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
