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DRV-017

Concrete quantities, and where the 1.54 comes from

The familiar "about eight bags per cubic metre for M20" has a provenance. Here it is, along with why dry volume exceeds wet.

The setup

Dry ingredients occupy more volume than the wet concrete they produce, because water fills the voids between particles rather than adding to the total. Estimating from wet volume alone under-orders every material on the site.

The derivation

Step 1: Convert wet volume to dry

The 1.54 factor combines sand bulking of roughly 20% with aggregate voids of roughly 34%. Field values range from 1.52 to 1.57; 1.54 is the standard convention and should be an input rather than a buried constant.

dry volume = wet volume * 1.54

Step 2: Split by the mix ratio

For a mix a : b : c with parts summing to Σ, each material takes its share of the dry volume.

cement volume = dry volume * a / (a + b + c)

Step 3: Convert cement volume to bags

Cement has a bulk density of about 1440 kg/m³ and ships in 50 kg bags.

cement kg = cement volume * 1440 bags = cement kg / 50
bags = wet_volume * 1.54 * (a/sum) * 1440 / 50

Checks that prove it is right

A formula you cannot test is a formula you have to trust. These take seconds, and they are what separate a derivation from a formula restatement.

A richer mix → More cement, less aggregate, same total dry volume

The ratio redistributes a fixed dry volume. M25 at 1:1:2 takes 0.385 m³ of cement per cubic metre against M20's 0.28.

Doubling the pour → Everything doubles

The relationship is strictly linear, so a quantity estimate scales without recomputation.

Worked example

M20 (1 : 1.5 : 3), one cubic metre.

Dry volume is 1.54 m³ and Σ is 5.5. Cement takes 1.54 × 1/5.5 = 0.28 m³, which is 403.2 kg, which is 8.06 bags. Sand takes 0.42 m³ and aggregate 0.84 m³. The familiar rule of thumb (about eight bags per cubic metre for M20) now has a visible provenance, and that is the entire value proposition of publishing a derivation rather than a formula.

Computed by the material-quantity engine and asserted as a golden case.

What it assumes

  • Nominal mix proportions by volume.
  • Cement bulk density 1440 kg/m³.
  • The dry-volume factor accounts for sand bulking and aggregate voids.

Where the formula stops being valid

Stating limits plainly is more useful than pretending there are none, and it is the item competitors most consistently omit.

  • A design mix for a specified strength and workability is a laboratory exercise, not a ratio. Nominal mixes are for small works only.
  • No wastage allowance is included; add 3–5% on site.
  • Sand bulking varies with moisture content, which is exactly why the factor is an input.

Calculators built on this

Related: Why steel weight is d² ÷ 162