Enter the battery size, the charge levels, the charging loss and the electricity rate of your plan. Efficiency and distance per month are optional; enter them to also get the cost per km and per month.
A blank current charge level counts as 0%, a blank target as 100% (full charge) and a blank charging loss as 10%. If a fast charger bills by the minute, divide what you actually paid by the energy that went into the battery (kWh), enter that as the rate and set the loss to 0%; the same formulas then work.
Result and graph
Enter the battery size, the charge levels, the electricity rate and so on in the fields on the left and press "Calculate". The result and a graph 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 battery size (kWh), the charge levels (for example, 20% → 80%), the charging loss and your electricity rate, and you get the energy that goes into the battery, the energy you buy from the grid and the cost of that charge on the spot
- Enter your efficiency (mi/kWh) to get the cost per mile and an estimate of the driving range on a full charge. Add your miles per month to also get the monthly and yearly charging cost and a graph of monthly cost by miles driven
- Level 2 charging at home and DC fast charging billed per kWh use the same formulas; just change the rate ($ per kWh) and the loss
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
To find the electricity cost of a household appliance from its wattage and hours of use, use the Electricity Cost Calculator. EV and plug-in hybrid (PHEV) charging is calculated from the battery size and charge levels, so use this page. For the electricity rate, enter the rate of your plan (you can find it on your electric bill or your utility's website). Charging loss depends on the car, the charger and the temperature, so the result is an estimate for the conditions you enter.
What is this calculation used for?
Estimating your monthly electricity cost after switching to an EV for commuting
If you commute 1,000 miles a month in an EV that gets 3.5 mi/kWh and charge on Level 2 at home (10% loss) at $0.17 per kWh, the cost per mile is about $0.054, and the monthly charging cost is about $54 (both are estimates for these conditions).
With just two numbers, "how many miles a month" and "your home electricity rate", you can estimate your monthly charging cost, which helps when you are thinking about buying a car or how to commute. To compare with a gas car, put the gas cost for the same miles next to it (gas price ÷ mpg × miles; at $3.20 a gallon and 25 mpg, that is $128 for 1,000 miles).
Comparing the effective rate of home charging and DC fast charging
If a per-minute fast charger costs you $15 and puts 30 kWh into the battery, the effective rate is \(15 \div 30 = 0.50\) dollars per kWh. If your home rate is $0.17 per kWh with 10% loss, the effective price per kWh in the battery is \(0.17 \div 0.9 \approx 0.189\) dollars (the numbers are examples).
Fast charging is paying for speed. You can check with numbers that doing everyday charging at home and using fast chargers only on long trips saves money. The calculation also shows that with per-minute billing, the effective rate tends to rise as the battery gets fuller and charging slows down.
Finding the effect of overnight charging on a time-of-use plan
Many utilities offer time-of-use or EV plans with cheaper rates at night. For example, with $0.10 per kWh off-peak and $0.30 per kWh on-peak, 1,000 miles a month at 3.5 mi/kWh with 10% loss costs about $31.75 a month charged off-peak and about $95.24 charged on-peak (the rates are examples; check your own plan).
An EV lets you choose when to charge, so simply charging when the rate is low greatly changes the cost of driving the same distance. It is useful when you set up scheduled charging in the car or its app.
Knowing the cost of the electric-only miles of a plug-in hybrid
Charging a plug-in hybrid with a 13.6 kWh battery from 30% to full puts about 9.5 kWh into the battery. With a 15% loss and $0.17 per kWh, one charge costs about $1.90, and at 3 mi/kWh it is enough for about 29 miles on electricity alone (estimates for these conditions).
A plug-in hybrid switches to gas when the battery runs out, so whether your daily miles fit within the electric-only range decides whether you get the benefit of cheap electricity.
Budgeting for electricity and planning solar charging with the loss in mind
Putting 45 kWh into the battery costs $7.65 at $0.17 per kWh with 0% loss, but about $8.50 with 10% loss and about $9.00 with 15% loss. You pay more by the amount lost.
