Choose the gas type (a typical heating value is filled in), enter the gas price and the electricity rate, and press "Calculate". You get the cost per kWh of heat for gas and electricity and a break-even graph. Set "How to set the heat" to "Heat water" to compare the cost of heating a tub or a day's hot water.
Enter the gas price per m³ and the electricity rate per kWh from your bills (without fixed monthly charges). Typical gas appliance efficiencies are about 80% for a water heater (about 95% for a condensing model) and about 40% for a gas cooktop. The electric appliance efficiency (COP) is 1 for appliances that turn electricity straight into heat (resistance heaters, electric water heaters) and about 3 for heat pumps. If blank, 80% efficiency and a COP of 1 are used.
Result and graph
Enter your gas price and electricity rate on the left and press "Calculate". The cost per kWh of heat for gas and electricity and a break-even 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
- From the gas type (natural gas, propane or your own), the gas price ($ per therm or per gallon) and the efficiency of the gas appliance, and from the electricity rate ($ per kWh) and the efficiency of the electric appliance (COP), compare the cost of getting the same 1 kWh of heat from gas and from electricity
- Enter a water heating job (gallons × temperature rise in °F) or an amount of heat (BTU), and it calculates the cost with gas and with electricity, the difference, and which is cheaper under your numbers
- It shows how many kWh of electricity 1 therm of natural gas or 1 gallon of propane is worth as heat (and the useful part after appliance efficiency)
- It finds the break-even gas price, where gas and electricity cost the same per kWh of heat, and shows it as the crossing point on a graph of gas price against cost per kWh of heat
- A plain-language explanation of "price per unit of heat", which works for water heating, cooking and space heating alike, and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
The default heat contents (natural gas 100,000 BTU per therm, propane about 91,500 BTU per gallon) are standard values used by this calculator; the actual values differ slightly by supplier. Gas prices and electricity rates depend on your utility, plan and usage, so enter the rates from your own bills. Both comparisons leave out fixed monthly charges and use only the price per unit used. Appliance efficiency and COP change with the model and conditions (season, water temperature, outdoor temperature). "Which is cheaper under these numbers" is a calculation result, not advice to replace an appliance or change your service. To find the cost of one appliance from its wattage and hours, use the electricity cost calculator. To compare electric heaters with each other, use the heating cost comparison calculator. This page compares gas and electricity by converting both to the price of the same amount of heat.
What is this calculation used for?
Is a gas or an electric (heat pump) water heater cheaper to run?
An average household uses about 64 gallons of hot water a day. Raising it from 55°F to 120°F takes \(64 \times 8.34 \times 65 \approx 34{,}694\) BTU (about 10.17 kWh). With natural gas at $1.40 per therm in a tank water heater (about 65% efficient), that is about $0.75 a day, or about $273 a year. A heat pump water heater (COP 3) at $0.17 per kWh costs about $0.58 a day ($210 a year), and a standard electric water heater (COP 1) about $1.73 a day ($631 a year).
So the same "electricity" can differ by 3 times depending on heat pump or resistance, and gas lands somewhere in between depending on its price and efficiency. Water heating is one of the biggest energy uses in a home, so working out "the cost per kWh of heat" first helps when you replace a water heater or look at a new home. Purchase price, lifespan and fixed charges need to be considered separately.
Gas range or induction cooktop - which costs less to cook with?
A gas cooktop loses a lot of heat around the pan (about 40% efficient), while an induction cooktop heats the pan itself (about 85%). (For an electric appliance with an efficiency below 1, like induction, enter it in the COP field as a value such as "0.85".) With natural gas at $1.40 per therm and 40% efficiency, 1 kWh of heat costs \(1.40 \div (29.31 \times 0.4) \approx 0.119\) dollars. With induction at $0.17 per kWh and 85% efficiency, it is \(0.17 \div 0.85 = 0.20\) dollars.
Even with the efficiency gap, gas can be cheaper per unit of heat, and with propane the result can flip. Cooking uses little heat per meal, so the difference is only a few cents at a time. The choice of cooktop is usually about safety, indoor air and ease of use rather than energy cost; this calculation shows how big the cost difference really is.
