# Background

### About physical units

When you hear a physical value like the speed of light or the fronta area of your car or even the height of your own body, the given value expresses a property or a state of something (or somebody).

A physical value consists of a number and a measurement unit:

- 6 feet (the height of a person)
- 20 miles per hour (the speed of a car)
- 2.5 gallons (the fuel in your car)

Actually, the physical value is the multiplication of the pure number and the belonging measurement unit. The measurement unit is a physical value too, having its own pure multiplication number and a measurement unit. There are some standardized base measurement units (Wikipedia: SI Base units) which are agreed internationally as ancestor of other derived units.

Symbol |
Name |
Quantity |

s |
second | time |

m |
metre | length |

kg |
kilogram | mass |

A |
ampere | electric current |

K |
kelvin | thermodynamic temperature |

mol |
mole | amount of substance |

cd |
candela | luminous intensity |

Derived units and any physical value can be expressed using these base units by multiplying/dividing with each other and with pure numbers.

Example:

The base unit of **length** is the **meter [m]**. Distance is the dimension (the art of physical value), its internationally agreed base unit is the well-known meter.

If I multiply length by length, I get a **surface or area** as art of the physical value. The measurement unit is accordingly [m*m] = [m^2] “square meter”. I can measure surfaces, cross sections, areas with this measurement unit.

When I multiply length by length and again by length, I get **volume**. Accordingly, the measurement unit for volume is [m*m*m] = [m^{3}] “cubic meter”. Although cubic meter is sometimes used in our daily life, it is more common to use “liter” (0.001 m^{3}) or gallon (0.00378541 m^{3}) instead, just because these are closer to our daily consumptions of drinks. Gallon, liter, m^{3 }and several other volume units (like “cubic light year” ?) can be translated into each other because they all express the same kind of physical meaning: volume (which is the 3^{rd} power of a length).

When I say “2.5 gallon equals 0.00946353 m^{3}“ I mean (as an engineer):

“if I multiply the number 2.5 with the meaning of gallon I get the same physical volume as when I would multiply the number 0.00946353 with the meaning of meter 3 times after each other” (to get to the 3^{rd} power of meter).

On the other hand, you **cannot simply convert gallon into hours** because they belong to different dimensions (volume vs time). The question “how many gallons is one hour?” makes not much sense because they are **not compatible**, you cannot give any well-defined answer.

Luckily, you are allowed to “play” with measurement units as far as you multiply or divide them with each other. Having some luck, you can find a meaning to the resulting derived dimensions and belonging measurement units.

Let us see some examples:

- Length divided by time is speed (m/s, miles per hour,…)
- Length divided by time and again divided by time is acceleration (m/s
^{2}or our famous G-force /9.80665 m/s^{2}/) - Acceleration (which itself is length/time
^{2}) multiplied with mass results force (we in Europe like to measure it in Newtons [kg*m/s^{2}])

Playing further: when I divide force with the square of length (which is area or surface) I get pressure. Pressure is finally mass divided by length divided by square of time. Depending on where you live you might use the unit of Pascal [kg/m/s^{2}] or Bar [100000 Pascal] or Psi (“pounds per square inch” = 6894.76 Pascal).

Now you might feel tired. **No worry, DockCalc is made for you**: it takes over the hurdle of all those conversions, so you can concentrate on your core topic.

Have Fun with **DockCalc**!