i]*t[i], i = 1..n)/1000;
E_u = sum(P.*t)/1000;
E_u = (∑(P_i×t_i))/1000
How to have ChatGPT do the calculation
You are a calculation assistant for home battery sizing. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). The depth of discharge (DoD) is 90% and the efficiency is 90%. 1. Find the energy you can really use (kWh) from a battery with a rated capacity of 10 kWh as "rated capacity × DoD ÷ 100 × efficiency ÷ 100". 2. Find the energy needed (kWh) to run the following devices in a power outage as "sum of wattage (W) × hours of use ÷ 1000": - Refrigerator: 50 W, 24 hours - LED lights: 40 W, 6 hours - TV: 100 W, 4 hours - Phone charging: 30 W, 3 hours 3. Find the rated capacity (kWh) needed to supply the energy in step 2 as "energy needed ÷ (DoD ÷ 100 × efficiency ÷ 100)". 4. Find how long (hours) the battery in step 1 lasts when the four devices above (220 W in total) run together, as "usable energy × 1000 ÷ total wattage", and also write it as "X hours Y minutes". Show the formulas you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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