# Energy Conversion Calculator

Created by Davide Borchia
Last updated: Jul 05, 2022

Energy has many forms and many units: learn how to convert and calculate energy with different units with our energy conversions calculator.

• What are the most important energy measurement units;
• What is the joule;
• How to calculate the joule conversions (and the other way round);

Use our energy conversions calculator for your homework or simply curiosity! From the joules in a calorie to the energy corresponding to a kilogram of matter, we can help you!

## What is energy?

Energy is not an easy concept to grasp: usually, we describe it as the ability to perform work (in the physical meaning).

Energy has many forms. We can't list them all, but think of:

And so on. The most advantageous fact is that even considering the man faces of this quantity, we can measure it using the same units.

## How do we measure energy?

The measurement of energy depends on its form. While we can measure chemical energy with a thermometer, gravitational energy may be better suited to be measured by a scale. However, once the measurement is done, we can express the result in a set of units shared across all the various forms.

The International System of unties chose the joule, symbol $\text{J}$, to measure energy. A joule corresponds to the energy used to apply a force of $1\ \text{N}$ over the distance of $1\ \text{m}$.

From the joule, we can define many other units for the energy. In the next sections, we will analyze the most common one, and we will learn how to convert energy between those units: you can find all of the units we will explain in our energy conversions calculator!

## Energy measurement unit: the food calorie

In the food industry and chemistry, the energy contained in a food or a substance is easily measured using the calorie. A calorie corresponds to the amount of thermal energy required to increase the temperature of a mass of water equal to $1\ \text{g}$ by 1 Celsius degree, from a starting temperature of $14.5\ \degree\text{C}$, at a pressure of $1\ \text{atm}$. A calorie equals $4.184\ \text{J}$.

Again, this value is pretty small. A calorie is an energy associated with $0.26$ milligrams of sugar: that's why we commonly see the energy converted in kilocalories, equalling exactly $1000\ \text{cal}$.

This equality shows you how to calculate joules from calories:

$1\ \text{kcal} = 1,\!000\ \text{cal} = 4,\!186\ \text{J}$

And to calculate from joules to calories:

$1\ \text{J} = \frac{1}{4.186}\ \text{cal} = 0.239\ \text{cal}$

## Measuring bills: the kilowatt-hour

For the measurement of electricity (for example, the consumption of an appliance or the production of a power plant), we can use an energy measurement unit connected to power.

Power is a measurement of the rate of energy. In the SI, power is measured in watts. A watt is equal to a joule per second: you can easily see that we can calculate the joules from this definition, converting in energy again: the energy liberated by the power of a watt in a second, however, is relatively small.

The unit for energy was then defined as the amount of energy produced by a sustained power of $1000\ \text{W}=1\ \text{kW}$ in one hour: the kilowatt-hour, $\text{kWh}$. The energy conversion between joules and kilowatt-hours is:

\begin{align*} 1\ \text{kWh}&= 1,\!000\ \text{W}\cdot 1\ \text{h}\\ &= 1,\!000\ \text{W}\cdot 3,\!600\ \text{s} =\\ &=3,\!600,\!000\ \text{J} \end{align*}

The opposite conversion works better if we calculate the kilowatt-hours starting from the megajoule (a million joules). In this case, we have:

$1\ \text{MJ}=\frac{1}{3.6}\ \text{kWh} = 0.278\ \text{kWh}$

## How to convert energy between metric and imperial: the therm

Take a cube with sides $10 \text{ft}$ of natural gas: the energy it contains is one therm (symbol $\text{thm}$) is, approximately, equal to $100,000\ \text{BTU}$, the British thermal unit (imperial analog of the Joule: one BTU is the energy required to raise by one degree Fahrenheit the temperature of a pound of water).

This unit is useful when dealing with domestic consumption of gas or industrial processes: that's why we included it in our energy conversions calculator.

