Fineness Modulus of Sand Calculator (Sieve Analysis, ASTM C33)
Calculate the fineness modulus of fine aggregate from a sieve analysis — percent retained, cumulative retained and passing on each sieve, sand classification and the ASTM C33 grading check.
How it works
FM = Σ (cumulative % retained on 9.5, 4.75, 2.36, 1.18, 0.60, 0.30 and 0.15 mm sieves) ÷ 100 · % retained = mass on the sieve ÷ total mass × 100 · % passing = 100 − cumulative % retained · ASTM C33 fine aggregate: FM between 2.3 and 3.1, no more than 45% between two consecutive sieves.
The fineness modulus is a single number that describes how coarse a sand is: the sum of the cumulative percentages retained on the standard sieve series, each twice the size of the next, divided by 100. ASTM C136 describes the sieve analysis and ASTM C33 asks for a fine aggregate FM between 2.3 and 3.1 and grading within its limits. Concrete mix design (ACI 211.1) uses the FM of the sand to choose how much coarse aggregate goes in the mix: a finer sand (lower FM) needs more coarse aggregate. Enter the masses in grams; any unit works as long as all are the same.
Worked example
A 500 g sand sample leaves 0, 15, 60, 90, 110, 125 and 75 g on the 9.5 mm to 0.15 mm sieves and 25 g in the pan. The percentages retained are 0, 3, 12, 18, 22, 25 and 15%, so the cumulative percentages are 0, 3, 15, 33, 55, 80 and 95%. Their sum is 281, giving a fineness modulus of 2.81 — a medium sand, and the percentages passing (100, 97, 85, 67, 45, 20, 5) all fall within the ASTM C33 limits.
Sources: ASTM C33/C33M — Standard Specification for Concrete Aggregates · ASTM C136 — Sieve Analysis of Fine and Coarse Aggregates
Frequently asked questions
What is a good fineness modulus for concrete sand?
ASTM C33 accepts 2.3 to 3.1, and most concrete sands fall between 2.5 and 3.0. Values below about 2.5 increase water demand and shrinkage; values above 3.0 make harsh, hard-to-finish mixes. The FM should not vary by more than 0.20 from the value used in the mix design.
Which sieves are used for the fineness modulus?
The standard series 0.15, 0.30, 0.60, 1.18, 2.36 and 4.75 mm (Nos. 100, 50, 30, 16, 8 and 4), plus 9.5, 19, 37.5 mm and larger for coarse aggregate. Intermediate sieves such as 2 mm or 0.075 mm are not included in the sum.
Is the material in the pan included?
It counts in the total mass, so it affects the percentages, but the pan is not a sieve and is not added to the cumulative sum.
How is fineness modulus used in mix design?
In ACI 211.1 the volume of dry-rodded coarse aggregate per unit volume of concrete depends on the maximum aggregate size and the sand’s FM — for 19 mm stone it is 0.66 with FM 2.6 and 0.60 with FM 3.0.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.