Comparing the cost of heat from a gas furnace and a heat pump
The same formulas work for space heating. A high-efficiency gas furnace (AFUE 95%, enter "95" as the efficiency) with natural gas at $1.40 per therm gives 1 kWh of heat for about $0.050. A heat pump at $0.17 per kWh costs about $0.057 with a COP of 3 and about $0.049 with a COP of 3.5. The break-even COP is about \(0.17 \div 0.050 \approx 3.4\): above it, the heat pump is cheaper under these prices.
A heat pump's COP drops as the outdoor temperature drops, so in very cold climates gas can come out ahead in midwinter. Try COP values from 2 to 4 to see where the answer flips. To compare electric heaters with each other (heat pump, space heater and so on), the sister page, the heating cost comparison calculator, is a better fit.
Estimating how much heating costs change in a propane area
Propane is sold by the gallon, and 1 gallon holds about 91,500 BTU. At $2.50 per gallon and 80% efficiency, 1 kWh of heat costs \(2.50 \div (26.82 \times 0.8) \approx 0.117\) dollars, about 1.95 times natural gas at $1.40 per therm ($0.0597).
Saying "$2.50 per gallon is not much more than $1.40 per therm" is a mistake: always compare per unit of heat, including the heat content. Propane prices vary a lot by supplier, so put your quoted price into this calculator and check the break-even price against electricity (a heat pump or a heat pump water heater). In many propane areas, heat pumps come out cheaper.
Turning the therms on your gas bill into "what would it cost with electricity?"
Your gas bill shows how many therms you used. That is all the heat in the gas, so first multiply by the appliance efficiency to get the heat actually used, then choose "Enter the heat (BTU)" in "How to set the heat" and enter it to see the cost of the same heat with electricity. For example, if you used 50 therms in a month with an 80% efficient furnace, the heat actually used is \(50 \times 100{,}000 \times 0.8 = 4{,}000{,}000\) BTU. Entering it gives $70.00 for gas ($1.40 per therm) and about $66.43 for a heat pump with a COP of 3 ($0.17 per kWh).
Working from your actual usage shows the difference for the way your household really uses energy. Equipment prices, lifespan and changes in fixed charges are not included, so compare those too before changing equipment.
Formula
Cost per kWh of heat (gas)
Standard notation
(the usual math form)
\(c_{g}\)
\(=\)
\(p_{g}\)
\(\div\)
\((\)
\(H\)
\(\div\)
\(3412\)
\(\times\)
\(\eta\)
\()\)
In words
(symbols replaced with words)
⑤
\(c_g\): cost per kWh of heat from gas ($/kWh)
\(=\)
④
\(p_g\): gas price ($/therm)
\(\div\)
\((\)
①
\(H\): heat content (BTU/therm)
\(\div\)
②
3,412 (BTU to kWh)
\(\times\)
③
\(\eta\): gas appliance efficiency
\()\)
The formula in words
①
Take the
\(H\): heat content (BTU/therm)
②
divide it by
3,412 (BTU to kWh)
to turn the heat in 1 therm into kWh (kilowatt-hours)
③
multiply by the
\(\eta\): gas appliance efficiency
to get the heat you can actually use (the useful part)
④
divide the
\(p_g\): gas price ($/therm)
by that useful part
⑤
and you get the
\(c_g\): cost per kWh of heat from gas ($/kWh)
Quick example
For natural gas (100,000 BTU per therm) at $1.40 per therm in an appliance with 80% efficiency, the cost per kWh of heat is
\(c_g\): cost per kWh of heat from gas ($/kWh)
\(=\)
gas price ($1.40/therm)
\(\div\)
\((\)
heat content (100,000 BTU/therm)
\(\div\)
3,412
\(\times\)
efficiency (0.8)
\()\)
\(100{,}000 \div 3412 \approx 29.31\)
\(29.31 \times 0.8 \approx 23.45\)
\(1.40 \div 23.45 \approx 0.0597\)
Key idea
Natural gas is sold by the therm (or by the gallon for propane) and electricity by the kWh, so you cannot compare the prices directly. Convert both to the same yardstick, "1 kWh of heat". The heat in 1 therm is 100,000 BTU, and 1 kWh = 3,412 BTU, so dividing by 3,412 tells you how many kWh of heat 1 therm is (about 29.31 kWh).
