# What is the cost of converting one gram of mass into pure energy?

# $$ E = mc^2$$

Using the [SI system](https://en.wikipedia.org/wiki/SI_base_unit) of units:

[Physical quantity](https://en.wikipedia.org/wiki/Physical_quantity)|[Unit of measurement](https://en.wikipedia.org/wiki/Unit_of_measurement)|Value
:---:|:---:|---:
E - energy| J - joule| x
m - mass| kg - kilogram|**0.001**
c - [speed of light in vacuum](https://en.wikipedia.org/wiki/Speed_of_light)| $\frac{m}{s}$ - metres per second|**300,000,000**

:::info
The speed of light in vacuum, commonly denoted c, is a universal physical constant that is exactly equal to 299,792,458 metres per second (approximately 300,000 kilometres per second)
:::

$$E=0.001\,kg \cdot\left( {300\,000\,000\,{\frac{m}{s}}}\right)^2 =$$

$$=0,001\,kg \cdot\left( {90\,\cdot10^{15}\,{\frac{m^2}{s^2}}}\right)= {90 \cdot 10^{12}}\,\,kg\,\frac{m^2}{s^2}\,\,\left(J\right)\,\,\left(\left(Ws\right)\right)=$$

$$=90\,\cdot 10^{12}\,Ws=\frac{90\,\cdot 10^{12}}{3\,600}\,Wh= 25\,\cdot 10^9\,Wh= 25\,GWh$$

## $$1\,gram\,=\,25\,GWh$$
$$1\,kg\,=\,25\,TWh$$