Physics · Class 11 · Units and Measurements

Units, Dimensions and Errors for JEE

Everything you need for this topic on one page: the ideas, the formulas, the traps, and free lectures that explain it well.

Last updated: 26 October 2026

Direct answer

Every physical quantity has a unit and a dimensional formula in terms of M, L, T, I, K, mol and cd.

Every physical quantity has a unit and a dimensional formula in terms of M, L, T, I, K, mol and cd. Dimensional analysis checks equations and derives relations; error analysis tells you how measurement errors combine.

Key ideas

Units, Dimensions and Errors: what you must understand

SI base units: kg, m, s, A, K, mol, cd
Only like dimensions can be added or compared
Dimensional method cannot find dimensionless constants (like 2π)
Significant figures and least count decide reported precision

Formula sheet

Must-know formulas for Units, Dimensions and Errors

If Z = AᵖBᵠ/Cʳ, then ΔZ/Z = p·ΔA/A + q·ΔB/B + r·ΔC/C
Absolute error in a sum or difference: ΔZ = ΔA + ΔB
Vernier reading = MSR + VSR × least count
Screw gauge least count = pitch ÷ number of circular divisions

One-page formula sheet

Printable Units, Dimensions and Errors formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

Avoid

Common mistakes students make

Subtracting errors for a difference (errors always add)
Forgetting zero error in vernier and screw gauge
Treating angle as dimensional (radian is dimensionless)

For the exam

How this topic is asked in JEE

Appears regularly; quick marks. One question almost every shift, usually 3–4 minutes. Learn the dimensions of common constants (G, h, ε₀, μ₀) as a list.

NCERT map

Where Units, Dimensions and Errors is in NCERT

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Class	Book	Chapter	Sections JEE asks from
Class 11	Physics Part I	Units and Measurement	The International System of Units; Dimensional Formulae and Dimensional Equations; Dimensional Analysis and its Applications; Significant Figures; Errors in Measurement

JEE Advanced level

A JEE Advanced-level example on Units, Dimensions and Errors

Question. The time period T of a satellite orbiting close to Earth's surface depends on Earth's radius R, mean density ρ, and gravitational constant G as T = k × R^a × ρ^b × G^c, where k is dimensionless. Using dimensional analysis, find a, b, and c. If R, ρ, and G are measured with percentage errors of 2%, 3%, and 4% respectively, calculate the maximum percentage error in T.

Show solution

Write dimensions: [T] = [T], [R] = [L], [ρ] = [ML⁻³], [G] = [M⁻¹L³T⁻²]
Set up: [T¹] = [L]^a × [ML⁻³]^b × [M⁻¹L³T⁻²]^c = [M^(b−c) L^(a−3b+3c) T^(−2c)]
Compare powers: For M: b − c = 0, For T: −2c = 1, For L: a − 3b + 3c = 0
Solve: c = −1/2, b = −1/2, and a = 0. So T = k/√(ρG) and R drops out
Error formula: ΔT/T × 100 = (1/2)(3%) + (1/2)(4%) = 1.5% + 2% = 3.5%

Answer: a = 0, b = −1/2, c = −1/2; Maximum percentage error in T = 3.5%

This example was solved twice independently and both solutions agree.

Free lectures

Best free lectures for Units, Dimensions and Errors

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

UNIT AND DIMENSION Unit and Dimensions FULL CHAPTER | Class 11th Chapter 1 | Arjuna JEE — Arjuna JEE, 3:51:51
Jump to a subtopic (11)
- 00:00 Introduction
- 13:11 Unit & Dimension
- 27:23 Classification
- 40:53 Derived Physical Quantity
- 46:00 Systems of Units
- 57:39 Dimensions
- 1:12:56 Questions
- 1:56:00 Applications of dimensional analysis
- 2:28:20 Question
- 3:04:17 Limitations of this method
- 3:15:55 Question Practice
UNITS & DIMENSION in 52 Minutes | Full Chapter Revision | Class 11th JEE — JEE Wallah, 52:43
Jump to a subtopic (6)
- 00:00 Introduction
- 03:43 Overview of units and measurements
- 12:02 Physical quantity
- 15:14 Dimension formula
- 18:42 Dimension formula of unknown quantity
- 52:40 Thank You Bacchon!

Practise

Where to practise for free

12 JEE Main 2026 PYQs on Units, Dimensions and Errors, with solutions.
Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
See it move: interactive simulation.

FAQs

Frequently asked questions

Is Units, Dimensions and Errors important for JEE Main 2027?

Appears regularly; quick marks. It is part of the official 'Units and Measurements' unit in the JEE Main 2027 syllabus.

What are the most important formulas in Units, Dimensions and Errors?

If Z = AᵖBᵠ/Cʳ, then ΔZ/Z = p·ΔA/A + q·ΔB/B + r·ΔC/C; Absolute error in a sum or difference: ΔZ = ΔA + ΔB; Vernier reading = MSR + VSR × least count.

How should I study Units, Dimensions and Errors for JEE?

Understand the key ideas from NCERT or one full lecture, learn the formula sheet, then solve 25–30 past JEE questions on the topic. One question almost every shift, usually 3–4 minutes. Learn the dimensions of common constants (G, h, ε₀, μ₀) as a list.