But not all of the gas heat goes into the water or the room. Some escapes up the flue. The share that is used is the appliance efficiency \(\eta\): about 65% for a tank water heater (UEF 0.6 to 0.7), about 90% for a tankless or condensing water heater, 80 to 98% for a furnace (its AFUE rating) and about 40% for a gas cooktop. Dividing the gas price by the useful kWh gives the cost of 1 kWh of heat from gas.
If your utility bills natural gas in ccf (100 ft³) instead of therms, use about 103,600 BTU per ccf. For propane use about 91,500 BTU per gallon, and for heating oil about 138,500 BTU per gallon.
Cost per kWh of heat (electricity)
Standard notation
(the usual math form)
\(c_{e}\)
\(=\)
\(p_{e}\)
\(\div\)
\(\mathrm{COP}\)
In words
(symbols replaced with words)
③
\(c_e\): cost per kWh of heat from electricity ($/kWh)
\(=\)
①
\(p_e\): electricity rate ($/kWh)
\(\div\)
②
COP: electric appliance efficiency
The formula in words
①
Take the
\(p_e\): electricity rate ($/kWh)
②
divide it by the
COP: electric appliance efficiency
③
and you get the
\(c_e\): cost per kWh of heat from electricity ($/kWh)
(resistance heaters and electric water heaters have a COP of 1, so the rate itself is the cost per kWh of heat)
Quick example
At $0.17 per kWh, the cost of 1 kWh of heat from an electric (resistance) water heater (COP 1) and from a heat pump water heater (COP 3) is
electric water heater, cost per kWh of heat ($/kWh)
\(=\)
rate ($0.17/kWh)
\(\div\)
COP (1)
heat pump water heater, cost per kWh of heat ($/kWh)
\(=\)
rate ($0.17/kWh)
\(\div\)
COP (3)
\(0.17 \div 1 = 0.17\)
\(0.17 \div 3 \approx 0.0567\)
Key idea
Electricity is sold in kWh from the start, so for an appliance that turns all of its electricity into heat (a resistance heater, a standard electric water heater, COP = 1), the electricity rate itself is the cost of 1 kWh of heat.
A heat pump water heater or a heat pump for space heating does not "make" heat from electricity. It collects heat from the air and "moves" it into the water or the room, so it gets about 3 times the heat from the electricity it uses. This multiple is the COP (coefficient of performance), and the cost per kWh of heat drops to the rate divided by the COP. The key point of this formula: the same "electricity" can differ by 3 times in cost, depending on whether the appliance is a resistance heater or a heat pump.
The COP changes with the air and water temperatures and drops in cold weather. For a heat pump water heater, the UEF rating (often 3 to 4) is a good value to enter as the COP. For heat pump space heating, HSPF2 ÷ 3.412 gives roughly the average COP over the season.
Cost of the heat you need, and the difference
Standard notation
(the usual math form)
\(C_{g}\)
\(=\)
\(Q\)
\(\div\)
\(3412\)
\(\times\)
\(c_{g}\)
\(C_{e}\)
\(=\)
\(Q\)
\(\div\)
\(3412\)
\(\times\)
\(c_{e}\)
In words
(symbols replaced with words)
④
\(C_g\): cost with gas ($)
\(=\)
①
\(Q\): heat needed (BTU)
\(\div\)
②
3,412 (BTU to kWh)
\(\times\)
③
\(c_g\): cost per kWh of heat from gas ($/kWh)
⑥
\(C_e\): cost with electricity ($)
\(=\)
\(Q\): heat needed (BTU)
\(\div\)
3,412 (BTU to kWh)
\(\times\)
⑤
\(c_e\): cost per kWh of heat from electricity ($/kWh)
The formula in words
①
Take the
\(Q\): heat needed (BTU)
②
divide it by
3,412 (BTU to kWh)
to turn it into kWh
③
multiply by the
\(c_g\): cost per kWh of heat from gas ($/kWh)
④
and you get the
\(C_g\): cost with gas ($)
⑤
Multiply the same kWh by the
\(c_e\): cost per kWh of heat from electricity ($/kWh)
⑥
and you get the
\(C_e\): cost with electricity ($)
(the gap between the two is the difference)
Quick example
When a household's daily hot water needs 34,694 BTU (64 gallons raised by 65°F), the cost with gas ($0.0597 per kWh of heat) and with a heat pump water heater ($0.17 ÷ 3 per kWh of heat) is
\(C_g\): cost with gas ($)
\(=\)
heat (34,694 BTU)
\(\div\)
3,412
\(\times\)
gas, per kWh of heat ($0.0597/kWh)
\(C_e\): cost with electricity ($)
\(=\)
heat (34,694 BTU)
\(\div\)
3,412
\(\times\)
electricity, per kWh of heat ($0.17 ÷ 3/kWh)
\(34{,}694 \div 3412 \times 0.0597 \approx 0.61\)
\(34{,}694 \div 3412 \times 0.17 \div 3 \approx 0.58\)
\(0.61 - 0.58 = 0.03\)
Key idea
Once you have the cost per kWh of heat, the rest is "heat needed (kWh) × price". If the heat is given in BTU, divide by 3,412 to turn it into kWh first.
