Concrete mix ratios are how a site batch is stated, cement to sand to stone by volume, and the arithmetic behind them is the arithmetic of a small pour: how many batches the yards need, how many bags of cement, sand and stone that is, and what strength the ratio is expected to make. A 1:2:3 mix is one part cement, two of sand and three of stone; a 1:2:4 mix is leaner. The ratio does not set the strength on its own, because the water does as much, and the specifications the American Concrete Institute publishes say so in detail. This page works the batches and the materials for a 1:2:3 mix on a one-yard pour, says when a site batch makes sense against a truck, and points at the free concrete calculator on this site that works the yards the batches have to fill, with no account.
What the ratio means, and the water it leaves out
A ratio of 1:2:3 means one measure of cement to two of sand to three of coarse stone, all by loose volume, and the measure can be a bucket, a shovel count or a bag. The water is not in the ratio and decides the strength as much as the cement does: more water makes the mix easier to place and weaker when it cures, so the water is added to the workability the pour needs and no further. The American Concrete Institute and the Portland Cement Association publish the specifications a designed mix is made and tested to; a site ratio is the practical stand-in for a small pour where a designed mix is not being ordered.
Yield per batch, and batches per yard
Mixing fills the voids between the loose materials, so a batch yields less than the sum of its parts: one bag of cement with two bags' volume of sand and three of stone, six loose parts, yields about four and a half cubic feet of concrete rather than six. A cubic yard is 27 cubic feet, so a one-yard pour at that yield is 27 divided by 4.5, six batches, each with one bag of cement, two of sand and three of stone by the bag's volume. The concrete ratios and the yield together are the whole of the count; the free concrete calculator on this site gives the yards from the slab's dimensions, and the batches follow from the yield the contractor gets from their mix.
Materials for the pour: cement, sand and stone by the bag and the yard
For six batches of 1:2:3, the cement is six bags; the sand is twelve bag-volumes, and the stone eighteen. At a bag volume of one cubic foot each, that is 12 cubic feet of sand, 0.44 yards, and 18 cubic feet of stone, 0.67 yards, ordered loose by the yard or the ton from the supplier at the weight per yard they state. The waste allowance the contractor sets for a pour, 10% on the calculator's default, applies to the batches as it does to a truck load, so the one-yard pour is seven batches with the spill and the low spots covered.
When to batch on site, and when to order the truck
A site batch pays for a pour of a yard or two where the truck's minimum load and delivery fee would cost more than the bags and the labor to mix them, and where the pour can be placed in the time the batches take. Beyond that the truck is cheaper per yard and the mix is designed and tested rather than proportioned by the shovel. On the hub's worked slab, 18 by 18 feet at 6 inches, 6.6 yards with waste, the arithmetic says forty batches and a long day, which is why that pour is ordered by the yard at the supplier's price; the calculator on this site takes that price and gives the cost of the pour for the estimate and, later, the draw.
Questions people ask about concrete mix ratios
What does a 1:2:3 concrete mix ratio mean?
One part cement to two parts sand to three parts coarse stone, by loose volume, with the water added to the workability the pour needs. The water sets the strength as much as the cement does.
How many batches of 1:2:3 make a cubic yard?
About six, because a batch of one bag of cement with two of sand and three of stone yields about 4.5 cubic feet after mixing and a yard is 27. Add the contractor's waste allowance.
When is a site batch better than a truck?
For a pour of a yard or two where the truck's minimum load and delivery fee would cost more than the bags and the mixing labor. A slab of several yards is ordered by the yard.