Units & Measurement
Complete Formula Sheet & Shortcut Bible · BITSAT 2026
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Fundamental Units & Dimensional Analysis
7 Fundamental SI Units
Length (m) [L]
Mass (kg) [M]
Time (s) [T]
Current (A) [A]
Temperature (K) [K]
Luminous Intensity (cd) [J]
Amount of Substance (mol) [mol]
Mass (kg) [M]
Time (s) [T]
Current (A) [A]
Temperature (K) [K]
Luminous Intensity (cd) [J]
Amount of Substance (mol) [mol]
Principle of Homogeneity
Dimensions of each term in a physical equation must be the same.
[A] = [B] = [C] in A = B + C
[A] = [B] = [C] in A = B + C
Used to check correctness of formulas and find dimensions of constants.
Common Derived Dimensions
Force: [MLT⁻²]
Work/Energy: [ML²T⁻²]
Power: [ML²T⁻³]
Pressure: [ML⁻¹T⁻²]
Momentum: [MLT⁻¹]
Work/Energy: [ML²T⁻²]
Power: [ML²T⁻³]
Pressure: [ML⁻¹T⁻²]
Momentum: [MLT⁻¹]
Unit Conversion
n₁u₁ = n₂u₂
n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ
n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ
Where a, b, c are the dimensions of the quantity.
Error Analysis & Propagation
Error Types
Absolute Error: |aₘₑₐₙ - aᵢ|
Relative Error: Δaₘₑₐₙ / aₘₑₐₙ
Percentage Error: (Δaₘₑₐₙ / aₘₑₐₙ) × 100%
Relative Error: Δaₘₑₐₙ / aₘₑₐₙ
Percentage Error: (Δaₘₑₐₙ / aₘₑₐₙ) × 100%
Error in Sum/Difference
If Z = A ± B
Then ΔZ = ΔA + ΔB
(Absolute errors are always added)
Then ΔZ = ΔA + ΔB
(Absolute errors are always added)
Maximum possible error is the sum of individual absolute errors.
Error in Product/Division
If Z = A × B or Z = A / B
Then ΔZ/Z = ΔA/A + ΔB/B
(Relative errors are always added)
Then ΔZ/Z = ΔA/A + ΔB/B
(Relative errors are always added)
This is the most common type of error question.
Error in Power
If Z = AⁿBᵐ / Cᵖ
Then ΔZ/Z = n(ΔA/A) + m(ΔB/B) + p(ΔC/C)
Then ΔZ/Z = n(ΔA/A) + m(ΔB/B) + p(ΔC/C)
The power multiplies the relative error, regardless of being in numerator or denominator.
BITSAT Speed Hacks
In dimensional analysis, use options to eliminate. Check dimensions of each option instead of deriving from scratch.
For error propagation with powers, remember all percentage errors ADD UP. A term in the denominator still contributes positively to the total error.
Memorize dimensions of key constants: G [M⁻¹L³T⁻²], h [ML²T⁻¹], ε₀ [M⁻¹L⁻³T⁴A²]. They are direct questions.
For Vernier/Screw gauge, always check for Zero Error first. It's a common trap. Correct Reading = Observed - Zero Error (with sign).
Quantities with same dimensions are frequently asked: Work & Torque; Angular Momentum & Planck's Constant; Impulse & Momentum.
Significant Figures & Rounding Off
Counting Sig Figs
1. All non-zeros are significant.
2. Zeros between non-zeros are significant.
3. Trailing zeros are significant ONLY if there is a decimal point.
2. Zeros between non-zeros are significant.
3. Trailing zeros are significant ONLY if there is a decimal point.
e.g., 2.30 has 3 sig figs, but 230 has 2.
Addition/Subtraction Rule
The result should have the same number of decimal places as the number with the least decimal places.
e.g., 12.11 + 18.0 + 1.012 = 31.122 → rounds to 31.1
Multiplication/Division Rule
The result should have the same number of significant figures as the number with the least significant figures.
e.g., 4.237 × 2.51 = 10.63487 → rounds to 10.6 (3 sig figs)
Measurement Instruments
Least Count (LC)
LC = Value of 1 Main Scale Division (MSD) - Value of 1 Vernier Scale Division (VSD)
Also, LC = (Smallest division on main scale) / (Total divisions on vernier/circular scale)
Vernier Calipers Reading
Reading = MSR + (VSC × LC)
MSR: Main Scale Reading
VSC: Vernier Scale Coincidence
MSR: Main Scale Reading
VSC: Vernier Scale Coincidence
MSR is the reading on the main scale just before the zero of the vernier scale.
Screw Gauge Reading
Reading = PSR + (CSR × LC)
PSR: Pitch Scale Reading
CSR: Circular Scale Reading
PSR: Pitch Scale Reading
CSR: Circular Scale Reading
Pitch = Distance moved per revolution.
Zero Error & Correction
Correct Reading =
Observed Reading - Zero Error
(Zero Error is used with its sign)
Observed Reading - Zero Error
(Zero Error is used with its sign)
Positive Zero Error: Zero of vernier is to the right of main scale zero. Negative is to the left.
Instrument Quick Comparison
| Feature | Vernier Calipers | Screw Gauge |
|---|---|---|
Principle | Difference between two scales (Main and Vernier) | Micrometer screw (Pitch and Circular Scale) |
Typical Least Count | 0.1 mm or 0.01 cm | 0.01 mm or 0.001 cm |
Measures | Length, diameter (internal/external), depth | Diameter of thin wires, thickness of sheets |
Precision | Less precise | More precise |