A 1:2:3 concrete mix is 1 part portland cement, 2 parts sand and 3 parts gravel by volume, and one 94 lb bag of cement (1 cubic foot) makes about 4.3 cubic feet of it at a 0.55 water-cement ratio. A 10 × 10 ft slab 4 inches thick, with 10% extra, is 36.7 cubic feet: 9 bags of cement, 17 cubic feet of sand, 25 cubic feet of gravel and 53 gallons of water. The calculator scales any ratio you type to the slab or volume you enter, and sets the water from the strength you want.
How the mix ratio is calculated
Ratios count loose volume, so the parts do not add up to the concrete you get: the sand fills the gaps between the stones and the cement paste fills the rest. A batch's yield comes from absolute volumes, the method in the Portland Cement Association's Design and Control of Concrete Mixtures: each material's weight divided by its relative density and the weight of water.
Yield per bag = 94 ÷ (3.15 × 62.3) + sand lb ÷ (2.64 × 62.3) + gravel lb ÷ (2.68 × 62.3) + water lb ÷ 62.3
For 1:2:3 the sand is 2 cu ft and the gravel 3 cu ft, each taken at 100 lb per loose cubic foot (the PCA example's gravel; sand is assumed the same). Water at 0.552 of the cement's weight is 51.9 lb. That gives 0.48 + 1.22 + 1.80 + 0.83 = 4.32 cubic feet from a bag. Bags of cement = concrete needed ÷ yield, rounded up. Quikrete's portland cement data sheet lists this same 1:2:3 as its typical concrete mix and says five to six bags make a cubic yard; the rich 1:2:3 works out at 6.2, and leaner mixes fall inside that range.
Worked example: a 10 × 10 ft slab at 3,000 psi
A 10 × 10 × 4 in slab is 33.33 cubic feet; 10% extra makes 36.67. At 3,000 psi the calculator uses the PCA's ratio of 0.552 (below), so a bag makes 4.32 cubic feet and the slab needs 8.48 bags, so 9. The sand is 8.48 × 2 = 17.0 cubic feet and the gravel 25.4 cubic feet, about 0.85 and 1.27 tons. The water is 8.48 × 6.22 = 52.7 gallons. The same slab in bagged mix is 62 bags of 80 lb (concrete bag calculator).
Mix ratios compared at the same water
At a 0.55 water-cement ratio, per cubic yard of concrete, no waste:
| Ratio (cement:sand:gravel) | Concrete per bag | Bags per cu yd | Sand | Gravel |
|---|---|---|---|---|
| 1:1.5:3 | 4.02 cu ft | 6.7 | 10.1 cu ft | 20.2 cu ft |
| 1:2:3 | 4.32 cu ft | 6.2 | 12.5 cu ft | 18.7 cu ft |
| 1:2:4 | 4.92 cu ft | 5.5 | 11.0 cu ft | 21.9 cu ft |
| 1:3:6 | 6.73 cu ft | 4.0 | 12.0 cu ft | 24.1 cu ft |
A richer ratio uses more cement per yard. A lean one such as 1:3:6 uses the least, so check its strength before you trust it with anything structural. The PCA lists volumetric "1:2:3" proportioning as an arbitrary method that gives about the same mix as engineered ones after field adjustment, but it prefers proportions from test data.
Strength decides the water, not the ratio
Water is what sets the strength. PCA Table 9-3 (from ACI 211.1) relates the water-cementitious ratio by weight to 28-day strength in psi:
| Design average strength | Non air-entrained | Air-entrained |
|---|---|---|
| 3,000 psi | 0.68 | 0.59 |
| 4,000 psi | 0.57 | 0.48 |
| 5,000 psi | 0.48 | 0.40 |
| 6,000 psi | 0.41 | 0.32 |
A mix has to be designed above the strength you specify. With no test record, ACI 318 (PCA Table 9-11) adds 1,000 psi below 3,000 psi and 1,200 psi from 3,000 to 5,000 psi. So a 3,000 psi concrete is designed to 4,200 psi, which interpolates to 0.552; 3,500 psi gives 0.507; 4,000 psi gives 0.466 and needs 5.25 gallons of water a bag. Mix ratio 1:1.5:3 at 4,000 psi on the same slab takes 10 bags, 14.1 cubic feet of sand, 28.3 cubic feet of gravel and 49.5 gallons. These are moist-cured laboratory cylinders; concrete mixed and cured by hand usually lands lower.
Exposure sets a ceiling on the water
ACI 318 (PCA Table 9-1) caps the water-cement ratio at 0.50 with a 4,000 psi minimum for concrete needing low permeability in wet service, and at 0.45 with 4,500 psi for concrete that freezes while wet or meets deicers. Pick the exposure and the calculator holds the water at the cap and shows the check. Freeze-thaw exposure also calls for air entrainment, which the toggle uses.
Wet sand and other practical notes
The water figure is for dry sand and gravel. Damp sand carries water and bulks up, so cut the mix water and check the batch with a bucket. PCA's own example sand held 6% moisture. Quikrete's advice for any mix is the minimum water that gives the consistency you need, because extra water weakens concrete.
After the mix
Compare the bill with ready-mix for the same pour in the concrete yard calculator, see prices in the concrete cost calculator, or size the pour first with the concrete slab calculator. Convert sand and gravel deliveries to weight with the cubic yards to tons calculator, and reinforce a slab with the rebar calculator. All the concrete tools are in the concrete and masonry calculators.