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Units, Dimensions & Errors formula sheet

Every formula in the Units, Dimensions & Errors chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 39 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

SI units and measurement

SI base units
m, kg, s, A, K, mol, cd\text{m, kg, s, A, K, mol, cd}
Length, mass, time, current, temperature, amount of substance, luminous intensity. Radian and steradian are dimensionless.
Derived units
8× asked, last 2026
1 N=1 kg m s−2,1 J=1 N m1 W=1 J s−1,1 Pa=1 N m−2\begin{aligned}&1\,\text{N}=1\,\text{kg m s}^{-2},\quad 1\,\text{J}=1\,\text{N m}\\&1\,\text{W}=1\,\text{J s}^{-1},\quad 1\,\text{Pa}=1\,\text{N m}^{-2}\end{aligned}
Build each from its defining formula. Torque is N m; N m−2^{-2} is pressure or stress.
Changing the system of units
2× asked, last 2026
n2=n1[M1M2]a[L1L2]b[T1T2]cn_2=n_1\left[\frac{M_1}{M_2}\right]^{a}\left[\frac{L_1}{L_2}\right]^{b}\left[\frac{T_1}{T_2}\right]^{c}
Quantity of dimensions [MaLbTc][M^aL^bT^c]; the product nunu (number × unit) stays fixed.
Large and small lengths
1× asked, last 2023
1 AU≈1.5×1011 m,1 ly≈9.46×1015 m1 pc≈3.08×1016 m\begin{aligned}&1\,\text{AU}\approx1.5\times10^{11}\,\text{m},\quad 1\,\text{ly}\approx9.46\times10^{15}\,\text{m}\\&1\,\text{pc}\approx3.08\times10^{16}\,\text{m}\end{aligned}
1 pc ≈ 3.26 ly, so AU < ly < pc. 1 Å = 10−1010^{-10} m, 1 fermi = 10−1510^{-15} m.
Order of magnitude
1× asked, last 2024
N=a×10b  (1≤a<10)order=b  (a≤5),b+1  (a>5)\begin{aligned}&N=a\times10^{b}\ \ (1\le a<10)\\&\text{order}=b\ \ (a\le5),\qquad b+1\ \ (a>5)\end{aligned}
The order is a power of ten, never the prefactor aa.

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Practise Units, Dimensions & Errors

34 more formulas in 6 topics

Dimensions: mechanics and heat, Dimensions: electricity and magnetism, Dimensional analysis, Significant figures, Errors and their propagation and Vernier callipers and screw gauge. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Dimensions: mechanics and heat

  • Force, energy, power15×
  • Moment of inertia; force per length
  • Momentum and angular momentum16×
  • Pressure, stress, modulus; viscosity24×
  • Frequency-like quantities
  • Heat and gas constants9×
  • Heat flow and radiation constants6×
  • Gravitational constant

Dimensions: electricity and magnetism

  • Charge, field, potential12×
  • Resistance, capacitance, inductance7×
  • Permittivity and permeability11×
  • Magnetic quantities8×
  • Shortcut combinations9×

Dimensional analysis

  • Principle of homogeneity11×
  • Van der Waals constants6×
  • Arguments of sin, exp, log8×
  • Finding a relation by dimensions7×
  • Changing the base quantities8×
  • Planck units5×

Significant figures

  • Counting significant figures2×
  • Rounding off
  • Arithmetic5×

Errors and their propagation

  • Mean absolute and relative error2×
  • Sum and difference1×
  • Product, quotient, power24×
  • Volume and density7×
  • Resistivity and heat7×
  • Parallel resistors2×
  • Exponential factor
  • Simple pendulum7×
  • Young's modulus5×
  • Small changes (with sign)3×

Vernier callipers and screw gauge

  • Vernier callipers
  • Screw gauge; zero error2×

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