Derived SI Units: Speed, Volume, Density, Pressure and Pascal

Chemistry · Some Basic Concepts Of Chemistry · NEET

Derived SI units are units built by combining the seven base units. You get them straight from the formula: speed = distance/time so its unit is m/s; volume = length³ so m³; density = mass/volume so kg/m³ (or g/cm³ in the lab); pressure = force/area so its unit is the pascal, Pa. One pascal equals 1 N/m² = 1 kg m⁻¹ s⁻². Memory hook: "Write the formula, then swap each quantity for its base unit — the derived unit falls out."
Derive the unit: write the formula, swap in base unitsSpeeddist ÷ timem ÷ sm s⁻¹VolumeL × L × Lm × m × mDensitymass ÷ volkg ÷ m³kg m⁻³Pressureforce ÷ areaN ÷ m²Pa= kg m⁻¹ s⁻²
Every derived SI unit comes from its formula: replace each quantity with its base unit and simplify. Speed → m s⁻¹, Volume → m³, Density → kg m⁻³, Pressure → pascal (Pa = N m⁻² = kg m⁻¹ s⁻²).

Your doubts, answered

How do I get a derived unit from a formula? (the one trick that solves all of them)

Write the physical formula, then replace every quantity with its SI base unit. Speed = distance ÷ time → metre ÷ second = m/s (m s⁻¹). Volume = length × length × length → m × m × m = m³. Density = mass ÷ volume → kg ÷ m³ = kg/m³ (kg m⁻³). Pressure = force ÷ area → newton ÷ m² = N/m² = pascal. You never memorise the answer; you derive it. That is exactly why they are called 'derived' units.

What is the SI unit of density, and why does the lab use g/cm³ instead?

The SI unit of density is kg m⁻³ (kg/m³), because density = mass/volume = kg ÷ m³. But this number is very large for everyday chemicals (water = 1000 kg/m³). So chemists express density in g cm⁻³ instead, where water = 1 g/cm³. Both are correct; g/cm³ is just a smaller, handier unit. Conversion: 1 g/cm³ = 1000 kg/m³. NCERT itself says the SI unit is 'quite large' so chemists prefer g cm⁻³.

What is 1 pascal actually equal to? (in newton and in base units)

Pressure = force ÷ area. Force is measured in newton (N) and area in m². So 1 pascal = 1 N/m² = 1 N m⁻². Going one step deeper, 1 N = 1 kg m s⁻² (from F = ma). So 1 Pa = 1 kg m s⁻² ÷ m² = 1 kg m⁻¹ s⁻². NEET loves asking pascal in pure base units: remember Pa = kg m⁻¹ s⁻².

Why is pascal a DERIVED unit and not a base unit?

The seven SI base units (metre, kilogram, second, kelvin, ampere, mole, candela) are chosen as fundamental — they are not built from anything else. Pascal is made by combining them (kg, m, s), so it is derived. Speed, volume, density and pressure are all derived because their formulas contain base quantities multiplied or divided together. Only the seven fundamental quantities get base units.

Is litre an SI unit? Is 1 mL the same as 1 cm³?

No, litre (L) is NOT an SI unit — the SI unit of volume is m³. Litre is a common, allowed unit. Useful equalities: 1 L = 1000 mL, 1 mL = 1 cm³, and 1 L = 1 dm³ = 1000 cm³. So 1 dm³ = 1000 cm³. This matters in NEET density/molarity sums where data is given in g mL⁻¹ or g cm⁻³ (they are the same thing).

Speed vs velocity — do they have the same SI unit?

Yes. Speed = distance/time and velocity = displacement/time, so both have the SI unit m/s (m s⁻¹). The difference is that velocity is a vector (has direction) and speed is a scalar. For unit purposes in NEET, both are m s⁻¹.

⚠️ The NEET trap
1 pascal = 1 kg m s⁻²
1 pascal = 1 kg m⁻¹ s⁻² (= 1 N m⁻²)
🧠 kg m s⁻² is the newton (force), NOT the pascal. Pressure divides force by area (m²), so you must subtract 2 from the metre power: m¹ ÷ m² = m⁻¹. Always finish the division — Pa = kg m⁻¹ s⁻².

Real NEET questions

NEET 2019 (Odisha)

The density of a 2 M aqueous solution of NaOH is 1.28 g cm⁻³. The molality of the solution is (molar mass of NaOH = 40 g mol⁻¹)

A · 1.20 m
B · 1.56 m
C · 1.67 m
D · 1.32 m
Solution: Density is a derived unit (mass/volume), given here as g cm⁻³. Take 1 L (= 1000 cm³) of solution holding 2 mol NaOH. Mass of solution = volume × density = 1000 × 1.28 = 1280 g. Mass of NaOH = 2 × 40 = 80 g. Mass of water (solvent) = 1280 − 80 = 1200 g = 1.2 kg. Molality = moles solute ÷ kg solvent = 2 ÷ 1.2 = 1.67 m. Answer (C). Note how the g cm⁻³ density lets you convert volume to mass.
NEET 2023 (Phase 2)

The density of a 1 M solution of a compound X is 1.25 g mL⁻¹. The molality of the solution is (molar mass of X = 85 g mol⁻¹)

A · 1.165 m
B · 0.858 m
C · 0.705 m
D · 1.208 m
Solution: Here density is given in g mL⁻¹, and 1 mL = 1 cm³, so this is the same derived unit as g cm⁻³. Take 1 L (1000 mL) of solution with 1 mol X. Mass of solution = 1000 × 1.25 = 1250 g. Mass of solute = 1 × 85 = 85 g. Mass of solvent = 1250 − 85 = 1165 g = 1.165 kg. Molality = 1 ÷ 1.165 = 0.858 m. Answer (B).

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Frequently asked

What are derived SI units in one line?

Units made by combining the seven base units through a formula — for example speed (m/s), volume (m³), density (kg/m³) and pressure (pascal, Pa).

What is the SI unit of pressure?

The pascal (Pa). 1 Pa = 1 N/m² = 1 kg m⁻¹ s⁻². It equals force per unit area.

What is the SI unit of volume, and is litre allowed?

The SI unit of volume is the cubic metre, m³. Litre is not an SI unit but is commonly used: 1 L = 1 dm³ = 1000 cm³ = 1000 mL.

Are g/cm³ and g/mL the same for density?

Yes. Since 1 mL = 1 cm³, density in g mL⁻¹ equals density in g cm⁻³. Both convert to SI as 1 g/cm³ = 1000 kg/m³.

How many pascal are in the pressure of air at sea level in NCERT problem 1.13?

NCERT gives air mass ≈ 1034 g cm⁻². Converting force per area to SI gives about 1.01 × 10⁵ Pa, close to standard atmospheric pressure. It shows pascal = force/area in action.