Cost Per Joule Calculator
Use this tool to calculate the cost of energy per single Joule. This helps compare the true efficiency and cost-effectiveness of different energy sources or devices.
Enter the total cost you paid for a specific amount of energy and that amount of energy precisely measured in Joules.
Enter Energy Cost and Amount
Understanding Cost Per Joule
What is Cost Per Joule?
Cost Per Joule is a metric that expresses the price paid for one unit of energy, where the unit is the Joule (J). The Joule is the standard international unit of energy. Calculating cost per Joule allows for a direct, apples-to-apples comparison of the cost-efficiency of different energy sources, devices, or services, regardless of how the energy was initially measured (e.g., kilowatt-hours, gallons of fuel, food calories).
How is it Calculated?
The calculation is simple:
Cost Per Joule = Total Cost / Total Energy (in Joules)
For example, if you paid $5 for 10,000,000 Joules of energy, the Cost Per Joule would be $5 / 10,000,000 J = $0.0000005 per Joule.
Why Use Joules?
While energy is often sold in units like kilowatt-hours (kWh) for electricity, cubic feet or liters for natural gas, or gallons for liquid fuels, the Joule is the fundamental unit in physics. Converting all energy measurements to Joules provides a universal basis for comparison. Using Cost Per Joule helps reveal which energy option delivers the most energy for the least money.
Common Conversions to Joules:
- 1 kilowatt-hour (kWh) = 3,600,000 Joules (3.6 MJ)
- 1 calorie (cal) ≈ 4.184 Joules
- 1 British Thermal Unit (BTU) ≈ 1055 Joules
- 1 therm (US) = 100,000 BTU ≈ 105,500,000 Joules (105.5 MJ)
- 1 gallon of gasoline ≈ 120,000,000 Joules (120 MJ)
- 1 cubic meter of natural gas ≈ 39,000,000 Joules (39 MJ) (varies by gas composition)
Cost Per Joule Examples
See how to calculate Cost Per Joule for different scenarios:
Example 1: Electricity Bill
Scenario: Your electricity bill shows usage of 500 kWh and a cost of $60.
1. Total Cost: $60
2. Total Energy (Joules): Convert kWh to Joules. 500 kWh * 3,600,000 J/kWh = 1,800,000,000 Joules.
3. Calculation: Cost Per Joule = $60 / 1,800,000,000 J
4. Result: Cost Per Joule ≈ $0.0000000333 per Joule.
Conclusion: Each Joule of electricity cost approximately $0.0000000333.
Example 2: Natural Gas Bill
Scenario: Your gas bill shows usage of 10 therms and a cost of $15.
1. Total Cost: $15
2. Total Energy (Joules): Convert therms to Joules. 10 therms * 105,500,000 J/therm = 1,055,000,000 Joules.
3. Calculation: Cost Per Joule = $15 / 1,055,000,000 J
4. Result: Cost Per Joule ≈ $0.0000000142 per Joule.
Conclusion: Each Joule of natural gas cost approximately $0.0000000142.
Example 3: Battery Energy Storage
Scenario: You buy a battery pack rated at 100 Wh for $25.
1. Total Cost: $25
2. Total Energy (Joules): Convert Watt-hours to Joules. 100 Wh = 0.1 kWh. 0.1 kWh * 3,600,000 J/kWh = 360,000 Joules.
3. Calculation: Cost Per Joule = $25 / 360,000 J
4. Result: Cost Per Joule ≈ $0.0000694 per Joule.
Conclusion: Energy stored in this battery cost approximately $0.0000694 per Joule (before losses). Note this is much higher than grid electricity/gas!
Example 4: Food Energy
Scenario: A snack bar costs $1 and contains 200 food Calories (kcal).
1. Total Cost: $1
2. Total Energy (Joules): Convert food Calories to Joules. 1 kcal = 1000 cal. 200 kcal * 1000 cal/kcal = 200,000 cal. 200,000 cal * 4.184 J/cal = 836,800 Joules.
3. Calculation: Cost Per Joule = $1 / 836,800 J
4. Result: Cost Per Joule ≈ $0.000001195 per Joule.
Conclusion: The energy from this snack bar costs roughly $0.0000012 per Joule.
Example 5: Comparing Fuels (Simplified)
Scenario: Propane costs $2.50 per gallon. 1 gallon of propane ≈ 90,000,000 Joules.
1. Total Cost: $2.50
2. Total Energy (Joules): 90,000,000 Joules.
3. Calculation: Cost Per Joule = $2.50 / 90,000,000 J
4. Result: Cost Per Joule ≈ $0.0000000278 per Joule.
Conclusion: Propane energy costs approximately $0.0000000278 per Joule.
Example 6: Another Electricity Scenario
Scenario: You paid £45 for 350 kWh of electricity.
