A Guide to Units and Prefixes in Electronics

When writing specifications, numerical values are often expressed using units. However, numbers with many digits can be difficult to read. To address this, prefixes (also known as SI prefixes) are used to denote multiples or fractions of base units.

SI prefixes generally change in steps of $10^3$. Common examples include "kilo" (k), representing 1000 times, and "mega" (M), representing one million times. Conversely, "milli" (m) represents 1/1000. The following table lists the standard SI prefixes.

In specifications adhering to the SI unit system, these prefixes are standard. As indicated by the adoption years, new prefixes are added over time. For instance, the "exabyte" is already used in data storage, and the "zettabyte" is expected to become common in the near future as data volumes increase.

Note that in computer science, these prefixes traditionally have different values based on powers of 2 (binary). For example, a kilobyte often refers to 1,024 (2¹⁰) bytes rather than 1000 bytes, and a megabyte refers to 1,048,576 (2²⁰) bytes.

So far, we have explained the SI prefix, which is used in the SI unit system (although it may be used in some computer-related fields).

The SI system of units defines length as meters (m), weight as kilograms (kg), and time as seconds (s). Of course, these are the units used in dynamics, so other units are set for the field of electromagnetics such as batteries. By the way, most units have been changed to a new definition by 2019 so that they do not depend on artificial objects.

Length: meters (m)

Originally, the total circumference of the meridian of the earth was defined as 40,000 km, but now it is set by setting the value of the speed of light c in vacuum to be exactly 299,792,458 m/s.

The word "meter" is derived from the ancient Greek word "µέτρον καθολικóν (Metron Catholicon)". This was the origin of the Italian scientist Tito Livio Burtini coining the term "metro cattolico" which means "universal unit of measure".

Mass: kilogram (kg)

In 2019, the definition was changed to be based on a fixed value of the Planck constant (h). The kilogram is now defined by taking the fixed numerical value of the Planck constant h to be 6.62607015 × 10⁻³⁴ when expressed in the unit J⋅s, which is equal to kg⋅m²⋅s⁻¹.

Time: seconds (s)

Originally, 1/86400 of the length of the day was defined as 1s. It is now defined as a duration of 9,192,631,770 times the period of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the atom of cesium-133.

Frequency: Hertz (Hz)

The Hz used as the frequency of the wave is defined as the reciprocal of time (s). Hz = s^-1. In the past, there was a time when the unit "cycle per second (c/s)" was used.

The word "Hertz" comes from the German physicist Heinrich Rudolf Hertz, who contributed to the field of electromagnetism.

Current: Ampere (A)

The current that flows 1C (coulomb) charge per second is 1A. When written in the formula, 1A = 1C/s. The word "ampere" comes from André-Marie Ampère, a French physicist known for "Ampere's Law," which describes the relationship between electric current and magnetic fields.

Voltage: Volt (V)

When 1J of work is required to carry 1C of electric charge between two points of a conductor, the voltage between the two points is 1V. The formula is V = J/C.

The word "volt" comes from the Italian physicist Alessandro Volta (Il Conte Alessandro Giuseppe Antonio Anastasio Volta), known for his "Voltaic Batteries".

Resistance: Ohm (Ω)

The electrical resistance at which a voltage of 1A flows when a voltage of 1V is applied is 1 Ω. The formula is Ω = V/A.

The word "Ohm" comes from Georg Simon Ohm, a German physicist who discovered "Ohm's Law" on electrical resistance.

Capacitance: Farad (F)

Used for capacitors, 1 Farad is defined as the capacitance that stores a charge of 1 Coulomb (C) across a potential difference of 1 Volt (V). The relationship is expressed as F = C/V or F = A⋅s/V.

Named after Michael Faraday, a British physicist and chemist renowned for his contributions to electromagnetism and electrochemistry.

Inductance: Henry (H)

The Henry is the unit of inductance. It is defined as the inductance of a closed circuit (such as a coil) in which an electromotive force of 1 V is produced when the electric current varies uniformly at a rate of 1 A per second. (H = V⋅s/A).

Named after the American physicist Joseph Henry, who discovered electromagnetic induction independently around the same time as Faraday.

Basically, it will be described using these SI unit systems. However, some countries/regions and industries use other unit systems. For example, astronomy uses the cgs unit system (unit system represented by cm, g, s) in part, and the United States and the United Kingdom still use the Imperial system.

There are remnants of the cgs unit system here and there. For example, the unit of atmospheric pressure used in the weather forecast uses hectopascal (100 Pa) as a standard, but this was when the cgs unit system millibar (mb) was used in the past. A hectopascal is the same value as a millibar.

On the other hand, the imperial system uses inches (1 inch = about 2.54 cm), feet (1 foot = 12 inch = about 30.5 cm), and yards (1 yd = 3 feet = about 91.4 cm). It weighs pounds, previously slightly different from country to country, but was unified in 1958 and now weighs 0.45359237 kg per pound.

Mixing Imperial and SI units can lead to critical failures. A notable example is the 1999 loss of the Mars Climate Orbiter. The spacecraft disintegrated because the manufacturing team calculated engine thrust in Imperial units (pound-force), while the flight operations team used SI units (Newtons). This incident underscores the importance of clearly defining and standardizing units in engineering and control systems.