Formula
Cement C = W ÷ (w/c) Absolute volume of each material = mass ÷ (density × 1000) [m³] Aggregate volume Va = 1 − W/1000 − C/(ρc·1000) − air/100 Sand S = Va · (s/a) · ρs · 1000 Gravel G = Va · (1 − s/a) · ρg · 1000
The absolute volume method treats one cubic metre of concrete as the sum of the solid volumes of water, cement, air and aggregate. Whatever is left after water, cement and air is filled by aggregate, and the sand ratio s/a splits that volume between sand and gravel. Water is taken as 1.0 g/cm³.
Choosing inputs
- Water-cement ratio: set by the strength and durability (exposure class) you need. If the specification gives a maximum, stay below it.
- Water content: set by the slump you want and the maximum aggregate size. For the same workability, less water means less cement and less drying shrinkage.
- Air content: for air-entrained concrete, use the target air content from the design. Without an air-entraining agent only entrapped air remains; IS 10262 uses 3, 2 and 1 % for 10, 20 and 40 mm maximum aggregate size.
- Densities: use tested saturated surface-dry (SSD) densities for aggregates. The defaults (cement 3.15, sand 2.60, gravel 2.65) are only typical examples.
Worked example
Water 175 kg/m³, w/c 50 %, air 4.5 %, sand ratio 42 %, densities cement 3.15, sand 2.60, gravel 2.65, pour 6 m³:
- Cement = 175 ÷ 0.50 = 350 kg
- Aggregate volume = 1 − 0.175 − 350/3150 − 0.045 = 1 − 0.175 − 0.1111 − 0.045 ≈ 0.6689 m³
- Sand = 0.6689 × 0.42 × 2600 ≈ 730 kg; gravel = 0.6689 × 0.58 × 2650 ≈ 1,028 kg
- For 6 m³: cement 2,100 kg, sand about 4.38 t, gravel about 6.17 t, water 1,050 kg
The calculator opens with these values. Automated tests also check it against the absolute volume example in IS 10262:2019 (cement 372 kg, water 186 kg, air 2 %, sand 38 % → sand 681 kg, coarse aggregate 1,123 kg).
Limitations
- Aggregate masses are for the SSD condition. Adjust batch water and aggregate weights for surface moisture and absorption on site; this calculator does not.
- Supplementary materials (fly ash, slag) and admixture volumes are not included. With supplementary materials, calculate with total binder instead of cement alone.
- These quantities are a starting point for trial mixes. Mixes for structures must be confirmed by trial batches for slump, air content and strength under the governing specification. Reference values; review by a qualified person is required.
References
- IS 10262:2019 Concrete Mix Proportioning — Guidelines (Bureau of Indian Standards), clause 4.6, aggregate content by absolute volume, and the M25 worked example