The heat needed \(Q\) for heating water comes from the next formula, using the gallons and the temperature rise. For a water heater, a cooktop or space heating, once the heat needed is known, this formula tells you "what it costs with gas and what it costs with electricity". In this example, gas and a heat pump water heater come out almost the same (about 3 cents a day apart), while a standard electric water heater (COP 1) would cost about \(34{,}694 \div 3412 \times 0.17 \approx 1.73\) dollars a day.
Once you know which cost per kWh of heat is lower, the answer to "which is cheaper" is the same for any amount of heat (the heat multiplies both sides equally). Entering the heat tells you how big the difference actually is in dollars.
Heat needed to heat water
Standard notation
(the usual math form)
\(Q\)
\(=\)
\(V\)
\(\times\)
\(8.34\)
\(\times\)
\(\Delta T\)
In words
(symbols replaced with words)
④
\(Q\): heat needed (BTU)
\(=\)
①
\(V\): water (gal)
\(\times\)
②
8.34 (BTU to raise 1 gal of water by 1°F)
\(\times\)
③
\(\Delta T\): temperature rise (°F)
The formula in words
①
Take the
\(V\): water (gal)
②
multiply it by
8.34
(it takes 8.34 BTU to raise 1 gallon of water by 1°F)
③
multiply by the
\(\Delta T\): temperature rise (°F)
④
and you get the
\(Q\): heat needed (BTU)
Quick example
The heat needed to warm a household's daily hot water, 64 gallons, from 55°F to 120°F is
\(Q\): heat needed (BTU)
\(=\)
water (64 gal)
\(\times\)
8.34
\(\times\)
temperature rise (65°F)
\(64 \times 8.34 \times 65 = 34{,}694.4\)
Key idea
One gallon of water weighs about 8.34 pounds, and 1 BTU is the heat that warms 1 pound of water by 1°F. So warming 1 gallon by 1°F takes 8.34 BTU, and the heat needed is "gallons × 8.34 × degrees of rise". The 34,694 BTU in the example is \(34{,}694 \div 3412 \approx 10.17\) kWh, the same heat as running a resistance heater for about 10 kWh.
The temperature rise is "target temperature − incoming water temperature". Cold tap water changes with the season (around 70°F in summer and 40 to 50°F in winter in many places), so heating water in winter can take much more heat than in summer. This formula does not include the water heater's efficiency (that is handled in the first formula). The US Department of Energy recommends a water heater setting of 120°F, and an average household uses about 64 gallons of hot water a day.
You can compare the cost of gas and electricity by converting both to "the cost per kWh of heat". For gas, it is "price ($/therm) ÷ (heat content ÷ 3,412 × appliance efficiency)", and for electricity, "rate ($/kWh) ÷ COP". The cost of a given amount of heat is "heat (kWh) × each cost per kWh of heat", and the heat for heating water is "gallons × 8.34 × temperature rise (°F)" in BTU.
