Cement, sand and aggregate calculator

How to calculate cement, sand and aggregate

Multiply the finished (wet) volume by a dry-volume factor, then split it by the mix ratio. Cement's share × 1,440 kg/m³ gives kilograms; divide by the bag size for bags.

Dry volume  = wet volume × dry-volume factor (1.54 concrete, 1.33 mortar and plaster)
Parts       = cement + sand + aggregate   (1 + 2 + 4 = 7 for 1:2:4)
Cement, m³  = dry volume × cement ÷ parts
Cement, kg  = cement m³ × 1,440 kg/m³;   bags = kg ÷ bag size
Sand        = dry volume × sand ÷ parts
Aggregate   = dry volume × aggregate ÷ parts

Cement's loose bulk density, 1,440 kg/m³, is from IS 875 Part 1, which also gives 1,540–1,600 kg/m³ for dry sand; the calculator uses 1,600 for sand tonnes and 1,500 for aggregate. A 50 kg bag therefore holds 0.0347 m³, or 1.23 cft.

Worked example: 1 m³ of M20 concrete (1 : 1.5 : 3)

1 m³ of 1:1.5:3 concrete needs 8.06 bags of 50 kg cement (403.2 kg), 0.42 m³ of sand and 0.84 m³ of coarse aggregate, using a dry-volume factor of 1.54.

1. Dry volume: 1 × 1.54 = 1.54 m³.
2. Parts: 1 + 1.5 + 3 = 5.5.
3. Cement: 1.54 × 1 ÷ 5.5 = 0.28 m³ × 1,440 = 403.2 kg ÷ 50 = 8.06 bags.
4. Sand: 1.54 × 1.5 ÷ 5.5 = 0.42 m³ (14.8 cft).
5. Aggregate: 1.54 × 3 ÷ 5.5 = 0.84 m³ (29.7 cft).

Working in cubic feet: 100 cft of 1:2:4 concrete needs 17.9 bags of cement, 44 cft of sand and 88 cft of crush.

Cement, sand and aggregate per m³ and per 100 cft

These are the quantities for the nominal mixes at a dry-volume factor of 1.54 for concrete and 1.33 for mortar, with 50 kg bags and no wastage. Use the calculator to change any of them.

Concrete

Brick mortar

Plaster: 10 m² at 12 mm

Mortar and plaster share the same factor, so 1 m³ of 1:6 plaster needs the same materials as 1 m³ of 1:6 mortar.

Why multiply by 1.54 (or 1.33)?

Loose cement, sand and stone have air between the particles. When water is added and the mix is compacted, the fine materials fill the gaps, so the finished volume is smaller than the loose dry volume you start with.

1.54 for concrete and 1.33 for mortar and plaster are site conventions in South Asian rate analysis, not values from a standard. Quoted figures range from about 1.52 to 1.57 for concrete (1.52 in course notes) and 1.27 to 1.35 for mortar. We found no code that fixes either value, so the calculator treats them as editable defaults. US, UK and Australian estimates usually work from ready-mix volume or premix bag yield instead.

Nominal mix by volume vs IS 456 by mass

The 1:1.5:3 and 1:2:4 ratios are volume ratios used on site. IS 456 specifies nominal mixes by mass, and for M20 its Table 9 works out to about 10% less cement than 1:1.5:3 by volume.

IS 456 allows nominal mixes only up to M20. Its Table 9 gives, per 50 kg of cement, a total mass of fine and coarse aggregate (250 kg for M20, 330 kg for M15, 480 kg for M10) and a maximum water content (30, 32 and 34 litres). The volume ratios commonly matched to those grades (1:1.5:3, 1:2:4, 1:3:6) are site practice; the code doesn't list them.

Worked through with a typical fresh concrete density, Table 9's M20 comes out roughly 10% leaner in cement than 1:1.5:3 by volume, so the volume method uses more cement, not less. For structural concrete, use a designed mix from your engineer or supplier.

How to use the calculator

Choose concrete, brick mortar or plaster, pick or type a mix ratio, then enter the wet volume or the length, width and thickness.

1. Region presets set the units and the usual cement bag size; change either at the top.
2. Choose what you're mixing. Mortar and plaster hide the aggregate.
3. Pick a nominal mix or choose Custom and type the parts.
4. Enter the finished volume, or switch to Dimensions for a slab, floor or layer.
5. Need the volume first? Use the concrete calculator or the brick calculator.

Sources

Constants and limits come from these standards, manufacturers' data and trade bodies. Where practice varies, the calculator lets you change the value.

• IS 456:2000 Plain and Reinforced Concrete: Code of Practice (Table 9, nominal mixes)Bureau of Indian Standards · 2000, reaffirmed
• IS 875 (Part 1):1987 Unit weights of building materials (Table 1)Bureau of Indian Standards · 1987
• NIST Guide to the SI, Appendix B.9: conversion factorsNational Institute of Standards and Technology · SP 811

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