When you set a monthly electricity budget, or plan how much extra solar power to send to your EV, estimate with "the energy bought (or used) including the loss", not "the energy into the battery", for a more realistic number. In cold weather the car uses energy to warm the battery, so the loss tends to grow; allowing a little extra is a safe choice.
Formula
Energy into the battery (kWh)
Standard notation
(the usual math form)
\(E\)
\(=\)
\(B\)
\(\times\)
\(\dfrac{s_2 - s_1}{100}\)
In words
(symbols replaced with words)
③
\(E\): energy into the battery (kWh)
\(=\)
①
\(B\): battery size (kWh)
\(\times\)
②
(target charge \(s_2\) − current charge \(s_1\)) ÷ 100
The formula in words
①
Take the
\(B\): battery size (kWh)
②
multiply it by the
increase in charge (target \(s_2\) − current \(s_1\), in %) divided by 100
③
and you get the
\(E\): energy into the battery (kWh)
Quick example
When an EV with a 75 kWh battery is charged from 20% to 80%, the energy that goes into the battery is
\(E\): energy into the battery (kWh)
\(=\)
battery size (75 kWh)
\(\times\)
(80% − 20%) ÷ 100
\(75 \times \dfrac{80 - 20}{100} = 75 \times 0.6 = 45\)
Key idea
The battery level is shown in percent, but what you pay for is how many kWh you put in. The percent is a share of the battery size, so divide the increase in percent by 100 to make it a decimal, then multiply by the battery size to get kWh.
A full charge from 0% to 100% is an increase of 100%, or 1 times, so the energy that goes in equals the battery size itself.
Note that the gross battery capacity in the specs and the usable capacity (with a buffer kept at the top and bottom to protect the battery) are different numbers, and many cars show the charge level with the usable capacity as 100%. Entering the gross capacity gives a slightly higher result, so if you know your car's usable capacity, use it for a more realistic estimate.
Energy bought from the grid (kWh, with loss)
Standard notation
(the usual math form)
\(E_b\)
\(=\)
\(E\)
\(\div\)
\(\left(1 - \dfrac{L}{100}\right)\)
In words
(symbols replaced with words)
③
\(E_b\): energy bought from the grid (kWh)
\(=\)
①
\(E\): energy into the battery (kWh)
\(\div\)
②
(1 − charging loss \(L\) (%) ÷ 100)
The formula in words
①
Take the
\(E\): energy into the battery (kWh)
②
divide it by
"1 − charging loss \(L\) (%) ÷ 100", the share that reaches the battery
③
and you get the
\(E_b\): energy bought from the grid (kWh)
Quick example
To put 45 kWh into the battery with a charging loss of 10%, the energy you buy from the grid is
\(E_b\): energy bought from the grid (kWh)
\(=\)
energy into the battery (45 kWh)
\(\div\)
(1 − 10% ÷ 100)
\(45 \div \left(1 - \dfrac{10}{100}\right) = 45 \div 0.9 = 50\)
Key idea
It is tempting to think "10% loss means 10% more", but the correct step is "÷ 0.9". Only 90% of the electricity you buy reaches the battery, so to deliver 45 kWh you must buy \(45 \div 0.9 = 50\) kWh. The extra is 5 kWh, not the 4.5 kWh you would get from "10% more". It is a division, not a multiplication, because you are working backward from the energy that goes into the battery to the energy you buy.
The loss comes from the onboard charger, which turns the AC from your outlet into DC for the battery, and from the cooling and control systems that run while charging. For Level 2 charging at home (240 V), about 10% is typical; Level 1 (120 V) charging is often less efficient. It depends on the car, the charger and the temperature. A DC fast charger turns AC into DC inside the charger and sends it straight to the battery, so if the kWh you pay for are counted at the charger's output, the loss that affects your bill is only in the cable and the car's controls and cooling, likely a few percent. Where the energy is measured depends on the charger and the network, so check the charger's information.