Symbols and terms
Symbols
| \(p_g\) | p sub g | The gas price - the price of one billing unit of gas ($ per therm, or per gallon for propane), the usage charge on your bill. \(p\) is for price, and the small \(g\) below the line is for gas. |
| \(H\) | H | The heat content - the heat released by burning one billing unit of gas (BTU per therm or per gallon), from "heating value". The standard values in this calculator are 100,000 BTU per therm of natural gas and 91,500 BTU per gallon of propane. |
| \(\eta\) | eta | The efficiency of the gas appliance - the share of the gas heat that actually goes into the water or the room. 80% is used as 0.8 in the calculation. The Greek letter eta is the usual symbol for efficiency in physics and engineering. |
| \(p_e\) | p sub e | The electricity rate - the price of 1 kWh ($/kWh). The small \(e\) below the line is for electricity. |
| \(\mathrm{COP}\) | C-O-P | The coefficient of performance - how many times the electricity used comes out as heat. It is 1 for resistance heaters and standard electric water heaters and about 3 for heat pump water heaters. |
| \(c_g\), \(c_e\) | small c sub g, small c sub e | The cost per kWh of heat ($/kWh). \(c\) is for cost, \(g\) for gas and \(e\) for electricity. They are lowercase to tell them apart from \(C_g\) and \(C_e\), the costs of a given amount of heat. |
| \(Q\) | Q | The heat needed (BTU). In physics, \(Q\) is the usual letter for an amount of heat (said to come from "quantity of heat"). |
| \(C_g\), \(C_e\) | capital C sub g, capital C sub e | The cost of getting the heat you need ($): \(C_g\) with gas, \(C_e\) with electricity. |
| \(V\) | V | The amount of water to heat (gal), from "volume". One gallon of water weighs about 8.34 pounds. |
| \(\Delta T\) | delta T | The temperature rise (°F). \(\Delta\) (delta) is the Greek letter for "change" or "difference", and \(T\) is for temperature. It is "target temperature − incoming water temperature". |
| 3,412 | three thousand four hundred twelve | The conversion constant 1 kWh = 3,412 BTU (more precisely 3,412.14). Divide BTU by 3,412 to get kWh, and multiply kWh by 3,412 to get BTU. In metric units the same role is played by 1 kWh = 3.6 MJ. |
| 8.34 | eight point three four | The heat (BTU) needed to raise 1 gallon of water by 1°F. One gallon of water weighs about 8.34 pounds, and 1 BTU raises 1 pound of water by 1°F. In metric units the specific heat of water is 4.186 kJ per kg per °C. |
Terms
| heat content | The heat released by burning a fuel. For natural gas it is 100,000 BTU per therm by definition (about 1,036 BTU per cubic foot, so about 103,600 BTU per ccf), and for propane about 91,500 BTU per gallon. The same "1 unit" of different fuels holds different amounts of heat, so comparing prices per unit alone does not tell you which is cheaper. |
| natural gas | Gas delivered to homes through underground pipes, mostly methane. In the US it is usually billed in therms (1 therm = 100,000 BTU), sometimes in ccf (100 cubic feet). The bill also has a fixed monthly charge that does not depend on use. |
| propane | Liquefied petroleum gas (LPG) delivered by truck to a tank at the home, mostly propane. It is sold by the gallon, and 1 gallon holds about 91,500 BTU. Its price per unit of heat is usually higher than natural gas, and prices vary a lot by supplier and season, so always calculate with the price on your own bill or quote. |
| efficiency | The share of the energy in the fuel or electricity that actually does the job (heats the water or the room). Gas water heaters are rated by UEF (about 0.6 to 0.7 for tank models, about 0.9 for tankless and condensing models), furnaces by AFUE (80 to 98%), and gas cooktops lose much of their heat around the pan (about 40%). |
| COP (coefficient of performance) | A number that shows how many times the electricity used comes out as heat. Appliances that turn electricity straight into heat (resistance heaters, standard electric water heaters) have a COP of 1. Heat pumps that move heat from the air (heat pump water heaters, heat pumps for space heating) have about 3 to 4. It changes with the outdoor and water temperatures and drops in winter. |
| heat pump | A system that does not "make" heat from electricity but collects heat from the air (or the ground) and "moves" it somewhere else. It pumps heat uphill the way a pump lifts water, hence the name. Moving heat takes less electricity than making it, so heat pumps give the same heat for less electricity than resistance heaters. |