To convert joules in therm and vice versa, follow these rules:

\begin{align*} 1\ \text{J} = 9.48\cdot 10^{-9}\ \text{thm}\\ 1\ \text{thm}=105,\! 480,\! 400\ \text{J} \end{align*}

## How many joules in that bomb? Tons of TNT

What is more energetic than an explosion? A big explosion.

Scientists and engineers measure the energy released by an explosion with a relatable measurement unit: the TNT equivalent. The TNT equivalent is the energy associated with the detonation of a metric ton of ($1,000\ \text{kg}$). The conversion between joule and TNT equivalent is:

\begin{align*} 1\ \text{ton of TNT} &= 4.184\cdot 10^{-9}\ \text{J}\\ &=4.184\ \text{GJ}\\ 1\ \text{J}&=0.239\ \text{ton of TNT} \end{align*}

The TNT equivalent is mostly known for its use in the determination of the yield of nuclear explosions. The most powerful nuclear test ever conducted, the detonation of the Tsar Bomba released almost $50\ \text{Mt}$ equivalent: the energy of $50$ million tons of TNT at once. We truly have become death, the destroyers of worlds.

## Microscopic measurements unit of energy

In the field of particle physics or fundamental theory of matter, the joule stops being a handy unit and becomes rather difficult to manage. Physicists introduced the electronvolt, the energy acquired (or lost) by an electron whilst traveling across a potential difference of $1\ \text{V}$, regardless of the distance and other factors.

$1\ \text{eV} = 1\ e \cdot 1\ \text{V} = 1.60217 \cdot 10^{-19}\ \text{C} \cdot \text{V} = 1.60217\cdot 10^{-19} \ \text{J}$

As you can see, we inherited the order of magnitude of the electron charge in the SI. As for the opposite conversion, with the next equation you'll learn how to calculate from joules to electronvolts:

$1\ \text{J} = 6.2415 \cdot 10^{18}\ \text{eV}$

Other microscopic quantities that fit as useful energy measurement units are, rather unexpectedly, mass and length.

We need to thank Einstein for the discovery of the relation between mass and energy (or mass-energy equivalence). This fundamental property of physics that controls the nuclear reactions that power the stars, atomic weapons, and the ideal annihilation of matter and antimatter fits in three characters and a number, and everyone knows it:

$E = m\cdot c^2$

We can calculate the conversion of energy and mass just by knowing the value of $c$, the speed of light:

$c = 2.998 \cdot 10^{8}\ \text{m}/\text{s}$

Thus:

\begin{align*} 1\ \text{kg} &= 8.99\cdot 10^{16}\ \text{J}\\ 1\ \text{J}&=1.1127\cdot 10^{-17}\ \text{kg} \end{align*}

As you can see, joule and kilogram are not the best units for this kind of conversion. Scientists prefer to use the electronvolt and the mass of a particle (the electron, the proton, etc.). For example, this is the conversion between megaelectronvolt and electron masses:

$1\ \text{MeV} = 1.957\ \text{me}$

We can relate energy and length thanks to the relation between wavelength and energy described by Planck's equation. The relation is:

$E = h\cdot\nu = h\cdot \frac{c}{\lambda}$

Where you can see two fundamental constants of Nature:

• $h$, the Planck's constant; and
• $c$, the speed of light.

We can also describe the relationship between energy and temperature: in thermodynamics, we can often find the quantity $k_\text{B}\cdot T$, the product of the Boltzmann constant and the temperature.

This is the conversion between joule and kelvin:

\begin{align*} T &= \frac{E}{k_{\text{B}}} = \frac{1\ \text{J}}{1.3806 \cdot 10^{-23}\ \frac{\text{J}}{\text{K}}} \\ \\ &= 7.2432 \cdot10^{22}\ \text{K} \end{align*}
Davide Borchia
SI unit for energy
Joule
J
Big energies
Calorie
kcal
Watt-hour
kWh
Therm
therms
Ton of TNT
tons of TNT
Microscopic world
Electronovolt
eV
Temperature
K
Reciprocal length
cm
⁻¹
Mass
me
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