Cost of this charge ($)
Standard notation
(the usual math form)
\(C\)
\(=\)
\(E_b\)
\(\times\)
\(u\)
In words
(symbols replaced with words)
③
\(C\): cost of the charge ($)
\(=\)
①
\(E_b\): energy bought from the grid (kWh)
\(\times\)
②
\(u\): electricity rate ($/kWh)
The formula in words
①
Take the
\(E_b\): energy bought from the grid (kWh)
②
multiply it by the
\(u\): electricity rate ($/kWh)
③
and you get the
\(C\): cost of the charge ($)
Quick example
With 50 kWh bought from the grid (the example for formula 2) and an electricity rate of $0.16 per kWh, the cost of the charge is
\(C\): cost of the charge ($)
\(=\)
energy bought (50 kWh)
\(\times\)
rate ($0.16/kWh)
\(50 \times 0.16 = 8\)
Key idea
Your electricity bill is "energy bought (kWh) × rate ($ per kWh)", so the rate is multiplied by the energy you bought including the loss, not by the energy that went into the battery. Putting formulas 2 and 3 together gives "cost = energy into the battery × rate ÷ (1 − loss ÷ 100)", and the part "rate ÷ (1 − loss ÷ 100)" is the effective price per kWh in the battery (for example, at $0.16 per kWh and 10% loss, \(0.16 \div 0.9 \approx 0.178\) dollars per kWh).
DC fast chargers bill either per kWh delivered or per minute connected, depending on the network and the state. With per-minute billing, divide what you paid by the energy that went into the battery (kWh) to get an effective rate you can use in this formula (the loss is already included because you divided by the energy in the battery, so set the loss to 0% on the calculator). With per-minute billing, the effective rate changes from charge to charge: the fuller the battery, the slower it charges, and the less energy you get in the same time.
Cost per mile ($/mi)
Standard notation
(the usual math form)
\(c\)
\(=\)
\(u\)
\(\div\)
\(\left(1 - \dfrac{L}{100}\right)\)
\(\div\)
\(\eta\)
In words
(symbols replaced with words)
④
\(c\): cost per mile ($/mi)
\(=\)
①
\(u\): electricity rate ($/kWh)
\(\div\)
②
(1 − charging loss \(L\) (%) ÷ 100)
\(\div\)
③
\(\eta\): efficiency (mi/kWh)
The formula in words
①
Take the
\(u\): electricity rate ($/kWh)
②
divide it by
"1 − charging loss \(L\) (%) ÷ 100"
to get the effective price per kWh in the battery,
③
divide that by the
\(\eta\): efficiency (mi/kWh)
④
and you get the
\(c\): cost per mile ($/mi)
Quick example
With an electricity rate of $0.17 per kWh, a charging loss of 10% and an efficiency of 3.5 mi/kWh, the cost per mile is
\(c\): cost per mile ($/mi)
\(=\)
rate ($0.17/kWh)
\(\div\)
(1 − 10% ÷ 100)
\(\div\)
efficiency (3.5 mi/kWh)
\(0.17 \div 0.9 \div 3.5 = 0.05396\cdots \approx 0.054\)
Key idea
Efficiency in mi/kWh is how many miles the car goes on 1 kWh from the battery; it is the EV version of a gas car's mpg. One kWh in the battery costs "rate ÷ (1 − loss ÷ 100)", so dividing that by the efficiency gives the cost of one mile. It has the same shape as "gas price ($ per gallon) ÷ fuel economy (mpg) = gas cost per mile" for a gas car. Here it is about 5.4 cents per mile.
The EPA label shows EV efficiency as kWh per 100 miles (and as MPGe). To turn kWh/100 mi into mi/kWh, divide 100 by it (29 kWh/100 mi is about 3.4 mi/kWh). Real efficiency depends more on how you drive than on the rating, and it tends to drop with heating in winter and at highway speeds, so the average shown in your car gives a more realistic result.
