5.4 Yield, Relative Yield, and Batch Comparison

Yield: How Much Concrete the Batch Made

Yield (Y) is the volume of concrete produced from a batch of known total mass. C138 computes it directly from density:

Y = (total batch mass) / D

The total batch mass is the sum of all ingredient masses actually weighed into the batch — cement, supplementary cementitious materials, all aggregates, water, and admixtures (in pounds). Dividing by density (lb/ft³) yields a volume in cubic feet. To express it in cubic yards, divide by 27 (since 1 yd³ = 27 ft³).

Worked yield example

A batch contains the following masses:

Measured density D = 145.0 lb/ft³. Yield Y = 3,886 / 145.0 = 26.80 ft³ = 26.80 / 27 = 0.993 yd³.

Relative Yield: Did the Batch Deliver What Was Designed?

Relative yield (Ry) compares the actual yield to the design volume (Vd) the mix was proportioned to make:

Ry = Y / Vd

• Ry = 1.00 → the batch produced exactly the designed volume.
• Ry > 1.00 → overyield: more concrete than designed (you'll have extra; the mix is slightly 'light').
• Ry < 1.00 → underyield/shortfall: less concrete than designed — a paving or slab order could come up short.

Worked relative-yield example

Using the batch above, the mix was designed to make Vd = 27.00 ft³ (1.000 yd³). Ry = 26.80 / 27.00 = 0.993. Because 0.993 < 1.00, the batch underyielded by about 0.7% — it produced slightly less concrete than ordered. If the same batch had measured a density of only 143.0 lb/ft³, yield would be 3,886 / 143.0 = 27.18 ft³ and Ry = 27.18 / 27.00 = 1.007, an overyield. Higher density → lower yield → lower relative yield, and vice versa.

Cement Content From Yield

C138 also lets you back out the actual cement content (C) delivered per unit volume:

C = (total mass of cement in the batch) / Y

Using the example: 564 lb cement ÷ 0.993 yd³ = 568 lb/yd³. If a specification calls for 564 lb/yd³ (a six-bag mix), the slightly low yield means each cubic yard actually carries a hair more cement than designed — an underyield concentrates the cement. Conversely, overyield dilutes cement content below the target. This is why owners care about relative yield: it ties directly to whether the hardened concrete will meet its strength-driving cement factor.

Why These Numbers Matter on the Job

Yield and relative yield are the producer's quality-control link between the batch ticket and the truck:

• A consistent Ry near 1.00 confirms the plant's batch weights and the assumed aggregate specific gravities are accurate.
• A persistent underyield (Ry < 1.00) means trucks deliver less concrete than billed — costly and a contractual problem.
• A persistent overyield (Ry > 1.00) often signals higher-than-assumed air content or lighter materials, which can compromise strength.

Because all of this rests on the density number, sloppy C138 technique doesn't just mis-state density — it mis-states yield, relative yield, and cement content together.

Units and Conversions to Keep Straight

Yield problems trip candidates up on units more than on the formula. Keep these straight:

A disciplined approach: compute yield in ft³ first (batch mass ÷ density), then divide by 27 only when you need cubic yards. Many wrong answers come from dividing by 27 too early or forgetting it entirely. Likewise, relative yield is unitless — both yield and design volume must be in the same unit (both ft³ or both yd³) before you divide, or the ratio is meaningless.

A Fully Worked Batch

Put it all together with one clean example. A batch of total mass 3,950 lb is designed to produce 27.0 ft³ (1.00 yd³) and contains 611 lb of cement. The measured density is 148.0 lb/ft³.

1. Yield: 3,950 / 148.0 = 26.69 ft³ = 26.69 / 27 = 0.99 yd³.
2. Relative yield: 26.69 / 27.0 = 0.988 → rounds to 0.99. Below 1.00, so a slight underyield.
3. Cement content: 611 / 0.99 yd³ = 617 lb/yd³, slightly above the 611 lb/yd³ target because the underyield concentrates the cement.

Every one of these answers traces back to the single measured density of 148.0 lb/ft³ — which is exactly why the procedure sections (5.1–5.3) matter so much.

One more nuance: the total batch mass must include the water and admixtures actually added, not just the dry materials on the mix-design sheet. If a truck received extra tempering water at the site, that water is part of the batch mass for yield purposes. Using the design batch mass while testing a tempered batch mismatches the numerator and denominator and produces a misleading yield — so always pair the measured density with the as-delivered batch weights when one is computing yield in the field.