Units and Measurement

NCERT Class 11 Physics Chapter 1

Units and Measurement for Class 11 Physics, JEE and NEET: SI units, significant figures, errors, dimensions and dimensional analysis, with solved examples.

7 topics Updated 8 Nov 2026

For: Class 11, JEE and NEET, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus, NEET Class 11 syllabus

With your textbook

NCERT Physics Part I (Class 11), Chapter 1 “Units and Measurement”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.1 MB, ncert.nic.in) (opens in a new tab)

Checked on 19 Oct 2026.

Learn in this order

SI units
The seven base (fundamental) units, derived units, the radian and steradian, and prefixes, with solved examples.

NCERT Sections 1.1–1.2 14 min read 5 solved examples 6 practice questions
Significant figures
Counting rules, scientific notation, arithmetic and rounding rules, and uncertainty, with solved examples.

NCERT Section 1.3 14 min read 5 solved examples 6 practice questions
Errors in measurement
Accuracy and precision, systematic and random errors, absolute and percentage error, and combining errors.

JEE and NEET only 13 min read 5 solved examples 6 practice questions
Least count: vernier callipers and screw gauge
Least count formulas, how to take readings, and positive and negative zero error with corrections.

JEE and NEET only 12 min read 5 solved examples 6 practice questions
Dimensions of physical quantities
The seven base dimensions, dimensions of derived quantities, and dimensionless quantities.

NCERT Section 1.4 13 min read 5 solved examples 6 practice questions
Dimensional formulae and equations
What they are, how to find them, a table of common formulae, and solved examples.

NCERT Section 1.5 14 min read 5 solved examples 6 practice questions
Dimensional analysis and its applications
Checking equations, deducing relations such as the pendulum’s period, converting units, and limitations.

NCERT Section 1.6 15 min read 5 solved examples 6 practice questions

Key formulas in this chapter

SI units

dθ = ds/r (radian)
dΩ = dA/r^² (steradian)
full circle = 2π rad; full sphere = 4π sr
1° = (π/180) rad
N = kg m s^⁻²; J = kg m^² s^⁻²; W = kg m^² s^⁻³; Pa = kg m^⁻¹ s^⁻²

Significant figures

product or quotient: significant figures = fewest among the data
sum or difference: decimal places = fewest among the data
scientific notation: a × 10^b with 1 ≤ a < 10
relative error of a product = sum of relative errors

Errors in measurement

a_mean = (a₁ + a₂ + … + a_n)/n
Δa_mean = (|Δa₁| + |Δa₂| + … + |Δa_n|)/n
relative error = Δa_mean/a_mean; percentage error = relative error × 100%
Z = A ± B: ΔZ = ΔA + ΔB
Z = AB or A/B: ΔZ/Z = ΔA/A + ΔB/B
Z = A^p B^q/C^r: ΔZ/Z = pΔA/A + qΔB/B + rΔC/C

Least count: vernier callipers and screw gauge

vernier: LC = 1 MSD − 1 VSD = (1 MSD)/n
reading = MSR + VSR × LC
screw gauge: LC = pitch/N
reading = PSR + CSR × LC
corrected reading = observed reading − zero error

Dimensions of physical quantities

[velocity] = [L T^⁻¹]; [acceleration] = [L T^⁻²]
[force] = [M L T^⁻²]
[momentum] = [impulse] = [M L T^⁻¹]
[work] = [energy] = [torque] = [M L^² T^⁻²]
[power] = [M L^² T^⁻³]
[pressure] = [stress] = [M L^⁻¹ T^⁻²]
[G] = [M^⁻¹ L^³ T^⁻²]

Dimensional formulae and equations

dimensional formula: [M^a L^b T^c]
dimensional equation: [X] = [M^a L^b T^c]
[h] = [M L^² T^⁻¹] (Planck constant; same dimensions as angular momentum)
[η] = [M L^⁻¹ T^⁻¹] (viscosity); [Y] = [M L^⁻¹ T^⁻²] (Young’s modulus)
[s] = [L^² T^⁻² K^⁻¹] (specific heat capacity); [R] = [M L^² T^⁻² K^⁻¹ mol^⁻¹] (gas constant)
[q] = [A T] (charge); [V] = [M L^² T^⁻³ A^⁻¹] (potential difference); [R] = [M L^² T^⁻³ A^⁻²] (resistance)

Dimensional analysis

every term in an equation has the same dimensions
assume Q = k X_₁^ˣ X_₂^ʸ X_₃^ᶻ; equate the powers of M, L and T
T = k√(l/g), with k = 2π for small swings, from theory
n₂ = n₁ (M₁/M₂)^a (L₁/L₂)^b (T₁/T₂)^c (1 = old units, 2 = new)
arguments of sin, cos, log and exp are dimensionless