Monthly charging cost ($)
Standard notation
(the usual math form)
\(C_m\)
\(=\)
\(c\)
\(\times\)
\(d\)
In words
(symbols replaced with words)
③
\(C_m\): monthly charging cost ($)
\(=\)
①
\(c\): cost per mile ($/mi)
\(\times\)
②
\(d\): miles per month (mi)
The formula in words
①
Take the
\(c\): cost per mile ($/mi)
②
multiply it by the
\(d\): miles per month (mi)
③
and you get the
\(C_m\): monthly charging cost ($)
Quick example
With a cost per mile of about $0.054 (the example for formula 4) and 1,000 miles a month, the monthly charging cost is
\(C_m\): monthly charging cost ($)
\(=\)
per mile ($0.054/mi)
\(\times\)
miles per month (1,000 mi)
\(0.054 \times 1000 = 54\)
\(0.17 \div 0.9 \div 3.5 \times 1000 = 53.968\cdots \approx 53.97\)
Key idea
Once the cost per mile is known, the rest is simply proportional to the miles you drive. The yearly charging cost is 12 times the monthly cost.
The first line of the example uses the cost per mile rounded to $0.054 ($54), and the second line uses the unrounded value, $0.05396… (about $53.97). Rounding partway through shifts the answer a little, so the calculator uses the unrounded value.
On a graph, this is a straight line through the origin that rises to the right, and its slope is the cost per mile \(c\). A cheaper electricity plan or a more efficient car makes the slope gentler, which lowers the cost of driving the same distance.
Estimated driving range on a full charge (mi)
Standard notation
(the usual math form)
\(R\)
\(=\)
\(B\)
\(\times\)
\(\eta\)
In words
(symbols replaced with words)
③
\(R\): driving range on a full charge (mi)
\(=\)
①
\(B\): battery size (kWh)
\(\times\)
②
\(\eta\): efficiency (mi/kWh)
The formula in words
①
Take the
\(B\): battery size (kWh)
②
multiply it by the
\(\eta\): efficiency (mi/kWh)
③
and you get the
\(R\): driving range on a full charge (mi)
Quick example
The estimated driving range on a full charge of an EV with a 75 kWh battery and an efficiency of 3.5 mi/kWh is
\(R\): driving range on a full charge (mi)
\(=\)
battery size (75 kWh)
\(\times\)
efficiency (3.5 mi/kWh)
\(75 \times 3.5 = 262.5\)
Key idea
The range from this charge uses the same formula with the energy into the battery, \(E\), in place of the battery size (for the 45 kWh in the example for formula 1, \(45 \times 3.5 = 157.5\) miles).
The charging loss does not appear in this formula. The loss happens between the outlet and the battery, and it has nothing to do with how far the electricity already in the battery takes you. Like efficiency, real range changes with heating, speed and load.
The basic steps are to find the energy into the battery (kWh) with "battery size × increase in charge ÷ 100", correct for the extra energy you buy because of the loss with "÷ (1 − loss ÷ 100)", and then multiply by the electricity rate ($ per kWh). The cost per mile is "effective price per kWh ÷ efficiency", and the monthly cost is that times the miles you drive.
Symbols and terms
Symbols
| \(B\) | Battery size (kWh). How much electricity the battery can store. It is the first letter of "battery". |
| \(s_1,\ s_2\) | The charge level when you start charging, \(s_1\), and when you stop, \(s_2\) (%). The \(s\) comes from "state of charge". The small 1 and 2 are subscripts that tell "before" and "after" apart. |
| \(E\) | Energy into the battery (kWh). It is the first letter of "energy". |
| \(E_b\) | Energy bought from the grid (kWh). It is larger than \(E\) by the amount lost. The small \(b\) stands for "bought". |
| \(L\) | Charging loss (%). The share of the electricity you buy that does not reach the battery. It is the first letter of "loss". |
| \(u\) | Electricity rate. The price of 1 kWh ($ per kWh). It is the first letter of "unit price". |
| \(C\) | Cost of the charge ($). It is the first letter of "cost". |
| \(\eta\) | Efficiency (mi/kWh), how far the car goes on 1 kWh. The Greek letter eta is often used for efficiency; here it shows how well the car turns electricity into distance. |
| \(c\) | Cost per mile ($ per mile). It is lowercase to tell it apart from \(C\), the cost of one charge. |
| \(d\) | Miles per month. It is the first letter of "distance". |
| \(C_m\) | Monthly charging cost ($). The small \(m\) stands for "month". |
