Dimensional Formula and Dimensional Equation (Difference)
Physics · Units And Measurements · NEET
A dimensional formula is the bare expression that shows the powers of the base quantities in a physical quantity, like [M L^-1 T^-2] for stress. A dimensional equation is that same formula placed on the right side of an equals sign with the quantity in square brackets on the left, like [stress] = [M L^-1 T^-2]. Memory hook: formula is the "answer", equation is "quantity = answer".
The dimensional formula is only the bracketed expression [M L² T⁻²]. Adding the quantity in brackets and an equals sign, [E] = [M L² T⁻²], makes it a dimensional equation.
Your doubts, answered
Are a dimensional formula and a dimensional equation the same thing?
No, but they are very close. The dimensional formula is only the expression, for example [M L^2 T^-2] for energy. The dimensional equation writes the quantity equal to that expression, for example [E] = [M L^2 T^-2]. So the equation is the formula plus the left side [quantity] and the equals sign. In NEET most questions ask for the dimensional formula, so you usually just write the expression.
Why do we put square brackets around the quantity, like [E] or [v]?
The square brackets mean 'the dimensions of'. So [v] is read as 'the dimensions of velocity'. This tells the reader you are talking about dimensions, not the actual value with a number and unit. Without the brackets, v = L T^-1 would look wrong because velocity has a value like 5 m/s, but [v] = [L T^-1] is correct because it only shows the dimensions.
What does M^0 L^3 T^0 mean when the powers are zero?
A zero power means that base quantity does not appear. M^0 = 1 and T^0 = 1, so volume [M^0 L^3 T^0] only depends on length, cubed. We often write it short as [L^3]. In NEET you can write either form. Showing M^0 and T^0 is safer in match-the-column questions because it makes clear that mass and time are truly absent.
How do I turn a dimensional formula into a dimensional equation?
Take the physical quantity, put its symbol inside square brackets on the left, add an equals sign, then write its dimensional formula on the right. Example: acceleration has dimensional formula [M^0 L T^-2]. Its dimensional equation is [a] = [M^0 L T^-2]. That is the only extra step.
⚠️ The NEET trap ✗ Writing v = [L T^-1] (no brackets on the quantity) or writing the dimensional formula with an equals sign and calling it the formula. ✓ The dimensional formula is just [M^0 L T^-1]. The dimensional equation is [v] = [M^0 L T^-1], with the quantity inside brackets and an equals sign. 🧠 Formula = expression only. Equation = quantity in brackets, then equals, then the expression.
Real NEET questions
2020
Dimensions of stress are:
A · [M L^0 T^-2]
B · [M L^-1 T^-2] ✓
C · [M L T^-2]
D · [M L^2 T^-2]
Solution: Step 1: Stress = Force / Area. Step 2: Dimensional formula of force = [M L T^-2]. Step 3: Dimensional formula of area = [L^2]. Step 4: Divide: [M L T^-2] / [L^2] = [M L^(1-2) T^-2] = [M L^-1 T^-2]. So the dimensional formula of stress is [M L^-1 T^-2], and its dimensional equation is [stress] = [M L^-1 T^-2]. Answer: B.
Solved Units And Measurements NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the dimensional formula of speed or velocity?
It is [M^0 L T^-1], because speed = distance / time = length / time. The dimensional equation is [v] = [M^0 L T^-1].
Which does NEET usually ask for, the formula or the equation?
Almost always the dimensional formula, that is the expression like [M L^-1 T^-2]. The word 'equation' appears mostly in theory or match-the-column questions, so just know that it adds the [quantity] = part.
Can two different quantities share the same dimensional formula?
Yes. For example work and energy both have [M L^2 T^-2], and stress, pressure and Young's modulus all have [M L^-1 T^-2]. A shared dimensional formula does not make the quantities the same.
Is a dimensional formula the same as a unit?
No. The unit tells you the standard used, like m/s. The dimensional formula tells you the base-quantity powers, like [L T^-1]. Many units can map to one dimensional formula.