| heat pump water heater | A water heater that uses a heat pump to take heat from the surrounding air and put it into the water. It uses about a third of the electricity of a standard electric water heater for the same hot water. Its efficiency rating (UEF) is often 3 to 4, which you can enter as the COP on this page. Federal tax credits and utility rebates for heat pump water heaters have been available in recent years. |
| electric water heater | A standard water heater that heats water directly with electric resistance elements. The electricity used turns into heat as is (COP = 1), so its cost per kWh of heat is the electricity rate itself. |
| BTU (British thermal unit) | A unit of heat used in the US. 1 BTU raises 1 pound of water by 1°F. 1 therm = 100,000 BTU and 1 kWh = 3,412 BTU, so dividing BTU by 3,412 gives the same heat in kWh. |
| kWh (kilowatt-hour) | The unit for an amount of electricity used. Using 1 kW (1,000 W) for 1 hour is 1 kWh, and electric bills are based on it. On this page it is also the common yardstick for an amount of heat (1 kWh of heat = 3,412 BTU). |
| specific heat | The heat needed to raise a fixed amount of a substance by 1 degree. For water it is 1 BTU per pound per °F (4.186 kJ per kg per °C), large among everyday substances (water warms and cools slowly). That is why heating water takes more energy than you might expect. |
| break-even gas price | The gas price ($ per therm or per gallon) at which gas and electricity cost exactly the same per kWh of heat. This page finds it as "electricity's cost per kWh of heat × the useful kWh in one unit of gas". If your gas price is below it, gas is cheaper per unit of heat under those conditions; if above it, electricity is cheaper. |
| usage charge | The part of a gas or electric bill that grows with the amount you use. This page compares only these prices per unit. |
| fixed charge | The part of a gas or electric bill you pay even if you use nothing (a monthly customer or service charge). It is not included in this comparison, so if you are thinking of dropping gas and going all-electric (or the other way around), consider the change in fixed charges separately. |
| condensing water heater | A gas water heater that also captures the heat in the water vapor of the exhaust, which older models let escape. Its efficiency rises to about 90 to 95%, so you can enter "95" in the efficiency field. Condensing gas furnaces work the same way (AFUE 90% or more). |
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.
| Multiplying and dividing decimals (Grades 5–6) |
|
| Percents and multiples (Grades 6–7) |
|
| Unit rates and unit conversion (Grades 6–8) |
|
| Energy and heat (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 cost per kWh of heat (gas)
| Heat content (BTU/therm) | 100000 |
| Gas appliance efficiency (%) | 80 |
| Gas price ($/therm) | 1.40 |
| Heat in 1 therm (kWh) | =B1/3412 |
| Cost per kWh of heat ($/kWh) | =B3/(B4*B2/100) |
Table to find the cost per kWh of heat (electricity)
| Electricity rate ($/kWh) | 0.17 |
| Electric appliance efficiency (COP) | 3 |
| Cost per kWh of heat ($/kWh) | =B1/B2 |
Table to find the cost of the heat you need and the difference
| Heat needed (BTU) | 34694 |
| Gas, cost per kWh of heat ($/kWh) | 0.0597 |
| Electricity, cost per kWh of heat ($/kWh) | =0.17/3 |
| Cost with gas ($) | =B1/3412*B2 |
| Cost with electricity ($) | =B1/3412*B3 |
| Difference ($) | =ABS(B4-B5) |
Table to find the heat needed to heat water
| Water (gal) | 64 |
| Temperature rise (°F) | 65 |
| Heat needed (BTU) | =B1*8.34*B2 |
After pasting, the upper cells in column B are your inputs and the formula cells are calculated automatically.
The first table is natural gas (100,000 BTU per therm) at 80% efficiency and $1.40 per therm: B4 shows about 29.31 (kWh) and B5 about 0.0597 ($/kWh). For propane, change B1 to 91500 and the price to, for example, 2.50.
The second table is $0.17 per kWh with a COP of 3 (a heat pump water heater): B3 shows about 0.0567 ($/kWh). For a standard electric water heater, set B2 to 1.
The third table is a household's daily hot water (34,694 BTU): B4 shows about 0.61, B5 about 0.58 and B6 the difference of about 0.03 (dollars). The fourth table is the heat to raise 64 gallons by 65°F: B3 shows 34694.4 (BTU).
