Know The Unit And Dimensions - Dimension Formula

dimensional formula units

Everything you measure has two components. Number (n) is the first, followed by a unit (u) (u). Q is a number that does not exist. For instance, an object's length is 40 cm. The unit picked has an inverse effect on the number, indicating the size of a physical quantity. 

A physical quantity's numerical value, n1u1, is equal to n2u2 if n1u1 is the physical quantity's numerical value. For instance, 2.8 m is equal to 280 cm, and 6.2 kg is equivalent to 6200 g. So, let's learn about units and Dimensional Formulas

Quantities Derived From The Fundamentals 


The fundamental quantities are those that are not reliant on other quantities. To quantify these basic values, we use the term "fundamental unit". C.G.S., M.K.S., F.P.S., and SI are the four systems of units. 

Derived quantities are those that are derived from fundamental quantities. These derived values are measured in units referred to as derived units. It is common knowledge that most SI units are employed in scientific investigations. Units in the SI are logically linked together. 

When the units of derived quantities are multiples or submultiples of specific fundamental units, it is considered a cohesive system of units—an M.K.S. Ampere (RMKSA) system developed by Professor Giorgi is a complete, cohesive, and rationalised version of the SI system. 

An inch is equivalent to the wavelength of Krypton-86's light in a vacuum, which is 1650763.73 times longer than a metre. A revised metre definition was agreed upon at the 17th General Assembly of the International System of Units in 1983. According to this definition, a metre is a distance travelled by light in a vacuum in 1/299, 792, 458 of a second. 

● An ounce of platinum-iridium alloy weighs one kilogramme, and it is stored in the International Bureau of Weights and Measures archive in Serves (a suburb of Paris). 

● When it comes to the transition between cesium-133's ground state's two hyperfine levels, 9192631770 periods constitute one second. 

● Two parallel conductors of infinite length and negligible cross-section, spaced one metre apart in vacuum, produce a force of 2 10-7 newtons per metre of measurement in each other, known as one ampere of current. Amperage 

● Kelvin is the name given to the percentage of the triple point of water's thermodynamic temperature that is 1/273.16 of a degree Celsius. 

● The intensity of light emitted perpendicular to the surface of a black substance with an area of 1/600000 m2 at platinum-solidifying temperature and pressure. 

● One candela is defined as 101325 Nm-2. 

● As many atoms in a mole as 12 10-3 kg of carbon-12 are considered one mole of a given chemical. 

Radian: A radian is an angle formed by an arc of a circle with a radius equal to the circle's centre radius. The coordinates of 57o17l45ll are represented by one radian. 

Steradian: A steradian is an angle formed by a sphere with a one-metre radius and one square metre surface area. 


Checking the relationship between two or more physical quantities by determining the dimensions of the physical quantities is known as dimensional analysis. It is possible to represent all quantities in the world as a function of these essential dimensions independent of numerical multiples and constants. 

The Formula For The Dimensions 

The Dimensional Formulas of a derived quantity is the statement that shows how many basic units must be increased to get one unit of the derived quantity. 

MaLbTc is the dimensional formula, and the exponents a, b, and c are the dimensions if Q is a derived quantity given by Q = MaLbTc. 

Dimensional Constants: What Do They Mean? 

Dimensional constants are physical quantities that have dimensions and a fixed value. For example, the gravitational constant (G), the Planck constant (h), the universal gas constant (R), and the vacuum light speed constant (C) are all examples of fundamental physical constants. 

Dimensionless Quantities: What Are They? 

A dimensionless quantity does not have a fixed value but does not have dimensions. Quantities have no dimensions or units, such as e, sin, cos, tan, etc. Several non-dimensional quantities have units associated with them, such as radian, the Joule's constant, and many more. 

When It Comes To Dimensional Variables, What Exactly Are They? 

Physical quantities with dimensions but no set value are referred to as dimensional variables. For example, velocity, acceleration, force, work, and power are all examples of quantitative measures of quantitative quantities. 

What Are The Dimensionally Inaccessible Variables? 

Variables without dimensions and fixed values are known as dimensionless variables. For example, the specific gravity, the refractive index, the coefficient of friction, the Poisson's ratio, etc., are some examples. 

The Law Of Dimensional Homogeneity 

There must be no ambiguity in the dimensions of any terms in a good equation for a relationship between physical quantities. There must be no more than one space between words separated by a comma or a dash. 

When the basic units of length, mass and time are L2, M2 and T2, the numerical value of a physical quantity Q may be expressed as n1 for L1, M1 and T1 and n2 for L2 and M2 for T2 if the dimensions of the physical quantity are a, b, and c. 


{{n} {2}}={{n} {1}} 

In this case, the left-hand side of the equation is the same as the right-hand side of the equation. It's best to start with the 

left [frac] bleft [frac] tleft [frac] t right [c] 


Dimensional Analysis Has Its Limits 

We cannot use this approach to determine dimensional quantities, and this approach does not provide the constant of proportionality. The two methods of discovering them are experimentation and theory. 

In the case of trigonometric, logarithmic, or exponential functions, you cannot use this procedure. 

Using this strategy for physical quantities that rely on more than three other physical variables will be challenging. 

The proportionality constant may have dimensions in certain instances, and such situations make it impossible to utilise this technology. 

We can't use this approach to get the expression if one side of the equation has physical quantities added or subtracted. 

The Importance Of The Preceding Insights 

● To quantify light's wavelength, scientists utilise the acronym unit of length. One is equivalent to 10-10 m in height. 

● Nuclear distances are measured in Fermi units. A Fermi is around 10-15 metres in length. 

● Astronomical distances are measured in light-years. 

● Distance travelled by light in one year (the "light year") is 9.4605 1015 m. 

● Astronomical unit = 1.5 1011 m mean solar-earth distance. 

● 3.0841016 metre = 3.26 light years 

● The scattering cross-section of collisions is measured in barns, which are units of area, and the area of one barn is around 10-28 square metres. 

● We may use both a clock and a metronome to measure the passing of time, and time is the only quantity with the same unit across all measurement systems. 

● Deca, and one 101 decimal ten to one 

● Hecta is 102 centimetres in length. 10-2 


Hence, we hope you get a clear idea about the formulas of units and dimensions from this article. Read thoroughly and practice to learn these dimension formulas correctly.

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