| \(R\) | Estimated driving range on a full charge (miles). It is the first letter of "range". |
Terms
| kWh (kilowatt-hour) | A unit of electrical energy. Using 1 kW of power for 1 hour uses 1 kWh. Both EV battery sizes and electric bills are counted in this unit. |
| battery capacity | How much electricity the battery can store (kWh). Many EVs sold in the US have about 60 to 100 kWh, and plug-in hybrids about 10 to 25 kWh. To protect the battery, not all of it is used, so the usable capacity is a little smaller than the gross capacity, and many cars show the charge level with the usable capacity as 100%. |
| state of charge (SOC) | How much electricity is left in the battery, shown as a percentage of its capacity. It is the same idea as the battery percentage on a phone. Most cars show it with the usable capacity, not the gross capacity, as 100%. |
| charging loss | The part of the electricity you buy that is lost, mostly as heat, before it reaches the battery. The main causes are the onboard charger, which turns AC into DC, and the cooling and control systems that run while charging. About 10% is typical for Level 2 charging at home. |
| efficiency | How far an EV goes on 1 kWh (mi/kWh), the EV version of mpg. The larger the number, the better the car uses electricity. The EPA label shows it as kWh per 100 miles instead (a smaller number is better there). It changes with the car, speed, heating and temperature. |
| Level 2 charging | Charging with AC from a 240 V home charger or a public charger over several hours. Level 1 charging uses a regular 120 V outlet and is much slower. In both cases the onboard charger turns AC into DC, and that step causes the loss. At home, the cost depends on your electricity rate ($ per kWh). |
| DC fast charging | Charging with DC in a short time at a fast charger along highways or at shopping centers. Depending on the network and the state, you pay per kWh delivered or per minute connected. With per-minute billing, divide what you paid by the energy that went into the battery to find the effective rate. |
| driving range | How far the car can go on one full charge. This calculator estimates it as "battery size × efficiency". The EPA range on the window sticker comes from standard tests, and real range can be shorter with heating, high speed or a heavy load. |
| electricity rate | The price of 1 kWh of electricity ($ per kWh). It depends on your utility, your plan, how much you use and, on time-of-use plans, the time of day. Divide your bill by the kWh used to find your home's rough average rate. |
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 to these topics is the quickest way forward.
| Percents (Grades 6–7) |
|
| Multiplying and dividing decimals (Grades 5–6) |
|
| Unit rates (Grade 6) |
|
| Proportional relationships (Grades 6–7) |
|
| Power and energy (middle school 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 energy into the battery
| Battery size (kWh) | 75 |
| Current charge (%) | 20 |
| Target charge (%) | 80 |
| Energy into the battery (kWh) | =B1*(B3-B2)/100 |
Table to find the energy bought from the grid
| Energy into the battery (kWh) | 45 |
| Charging loss (%) | 10 |
| Energy bought from the grid (kWh) | =B1/(1-B2/100) |
Table to find the cost of this charge
| Energy bought from the grid (kWh) | 50 |
| Electricity rate ($/kWh) | 0.16 |
| Cost of this charge ($) | =B1*B2 |
Table to find the cost per mile
| Electricity rate ($/kWh) | 0.17 |
| Charging loss (%) | 10 |
| Efficiency (mi/kWh) | 3.5 |
| Cost per mile ($/mi) | =B1/(1-B2/100)/B3 |
Table to find the monthly charging cost
| Cost per mile ($/mi) | 0.054 |
| Miles per month (mi) | 1000 |
| Monthly charging cost ($) | =B1*B2 |
| Yearly charging cost ($) | =B3*12 |
Table to find the estimated range on a full charge
| Battery size (kWh) | 75 |
| Efficiency (mi/kWh) | 3.5 |
| Estimated range on a full charge (mi) | =B1*B2 |
After pasting, the upper cells in column B are your inputs and the formula cells are calculated automatically.
The first table is the example of a 75 kWh battery charged from 20% to 80%, and B4 shows 45 (kWh). The second table corrects those 45 kWh for a 10% loss, and B3 shows 50 (kWh). The third table multiplies by the $0.16 rate, and B3 shows 8 ($8.00).
