What is Fineness Modulus and how to calculate it

Definition of Fineness Modulus :

The fineness modulus is define in ACI terminology as “A factor obtained by adding the total percentages of material in the  sample that are coarser than each of the following sieves (cumulative  percentages retained), and dividing the sum by 100: 0.15 mm (No. 100),0.30 mm (No. 50), 0.60 mm (No. 30), 1.18 mm (No. 16),2.36 mm (No. 8), 4.75 mm (No. 4), 9.5 mm (3/8in.), 19.0 mm (3/4 in.), 37.5 mm  (1-1/2in.), 75 mm (3 in.), 150 mm (6 in.).”

Fineness modulus gives the idea about how course or fine the sand is. Lower FM indicates fine sand and higher FM indicates courser sand.Fine sand requires more cement paste due to high surface area and tendency to develop crack. On the other hand course sand produces a concrete mixture that is harsh and difficult to finish and will cause segregation.Therefore recommended FM range is 2.3 to 3.1.
Following table shows fineness modulus for different types of sand

Type of Sand	Fineness Modulus Range
Fine Sand	2.2 – 2.6
Medium Sand	2.6 – 2.9
Coarse Sand	2.9 – 3.2

How to calculate Fineness Modulus

Procure to determine Fineness Modulus

1. Sieve the aggregate using the appropriate sieves (80 mm, 40 mm, 20 mm, 10 mm, 4.75 mm, 2.36 mm, 1.18 mm, 600 micron, 300 micron & 150 micron)
2. Note down the weight of aggregate retained on each sieve.
3. Calculate the cumulative weight of aggregate retained on each sieve.
4. Find out the cumulative percentage of aggregate retained on each sieve.
5. Sum the cumulative weight of aggregate retained and divide the sum by 100.
   FM = ∑ Cumulative % retain on each Sieve  / 100

Calculation sheet to calculate Fineness Modulus

Sieve of Size (in mm)	Weight of sand Retained (g)	Cumulative weight of sand retained (g)	Cumulative percentage of sand retained (%)
80 mm	–
40 mm	–
20 mm	–
10 mm	0	0
4.75 mm	10	10	2
2.36 mm	50	60	12
1.18 mm	70	130	26
600 micron	90	220	44
300 micron	160	380	76
150 micron	80	460	92
Pan	40	500
Total	500	1760	252

Fineness Modulus = 252/100 = 2.52