Units and Dimensions Formulas

Units and dimensions formulas and measurements in SI or CGS systems in science are recommended by the International Union of Pure and Applied Chemistry (IUPAC). In the standard unit system or SI measurement system, we used the seven base units of physical quantities for analysis, measurement, and conversion. We generally use units and dimensions of mass, length, and time for measurement and conversion of force, density, energy, work, heat capacity, pressure, surface tension, etc. Therefore, these physical quantities can be derived from base units or dimensions data. The SI unit of luminous intensity or candela is not needed in physics or chemistry learning but it is included only for the sake of completeness.

International System of Units

International unit systems or simply SI systems of units are generally used for the measurement and study of most types of physical quantities. For the measurement of wavelengths or wavenumber in the electromagnetic spectrum, we used commonly the CGS system.

According to the International Union of Pure and Applied Chemistry (IUPAC), the seven base physical quantities are length, mass, time, electric power, thermodynamics temperature, amount of substance, and luminous intensity.

SI Measurement System

From these basic fundamental units and dimensions data, we derived the unit and dimension of activation energy, concentration, density, enthalpy, entropy, force, free energy function, the specific heat of gas, solid substances, etc.

Definition of Units of Measurement

Meter

A meter is the SI unit of length. A meter is the length of the path traveled by light in a vacuum during a time interval of 1/299792458 seconds.

Kilogram

The kilogram is the SI unit of mass. It is the weight of the platinum-iridium polished cylinder which is kept at the International Bureau of Weights and Measures in a suburb of Paris, France. Platinum-iridium alloy is chosen due to its durability and resistance to corrosion.

Second

The second is the duration of 9192631770 periods of the radiation corresponding to the transition between two hyperfine levels of the f-block element cesium-133 atom in the ground state.

Ampere

Ampere is that constant current folwing if we maintained two straight parallel conductors of infinite length which are placed one meter apart in a vacuum with negligible cross-section. The force produced between these two conductors is equal to 2 × 10⁻⁷ newtons per meter.

Kelvin Temperature

Kelvin is the SI unit of temperature. It is the fraction of 1/273.16 of the thermodynamic temperature of the triple point of the water.

Mole

Mole or simply mol is the SI unit of the amount of substances. It is the amount of substance in a system that contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12.

Candela

The candela is the unit of luminous intensity. Candela means the direction of a source that emits monochromatic radiation of frequency 540 × 10¹² hertz. The radiant intensity in that direction is 1/683 watt per steradian.

Unit Conversion Table

The below measurement table or chart is used to define the multiple and submultiple prefixes for unit conversion with the Roman symbol.

Derived Units Examples

Unit of Force

The SI unit of force is Newton and it can be derived from Newton’s second law of motion. From Newton’s second law of motion,

Force (F) = mass (M) × acceleration (F)

Again, acceleration = velocity/time
= length/time², where velocity = length/time

According to the above equation or formula, the CGS unit of force = g cm s⁻² or simply dyne and the SI unit of force = Kg m s⁻² or simply newton.

Dimension of Force

According to the dimension of length, mass, and time, the derived dimension of force = [M L T ⁻²].

Relation Between Newton and Dyne

According to the definition of newton,

1 Newton = (1 kg × 1 m)/(1 s)²

Again, 1 kg = 10³ g, and 1 m = 10² cm

Therefore, 1 Newton = (10³ g × 10² m)/(1 s)²
=10⁵ g cm s⁻² = 10⁵ dyne

Unit of Work and Energy

According to the definition of work,

The unit of work = unit of force × unit of displacement

Therefore, the CGS unit of work = g cm² s⁻² or simply erg. The SI unit of work = kg m² s⁻² or simply joule.

Dimension of Work

According to the definition,

The dimension of work = dimension of force × dimension of length = [M L T⁻²] × [L] = [M L² T⁻²].

Joule to erg Conversion

From the definition of joule,

1 Joule = 1 kg × (1 m)²/(1 s)²
Therefore, 1 Joule = 10³ g × (10² cm)²/(1 s)²
=10⁷ g cm² s⁻² = 10⁵ erg

Unit of Energy

The ability to do work is termed energy. Therefore, the SI unit of energy is the joule, and the CGS unit of energy is erg. The unit of the different forms of energy like kinetic energy, potential, mechanical, internal, electromagnetic, and surface energy is the same.

Unit of Heat Energy

Heat is another form of energy for the production of work. It is different from energy because all the other forms of energy are completely converted into work but heat is not wholly converted into work. The unit and dimension of heat and energy are identical. The SI unit of heat joule.

Unit of Power

The rate at which energy is transferred or converted is called power. Therefore, the SI unit of power = energy/time. From the above formula, the SI unit of power is joule/s or watt in honor of Scottish inventor James Watt.

SI Units Table

Important Topics