The fourth table is the cost per mile, and B4 shows about 0.054 ($ per mile). The fifth table multiplies that by 1,000 miles a month, for $54 a month and $648 a year (because the cost per mile is rounded to 0.054, this differs slightly from the calculator's $53.97). The sixth table is the estimated range, and B3 shows 262.5 (miles). Just replace the numbers in column B with the values for your car.
The first table is the example of a 75 kWh battery charged from 20% to 80%, and B4 shows 45 (kWh). The second table corrects those 45 kWh for a 10% loss, and B3 shows 50 (kWh). The third table multiplies by the $0.16 rate, and B3 shows 8 ($8.00).
The fourth table is the cost per mile, and B4 shows about 0.054 ($ per mile). The fifth table multiplies that by 1,000 miles a month, for $54 a month and $648 a year (because the cost per mile is rounded to 0.054, this differs slightly from the calculator's $53.97). The sixth table is the estimated range, and B3 shows 262.5 (miles). Just replace the numbers in column B with the values for your car.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the energy into the battery
| Battery size (kWh) | 75 |
| Current charge (%) | 20 |
| Target charge (%) | 80 |
| Energy into the battery (kWh) | =B1*(B3-B2)/100 |
Table to find the energy bought from the grid
| Energy into the battery (kWh) | 45 |
| Charging loss (%) | 10 |
| Energy bought from the grid (kWh) | =B1/(1-B2/100) |
Table to find the cost of this charge
| Energy bought from the grid (kWh) | 50 |
| Electricity rate ($/kWh) | 0.16 |
| Cost of this charge ($) | =B1*B2 |
Table to find the cost per mile
| Electricity rate ($/kWh) | 0.17 |
| Charging loss (%) | 10 |
| Efficiency (mi/kWh) | 3.5 |
| Cost per mile ($/mi) | =B1/(1-B2/100)/B3 |
Table to find the monthly charging cost
| Cost per mile ($/mi) | 0.054 |
| Miles per month (mi) | 1000 |
| Monthly charging cost ($) | =B1*B2 |
| Yearly charging cost ($) | =B3*12 |
Table to find the estimated range on a full charge
| Battery size (kWh) | 75 |
| Efficiency (mi/kWh) | 3.5 |
| Estimated range on a full charge (mi) | =B1*B2 |
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 numbers.
How to calculate it in Python
battery_kwh = 75 # battery size (kWh)
soc_from_percent = 20 # current charge (%)
soc_to_percent = 80 # target charge (%)
loss_percent = 10 # charging loss (%)
price_per_kwh = 0.17 # electricity rate ($ per kWh)
efficiency_mi_per_kwh = 3.5 # efficiency (mi/kWh)
monthly_mi = 1000 # miles per month
# energy into the battery (kWh) = battery size × increase in charge ÷ 100
charged_kwh = battery_kwh * (soc_to_percent - soc_from_percent) / 100
# energy bought from the grid (kWh) = energy into the battery ÷ (1 − loss ÷ 100)
bought_kwh = charged_kwh / (1 - loss_percent / 100)
# cost of this charge ($) = energy bought × rate
charge_cost = bought_kwh * price_per_kwh
# cost per mile ($/mi) = rate ÷ (1 − loss ÷ 100) ÷ efficiency
cost_per_mile = price_per_kwh / (1 - loss_percent / 100) / efficiency_mi_per_kwh
# monthly and yearly charging cost ($) and estimated range on a full charge (mi)
monthly_cost = cost_per_mile * monthly_mi
range_mi = battery_kwh * efficiency_mi_per_kwh
print(f"Energy into the battery: {charged_kwh:.2f} kWh")
print(f"Energy bought from the grid: {bought_kwh:.2f} kWh")
print(f"Cost of this charge: ${charge_cost:.2f}")
print(f"Cost per mile: ${cost_per_mile:.3f}/mi")
print(f"Monthly charging cost: ${monthly_cost:.2f} / yearly: ${monthly_cost * 12:.2f}")
print(f"Estimated range on a full charge: {range_mi:.1f} mi")
Runs with the standard library only. Replace the first seven values (battery size, charge levels, loss, rate, efficiency and miles) with the values for your car and your electricity plan and run it.
