The International System of Units, also known as the SI units (*Système International d’unités*) is a coherent system of units of measurement comprising seven **base** units and multiple further **derived** units. This content is one of the more obscure topics of the primary FRCA exam, however as with many things, remains highly examinable in both the written MCQ and OSCE/VIVA component.

Here on TeachMeAnaesthetics, we aim to cover the absolute key details of high yield exam topics, which can then be supplemented with further reading as needed.

In this short article, we will discuss the various SI units together with key definitions.

## The Base SI Units

Seven base units exist. These are the building blocks from which all other units of measurement may be derived. Each one of these seven base units has a definition which is based upon an unchangeable and fixed point of reference.

*For the interested reader please follow link for the 7 SI defining constants: https://www.bipm.org/en/measurement-units/si-defining-constants)*

Various acronyms exist which are designed to help memorise these units, the most common of which is **SMMACKK**.

**Seconds**, s (SI unit of time)**Moles**, mol (SI unit of amount of substance in a sample of matter)**Metres**, m (SI unit of distance)**Amperes**, A (SI unit of electrical current)**Candela**, cd (SI unit of luminous intensity)**Kelvin**, K (SI unit of temperature)**Kilogram**, kg (SI unit of mass)

### Definitions

Unfortunately, you may be expected to recall the following definitions of the base SI units. In certain books written prior to the update to these definitions in 2018, you may find different definitions.

Here are the most recent definitions:

- 1
**second**is the duration of a certain number of oscillations of a caesium-133 atom. - 1
**mole**is the amount of a substance which contains the same number of particles as 12g of carbon-12 (12g, or 0.012kg, is the molar mass of carbon-12) i.e. containing the same number of atoms as Avogadro’s constant. - 1
**metre**is the distance travelled by light in a vacuum in 1/(3 x 10^{8}) seconds. - 1
**ampere**is the flow of 1.60×10^{−19} times the elementary charge*e*per second. - 1
**candela**is the luminous intensity, in a given direction, of a source that emitting monochromatic light at a specific frequency. - 1
**Kelvin**is defined by taking the fixed numerical value of the Boltzmann constant (k) to be 1.380 649 ×10^{−23}when expressed in the unit J K^{−1}. (An easier definition is 1/273.16 of the temperature of the triple point of water) - 1
**kilogram**is defined by taking the fixed numerical value of the Planck constant*h*to be 6.626 070 15 x 10^{–34}when expressed in the unit J s, which is equal to kg m^{2}s^{–1}. (An easier definition is the mass of the prototype kilogram in Sèvres, France) (https://www.bipm.org/en/mass-metrology/ipk).

## The Derived SI Units

Derived SI units may be thought of as a composite of one or more **base units.**

The most simple example of a derived unit is area. Area is expressed as the product of two distances e.g. length x width and as such the **derived unit** of area is the square of the base unit for length i.e. m².

Some other common derived units are listed below:

Area | length x width | m² |

Volume | length x width x height | m³ |

Velocity | distance / time | m/s |

Density | mass / volume | kg/m³ |

Concentration | amount / volume | mol/m³ |

## The Eponymous/Named SI Units

Certain derived SI units are given special units. For example, the SI unit of force is the Newton, N.

An exam question may ask you to express this unit in terms of base units. To do this, it is necessary to know the relevant formula.

As an example, we know that **force** (N) = **mass** (kg) x **acceleration** (m/s²)

We can then see that in terms of units, N = kg x m/s².

Therefore 1 N = 1 kg.m/s².

Other named units include:

Measure of |
Unit |
Expressed in other units |
Expressed in base units |

Electrical charge | Coulomb (C) | – | A.s |

Pressure | Pascal (Pa) | N/m² | kg.m^{-1}.s^{-2} |

Energy | Joule (J) | N.m | kg.m².s^{-2} |

Work | Watt (W) | J/s | kg.m².s^{-3} |

Frequency | Hertz (Hz) | – | s^{-1} |

## Prefixes

Often the SI units are an inappropriate magnitude to describe a quantity. e.g. atmospheric pressure is approximately 101’000 Pa. As such we can use prefixes (multiples of base 10) to describe these more easily.

- Tera (T) = 10
^{12} - Giga (G) = 10
^{9} - Mega (M) = 10
^{6} - Kilo (k) = 10
^{3} - Hecto (h) = 10
^{2} - Deca (da) = 10
^{1} - Deci (d) = 10
^{-1} - Centi (c) = 10
^{-2} - Milli (m) = 10
^{-3} - Micro (μ) = 10
^{-6} - Nano (n) = 10
^{-9} - Pico (p) = 10
^{-12}

101,000 Pa is therefore better expressed as 101 kPa.

## Suggested Reading

Chapter 51. Standard International Units. The Primary FRCA structured oral examination Study Guide 1. 2nd edition. Wijayasiri and McCombe. 2016.

Section 1 – Mathematical Principles – The SI Units. Physics, Pharmacology and Physiology for Anaesthetists. Key Concepts for the FRCA. 2nd edition. Cross and Plunkett. 2014.

Website of the National Institute of Standards and Technology: https://www.bipm.org/en/measurement-units/si-base-units