# units conversion

Unit conversion is a fundamental process and widely applied in solving day-to-day problems and in solving many Physics exercises.

The conversion of units in Physics allows transforming the forms of representation of a quantity according to the need. Therefore, it is necessary to know the units established by the international system of units (SI) for each type of physical quantity.

**Conversion of units in Physics**

It is common that, when solving an exercise, it is necessary to carry out some conversions so that the informed units are **compatible** with each other. Thus, knowing the rules of conversion between units is **essential** to correctly develop exercises.

The international system of units relates some fundamental quantities of physics to their units. Look at some of these relationships:

Greatness |
Unit |

Length | m – meter |

Time | s – second |

Pasta | kg – kilogram |

Ampere | A – electric current |

mole | mole – number of mole |

candela | cd – candela |

All SI units have multiples and submultiples that are written using SI prefixes . Some of the SI prefixes are **k** (kilo – 10³), **c** (centi – 10 ^{-2} ), **M** (mega – 10 ^{6} ), **m** (milli – 10 ^{-3} ), among others.

**Conversion of length units**

The unit of **length** in the international system is **meter. **In this system, meter is defined from the speed of light, that is, it is the space traveled by light during a time interval of 1/299,792,458 s.

There are several units of **length** derived from the meter that are written using prefixes. Check the table below:

prefixed unit |
Correspondent in meter |

1 μm – micrometer |
0.000001 m |

1mm – millimeter |
0.001 m |

1 dm – decimeter |
0.1 m |

1 dam – dekameter |
10.0 m |

1 hm – hectometer |
100.0 m |

1 km – kilometer |
1000.0 m |

We can perform the conversion between these units of length through the following process:

for each subsequent unit between km and mm, we divide or multiply by 10 according to the desired transformation.

**Examples** :

**1 km** = 1 x 10 **hm** = 10 **hm**

**1 hm** = 1 x 10 x 10 **dam** = 10 **m**

**1 mm =** 1/10 **cm** = 0.1 **cm**

In addition to the SI units of length, there are several known but less commonly used units. Below are some units of length and their relation to meter:

Unit |
relationship with meter |

1 inch | 0.0254 m |

1 foot | 0.3048 m |

1 yard | 0.91 m |

1 mile | 1,609.34 m |

1 league | 4828.032 m |

To convert any measure from a league to a meter, simply multiply the value informed by the **corresponding** value of that unit in meter. For example:

**2.5 ****miles** = 2.5 x 1609.34 = 4023.36 **m**

**Conversion of area units**

The units of area of the international system of units and their **derivatives** can be easily transformed in a similar way to that used for the transformation of units of distance. Watch:

We can convert SI area measurements into other SI area measurements. In this case, we simply **multiply** or **divide** its value by **10** ² (100) as many times as necessary. For example:

**1 km²** = 1 x 100 **hm²** = 100 **hm²**

**1 hm²** = 1 x 100 x 100 **m²** = 10,000 **m²**

**1 mm²** = 1/100/100 **dm²** = 0.0001 **dm²**

There are some area units that are written in systems other than the SI. Check out some of them:

Unit |
Ratio with square meter (m²) |

1 hectare | 10000 m² |

1 acre | 4046, 86 m² |

1 square mile | 2,590,000 m² |

**Conversion of volume units**

In order to convert volumes into units of the international system, it is very simple, we just need to operate in a similar way to the transformations we do in meters, dividing or multiplying the value by the factor **10³** (1000) by the number of times that are necessary. Look at the figure below:

Check out some volume conversion examples:

1 **km** ³ = 1 x 1000 **hm** ³ = 1000 **hm** ³

1 **mm** ³ = 1 / 1000 / 1000 **dm** ³ = 0.000001 **dm** ³

**Conversion of time units**

The unit of time in the international system of units is **second** (s). Currently, second is defined as the time interval between 9,192,631,770 hyperfine transitions of the ground energy state of the **cesium** atom .

There are several units of time measurement, all of which can be related to the second. Look at the table below:

Unit |
Relationship to second(s) |

1 minute | 60 s |

1 hour | 3600 s |

1 day | 86,400 s |

1 year | 31,557,600.0 s |

**Conversion of speed units**

The most common speed unit conversion is the one that relates meters per second (m/s) to kilometers per hour (km/h). To perform this conversion, we simply multiply the speed by **3.6** if we want to convert it from meters per second to kilometers per hour. Look at the figure below:

Below are some examples of speed conversion:

**10 ****m/s** = 10 x 3.6 = **36 ****km/h**

**54 km/h =** 54/3.6 = **15 m/s**