1. Total Cost: 45 (implicitly £)
2. Total Energy (Joules): 350 kWh * 3,600,000 J/kWh = 1,260,000,000 Joules.
3. Calculation: Cost Per Joule = 45 / 1,260,000,000 J
4. Result: Cost Per Joule ≈ 0.0000000357 per Joule.
Conclusion: Each Joule cost approximately £0.0000000357.
Example 7: Wood Pellets
Scenario: A bag of wood pellets costs €5 and contains energy equivalent to about 70,000,000 Joules (approx. 20 kWh).
1. Total Cost: 5 (implicitly €)
2. Total Energy (Joules): 70,000,000 Joules.
3. Calculation: Cost Per Joule = 5 / 70,000,000 J
4. Result: Cost Per Joule ≈ 0.0000000714 per Joule.
Conclusion: Wood pellet energy costs around €0.0000000714 per Joule.
Example 8: Hydrogen Fuel (Simplified)
Scenario: You buy hydrogen fuel for a vehicle. 1 kg of hydrogen costs $10 and contains about 142,000,000 Joules of energy.
1. Total Cost: $10
2. Total Energy (Joules): 142,000,000 Joules.
3. Calculation: Cost Per Joule = $10 / 142,000,000 J
4. Result: Cost Per Joule ≈ $0.0000000704 per Joule.
Conclusion: Hydrogen energy costs around $0.0000000704 per Joule.
Example 9: Solar Panel Output (Hypothetical)
Scenario: Over a year, your solar panels generated 4,000 kWh of electricity. Let's say the *installed* cost of the system divided by its expected total lifetime energy output is $500 (very simplified long-term cost).
1. Total Cost (attributed): $500
2. Total Energy (Joules): 4,000 kWh * 3,600,000 J/kWh = 14,400,000,000 Joules.
3. Calculation: Cost Per Joule = $500 / 14,400,000,000 J
4. Result: Cost Per Joule ≈ $0.0000000347 per Joule.
Conclusion: The long-term cost per Joule from this solar system is hypothetically around $0.0000000347.
Example 10: Small Battery (e.g., AA)
Scenario: A disposable AA battery costs $1 and stores approximately 10,000 Joules (2700 mAh at 1.2V ≈ 3.24 Wh ≈ 11664 J).
1. Total Cost: $1
2. Total Energy (Joules): 10,000 Joules.
3. Calculation: Cost Per Joule = $1 / 10,000 J
4. Result: Cost Per Joule = $0.0001 per Joule.
Conclusion: Energy from a disposable AA battery is vastly more expensive per Joule ($0.0001) compared to grid energy (around $0.00000003 per Joule).
Frequently Asked Questions about Cost Per Joule
1. What does Cost Per Joule tell me?
It tells you the price you are paying for the smallest standard unit of energy. It's a way to standardize the cost comparison between different energy sources or energy-consuming activities.
2. Why is the Cost Per Joule number usually very small?
The Joule is a very small unit of energy. A typical household uses billions or trillions of Joules per year. So, the cost per single Joule will naturally be a very small fraction of a cent or other currency unit.
3. How do I convert my energy unit (like kWh or therms) to Joules?
You need conversion factors. Common ones are 1 kWh = 3,600,000 J and 1 therm ≈ 105,500,000 J. The educational section provides a few more.
4. Can I use this to compare the cost of heating with electricity vs. gas?
Absolutely. Convert the cost and energy used for both heating methods into Cost Per Joule. The method with the lower Cost Per Joule is the cheaper option *per unit of energy delivered*.
5. Does this calculator account for efficiency losses?
No, this calculator only uses the total cost and the total energy you input. If you input the energy *purchased* (e.g., energy in fuel bought), the result is the cost per Joule of purchased energy. If you can measure the energy *actually delivered or used* by a device (e.g., heat output from a furnace), you could use that energy figure to find the cost per Joule of *useful* energy, which implicitly accounts for the device's efficiency.
6. What currency should I use for the "Total Cost" input?
Use your local currency consistently. The resulting Cost Per Joule will be in that same currency per Joule (e.g., USD/Joule, EUR/Joule).
7. Can I use this for food energy?
Yes, if you can determine the cost of the food item and its energy content in Calories (kcal), you can convert the Calories to Joules (1 kcal ≈ 4184 J) and calculate the Cost Per Joule for food energy.
8. What are typical Cost Per Joule values?
They vary greatly depending on the energy source, location, and scale. Grid electricity and natural gas are generally among the cheapest per Joule, followed by liquid fuels. Stored energy (like in batteries) or highly processed energy (like food or small disposable batteries) is typically much more expensive per Joule.
9. Are there other units besides Joules I could use for comparison?
Yes, sometimes energy cost is compared using Cost Per kWh or Cost Per BTU. Cost Per Joule uses the base SI unit, making it universally applicable and easy to convert from *any* energy unit.
10. What happens if I enter zero energy?
Division by zero is not possible. The calculator requires a positive energy input to perform the calculation and will show an error if energy is zero or negative.