How to write it in LaTeX and other math languages (copy and paste)
Energy into the battery (kWh)
E = B × (s₂ − s₁) ÷ 100
E = B \times \frac{s_2 - s_1}{100}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>E</mi>
<mo>=</mo>
<mi>B</mi>
<mo>×</mo>
<mfrac>
<mrow><msub><mi>s</mi><mn>2</mn></msub><mo>−</mo><msub><mi>s</mi><mn>1</mn></msub></mrow>
<mn>100</mn>
</mfrac>
</mrow>
</math>
E = B * (s_2 - s_1) / 100
energy = capacity*(socTo - socFrom)/100
E := B*(s2 - s1)/100;
E = B*(s2 - s1)/100;
E = B×(s_2−s_1)/100
Energy bought from the grid (kWh, with loss)
E_b = E ÷ (1 − L ÷ 100)
E_b = \frac{E}{1 - \frac{L}{100}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>E</mi><mi>b</mi></msub>
<mo>=</mo>
<mfrac>
<mi>E</mi>
<mrow><mn>1</mn><mo>−</mo><mfrac><mi>L</mi><mn>100</mn></mfrac></mrow>
</mfrac>
</mrow>
</math>
E_b = E / (1 - L/100)
energyBought = energy/(1 - loss/100)
E_b := E/(1 - L/100);
E_b = E/(1 - L/100);
E_b = E/(1−L/100)
Cost of this charge ($)
C = E_b × u
C = E_b \times u
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>C</mi>
<mo>=</mo>
<msub><mi>E</mi><mi>b</mi></msub>
<mo>×</mo>
<mi>u</mi>
</mrow>
</math>
C = E_b * u
cost = energyBought*price
C := E_b*u;
C = E_b*u;
C = E_b×u
Cost per mile ($/mi)
c = u ÷ (1 − L ÷ 100) ÷ η
c = \frac{u}{\left(1 - \frac{L}{100}\right)\eta}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>c</mi>
<mo>=</mo>
<mfrac>
<mi>u</mi>
<mrow>
<mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mi>L</mi><mn>100</mn></mfrac><mo>)</mo>
<mi>η</mi>
</mrow>
</mfrac>
</mrow>
</math>
c = u / ((1 - L/100) * eta)
costPerKm = price/((1 - loss/100)*efficiency)
c := u/((1 - L/100)*eta);
c = u/((1 - L/100)*eta);
c = u/((1−L/100)η)
Monthly charging cost ($)
Cₘ = c × d
C_m = c \times d
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>C</mi><mi>m</mi></msub>
<mo>=</mo>
<mi>c</mi>
<mo>×</mo>
<mi>d</mi>
</mrow>
</math>
C_m = c * d
monthlyCost = costPerKm*monthlyDistance
C_m := c*d;
C_m = c*d;
C_m = c×d
Estimated driving range on a full charge (mi)
R = B × η
R = B \times \eta
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>R</mi>
<mo>=</mo>
<mi>B</mi>
<mo>×</mo>
<mi>η</mi>
</mrow>
</math>
R = B * eta
range = capacity*efficiency
R := B*eta;
R = B*eta;
R = B×η
How to have ChatGPT do the calculation
You are an EV charging cost calculation assistant. 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). An EV with a 75 kWh battery is charged at home from 20% to 80%. The charging loss is 10%, the electricity rate is $0.17 per kWh, the efficiency is 3.5 mi/kWh, and the car is driven 1,000 miles a month. Find the energy into the battery with "battery size × (target % − current %) ÷ 100", the energy bought from the grid with "energy into the battery ÷ (1 − loss ÷ 100)", and the cost with "energy bought × rate". Find each of the following: 1. The energy into the battery (kWh) and the energy bought from the grid (kWh) 2. The cost of this charge ($) 3. The cost per mile ($ per mile) = rate ÷ (1 − loss ÷ 100) ÷ efficiency 4. The monthly and yearly charging cost ($) 5. The estimated range on a full charge (miles) = battery size × efficiency 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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