Joule Calculator

What one joule buys you

A joule is the energy it takes to push with a force of one newton over a distance of one meter, which is close to lifting a small apple from the floor to a table. The apple weighs about 0.1 kg, gravity pulls with 9.81 newtons per kilogram, and lifting it one meter costs 0.1 x 9.81 x 1 = 0.98 J. That is the scale of the unit: one joule is a wink of energy, and almost everything worth measuring needs thousands or millions of them.

The joule connects directly to power, because power is energy per second. One watt equals one joule per second, so a 10 W LED night light draws 10 joules every second it runs, and a 900 W space heater draws 900 joules each second. Run a watt for an hour and you have 3,600 joules, which is one watt hour. A kilowatt hour is a thousand of those.

Because the joule is the SI unit of energy (defined by the BIPM in the SI Brochure), every other energy unit on this page has an exact or measured value in joules. That makes the joule the hub: to convert anything to anything, go through joules.

The conversion factors you will use

Here are the factors, and where each unit shows up. The calorie value is the thermochemical calorie, exactly 4.184 J by definition per the NIST Guide to the SI (SP 811). The electronvolt is exact at 1.602176634 x 10^-19 J per the NIST CODATA 2022 constants.

The calculator applies exactly these factors. Type 4184 into the box with joules selected and you get 1 kcal, 4.184 kJ, 3.97 BTU and 0.0012 kWh back, all from the one number. The BTU used here is the International Table value of 1,055.06 J; NIST also lists a thermochemical BTU of 1,054.35 J, about 0.07 percent smaller, and the difference never matters for a household number.

Calories on a food label are kilocalories

A small calorie raises one gram of water by one degree C. Nobody measures food that way, because the amounts would be enormous. A food Calorie, written with a capital C, is one thousand small calories, in other words a kilocalorie: 1 Cal = 4,184 J. When the label on a granola bar says 190 Calories, that is 190 x 4,184 = 794,960 J.

This double meaning trips people up in both directions. Chemists read cal as the small unit, labels mean the big one, and the factor between them is 1,000. If a page quotes a food value in kJ, divide by 4.184 to get the kcal that matches a US label: a 1,046 kJ snack is 1,046 / 4.184 = 250 kcal.

A full day of eating gives a feel for the scale. A 2,000 Calorie day is 2,000 x 4,184 = 8,368,000 J, about 8.4 megajoules. Your body spends that across 86,400 seconds, which averages out to about 97 joules per second, close to the draw of a bright old-fashioned light bulb running around the clock.

BTU and kWh, the units on your bills

A BTU, the unit on heaters and air conditioners, is the energy to raise one pound of water by one degree F, which comes to 1,055.06 J. A window air conditioner rated at 6,000 BTU per hour moves 6,000 x 1,055.06 = 6,330,360 J of heat each hour. Space heaters and grills use the same label, and it always refers to energy per hour, not energy.

The kilowatt hour is what the utility bills. One kWh is 3,600,000 J by definition: a thousand watts for 3,600 seconds. A 900 W space heater left on for 5 hours uses 900 x 5 = 4,500 Wh, which is 4.5 kWh, or 4.5 x 3,600,000 = 16,200,000 J. At a typical 17 cents per kWh, that evening costs 4.5 x 17 = 76.5 cents.

Everyday energy, side by side:

Notice the spread: the heater evening is 1,500 times the LED hour, and the mug of tea sits between them. The EIA energy units explainer uses the same factors when it compares heating fuels in BTU.

Electronvolts and the tiny end of the scale

Single atoms carry energies far too small to count in joules without trailing zeros, so physics borrows the electronvolt. One eV is the energy one electron gains crossing a potential difference of one volt. Since the 2019 SI redefinition the electronvolt is tied to the elementary charge and equals exactly 1.602176634 x 10^-19 J (NIST CODATA 2022).

The link to batteries is direct. A 1.5 V AA cell pushes each electron through 1.5 volts, so each electron that crosses picks up 1.5 x 1.602176634 x 10^-19 = 2.4 x 10^-19 J. A cell delivering a coulomb of charge hands over 1.5 J, and a full AA battery moves a few thousand coulombs, which is why the whole cell adds up to about 3 Wh, or 3 x 3,600 = 10,800 J.

The calculator shows the eV line so you can see the scale jump: 4,184 J, one food Calorie, is about 2.6 x 10^22 electronvolts. Same energy, twenty-two orders of magnitude apart in the units people happen to use.

What everyday energy costs in cents

Utilities bill in kWh, so the fastest route from joules to money is: joules divided by 3,600,000 gives kWh, then multiply by your price per kWh. The US average sits near 17 cents per kWh (EIA, 2025 data); check your bill for your own number, because states range from under 12 to over 30 cents.

The pattern worth keeping: lighting and charging cost pennies, heat costs dimes. Anything that makes warmth, like a heater, a dryer or an oven, pulls a kilowatt or more for hours, and that is where a bill grows. The widget's appliance line does this arithmetic for any watts, hours and price you enter.

Worked examples from daily life

A mug of tea. Half a liter of water, from 20 C to a boil, needs mass x specific heat x temperature change: 0.5 x 4.184 x 80 = 167.4 kJ, or 167,360 J. In other units that is 40 kcal, 158.63 BTU or 0.0465 kWh, about 0.8 cents of electricity. Enter 167,360 J in the calculator and it returns exactly those numbers.

A fired bullet. Kinetic energy is half mass times speed squared. A 9 g round at 350 m/s carries 0.5 x 0.009 x 350 x 350 = 551 J. All of that in 9 grams, at the speed of sound: energy depends on velocity squared, which is why fast small things can carry as much as slow heavy ones.

A mile run. A runner burns roughly 100 kcal per mile, and 100 x 4,184 = 418,400 J. A 5 mile jog is about 2.1 million joules, which is less than the space heater evening in the table above, a fact runners find either humbling or liberating.

A charged battery. An alkaline AA stores about 3 Wh, which is 3 x 3,600 = 10,800 J. Ten of them in a flashlight pack hold roughly the energy in half a mug of hot water, which says something about both batteries and hot water.

Why the meter and the label disagree

Rated is not delivered. A 900 W heater draws 900 W at the outlet, but a kettle rated 1,500 W puts most of its joules into water and some into the air. A boiling job that needs 167,360 J on paper takes more from the wall, because kettles run around 80 to 90 percent efficient. Plan on adding 10 to 25 percent for heat tasks.

Duty cycles. A refrigerator rated 150 W does not run 24 hours straight; it cycles on perhaps a third of the time, so its real daily use is closer to 150 x 24 / 3 = 1,200 Wh than to 3,600 Wh. Heaters with thermostats do the same. The calculator assumes you run the appliance flat out for the hours you enter.

Rounded labels. Food labels round Calories to whole numbers, so a snack listing 250 Calories carries 1,046,000 J only on paper. BTU definitions also differ by a whisker, as noted above. None of this moves a household total by much.

Where the factors come from. The calorie and BTU factors here follow the NIST Guide to the SI, appendix B, and the electronvolt comes from the NIST CODATA 2022 constants list. The kWh is exact by definition: a kilowatt is a thousand joules per second, an hour is 3,600 seconds, and 1,000 x 3,600 = 3,600,000.