The first table is natural gas (100,000 BTU per therm) at 80% efficiency and $1.40 per therm: B4 shows about 29.31 (kWh) and B5 about 0.0597 ($/kWh). For propane, change B1 to 91500 and the price to, for example, 2.50.
The second table is $0.17 per kWh with a COP of 3 (a heat pump water heater): B3 shows about 0.0567 ($/kWh). For a standard electric water heater, set B2 to 1.
The third table is a household's daily hot water (34,694 BTU): B4 shows about 0.61, B5 about 0.58 and B6 the difference of about 0.03 (dollars). The fourth table is the heat to raise 64 gallons by 65°F: B3 shows 34694.4 (BTU).
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 cost per kWh of heat (gas)
| Heat content (BTU/therm) | 100000 |
| Gas appliance efficiency (%) | 80 |
| Gas price ($/therm) | 1.40 |
| Heat in 1 therm (kWh) | =B1/3412 |
| Cost per kWh of heat ($/kWh) | =B3/(B4*B2/100) |
Table to find the cost per kWh of heat (electricity)
| Electricity rate ($/kWh) | 0.17 |
| Electric appliance efficiency (COP) | 3 |
| Cost per kWh of heat ($/kWh) | =B1/B2 |
Table to find the cost of the heat you need and the difference
| Heat needed (BTU) | 34694 |
| Gas, cost per kWh of heat ($/kWh) | 0.0597 |
| Electricity, cost per kWh of heat ($/kWh) | =0.17/3 |
| Cost with gas ($) | =B1/3412*B2 |
| Cost with electricity ($) | =B1/3412*B3 |
| Difference ($) | =ABS(B4-B5) |
Table to find the heat needed to heat water
| Water (gal) | 64 |
| Temperature rise (°F) | 65 |
| Heat needed (BTU) | =B1*8.34*B2 |
These formulas use only multiplication, division and ABS (absolute value), so the same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace column B with your own gas price and electricity rate.
How to calculate it in Python
gas_heat_btu_per_therm = 100000 # heat content (BTU per therm). Propane: about 91,500 BTU per gallon
gas_price_per_therm = 1.40 # gas price ($ per therm)
gas_efficiency = 0.8 # gas appliance efficiency (0.8 for 80%)
elec_price_per_kwh = 0.17 # electricity rate ($ per kWh)
cop = 3 # electric appliance efficiency (1 for resistance, about 3 for a heat pump water heater)
# Cost per kWh of heat (1 kWh = 3,412 BTU)
gas_kwh_per_therm = gas_heat_btu_per_therm / 3412 # heat in 1 therm (kWh)
gas_useful_kwh_per_therm = gas_kwh_per_therm * gas_efficiency # useful part after efficiency
gas_cost_per_kwh = gas_price_per_therm / gas_useful_kwh_per_therm # gas ($/kWh)
elec_cost_per_kwh = elec_price_per_kwh / cop # electricity ($/kWh)
print(f"1 therm = {gas_kwh_per_therm:.2f} kWh (useful {gas_useful_kwh_per_therm:.2f} kWh)")
print(f"Per kWh of heat: gas ${gas_cost_per_kwh:.4f} / electricity ${elec_cost_per_kwh:.4f}")
# Heat needed to heat water (BTU) and the cost of that heat
water_gallons = 64 # water (gal)
temp_rise_f = 65 # temperature rise (°F)
heat_btu = water_gallons * 8.34 * temp_rise_f # 8.34 BTU raises 1 gallon of water by 1°F
heat_kwh = heat_btu / 3412
gas_cost = heat_kwh * gas_cost_per_kwh
elec_cost = heat_kwh * elec_cost_per_kwh
print(f"Heat needed {heat_btu:,.0f} BTU ({heat_kwh:.2f} kWh)")
print(f"Cost: gas ${gas_cost:.2f} / electricity ${elec_cost:.2f} / difference ${abs(gas_cost - elec_cost):.2f}")
# Break-even gas price (where the cost per kWh of heat is equal)
break_even_gas_price = elec_cost_per_kwh * gas_useful_kwh_per_therm
print(f"Break-even gas price ${break_even_gas_price:.2f} per therm")
Runs with the standard library only. Change the heat content, prices, efficiency and COP at the top, and the gallons and temperature rise, to your own conditions and run it. If you only want to compare the cost per kWh of heat, the first half is enough.
How to write it in LaTeX and other math languages (copy and paste)
Cost per kWh of heat (gas)
c_g = p_g ÷ (H ÷ 3412 × η)
c_g = \frac{p_g}{\dfrac{H}{3412} \times \eta}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>c</mi><mi>g</mi></msub>
<mo>=</mo>
<mfrac>
<msub><mi>p</mi><mi>g</mi></msub>
<mrow>
<mfrac><mi>H</mi><mn>3412</mn></mfrac>
<mo>×</mo>
<mi>η</mi>
</mrow>
</mfrac>
</mrow>
</math>
c_g = p_g / (H / 3412 * eta)
gasCostPerKwh = gasPrice/(heatContent/3412*efficiency)
c_g := p_g/(H/3412*eta);
c_g = p_g/(H/3412*eta);
c_g = p_g/(H/3412×η)
Cost per kWh of heat (electricity)
c_e = p_e ÷ COP
c_e = \frac{p_e}{\mathrm{COP}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>c</mi><mi>e</mi></msub>
<mo>=</mo>
<mfrac><msub><mi>p</mi><mi>e</mi></msub><mi mathvariant="normal">COP</mi></mfrac>
</mrow>
</math>
c_e = p_e / COP
elecCostPerKwh = elecPrice/cop
c_e := p_e/COP;
c_e = p_e/COP;
c_e = p_e/COP
Cost of the heat you need, and the difference
C_g = Q ÷ 3412 × c_g, C_e = Q ÷ 3412 × c_e
C_g = \frac{Q}{3412} \times c_g, \quad C_e = \frac{Q}{3412} \times c_e
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>C</mi><mi>g</mi></msub>
<mo>=</mo>
<mfrac><mi>Q</mi><mn>3412</mn></mfrac>
<mo>×</mo>
<msub><mi>c</mi><mi>g</mi></msub>
<mo>,</mo>
<msub><mi>C</mi><mi>e</mi></msub>
<mo>=</mo>
<mfrac><mi>Q</mi><mn>3412</mn></mfrac>
<mo>×</mo>
<msub><mi>c</mi><mi>e</mi></msub>
</mrow>
</math>
C_g = Q/3412 * c_g, C_e = Q/3412 * c_e
gasCost = heatBtu/3412*gasCostPerKwh; elecCost = heatBtu/3412*elecCostPerKwh
C_g := Q/3412*c_g; C_e := Q/3412*c_e;
C_g = Q/3412*c_g; C_e = Q/3412*c_e;
C_g = Q/3412×c_g, C_e = Q/3412×c_e
Heat needed to heat water
Q = V × 8.34 × ΔT
Q = V \times 8.34 \times \Delta T
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>Q</mi>
<mo>=</mo>
<mi>V</mi><mo>×</mo><mn>8.34</mn><mo>×</mo><mi>Δ</mi><mi>T</mi>
</mrow>
</math>
Q = V * 8.34 * Delta T
heatBtu = gallons*8.34*tempRise
Q := V*8.34*DeltaT;
Q = V*8.34*deltaT;
Q = V×8.34×ΔT
How to have ChatGPT do the calculation
You are an assistant for comparing the cost of gas and electricity. 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). Conditions: natural gas at 100,000 BTU per therm and $1.40 per therm, gas water heater efficiency 80%. Electricity at $0.17 per kWh, heat pump water heater COP 3. Use 1 kWh = 3,412 BTU. 1. Turn the heat in 1 therm into kWh (heat content ÷ 3,412) and find the useful part after efficiency. 2. Find the cost per kWh of heat for gas (price ÷ useful kWh) and for electricity (rate ÷ COP). 3. Find the heat needed to raise 64 gallons of water by 65°F (gallons × 8.34 × temperature rise, in BTU), and the cost of that heat with gas and with electricity, and the difference. 4. Find the gas price at which gas and electricity cost the same per kWh of heat (the break-even price). Show the formulas you used and the numbers from the execution result. When you say which is cheaper, state that it is "under these conditions".
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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