Fineness Modulus Calculator

Reviewed By: Patrick Myers (BSME)

Enter sieve analysis results (percent retained or cumulative percent retained on each sieve in a standard series) into the calculator to determine the fineness modulus (FM) of the aggregate.

Enter values for the listed sieves to calculate FM. Leave a field blank to treat it as 0.

Input Type Percentage Unit

Sieve sizes are listed from largest to smallest (mm). FM is dimensionless.

38.1 mm sieve 19.0 mm sieve 9.5 mm sieve 4.75 mm sieve 2.36 mm sieve 1.18 mm sieve 0.60 mm sieve 0.30 mm sieve 0.15 mm sieve Fineness Modulus (FM)

Fineness Modulus Formula

The following formula is used to calculate the fineness modulus of an aggregate from a specified sieve series.

FM = \frac{\sum_{i=1}^{n} CP_i}{100}

Variables:

FM is the fineness modulus of the aggregate (dimensionless)
CP_i is the cumulative percent retained on sieve i in the chosen sieve series
n is the number of sieves included in the series

To calculate the fineness modulus (FM), add the cumulative percentages retained on each sieve in the series, then divide the sum by 100.

What is Fineness Modulus?

Fineness modulus (FM) is an empirical, dimensionless index that describes aggregate gradation. It is computed by summing the cumulative percent retained on each sieve in a specified sieve series and dividing that sum by 100. The exact sieve series used depends on the applicable standard and whether fine, coarse, or combined aggregate is being evaluated; a commonly used progression includes 0.15 mm, 0.30 mm, 0.60 mm, 1.18 mm, 2.36 mm, 4.75 mm, and often larger sieves such as 9.5 mm and above for coarser materials. Higher FM values indicate a coarser aggregate gradation, and lower FM values indicate a finer gradation.

How to Calculate Fineness Modulus?

The following steps outline how to calculate the Fineness Modulus.

Perform a sieve analysis and determine the percent retained on each sieve in the selected FM sieve series.
Compute the cumulative percent retained at each sieve (a running total from the largest sieve down to the smallest sieve in the series).
Add the cumulative percent retained values for all sieves in the series.
Divide the sum by 100 to calculate the fineness modulus (FM).
After calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Cumulative percent retained on each sieve: 38.1 mm = 0%, 19.0 mm = 0%, 9.5 mm = 0%, 4.75 mm = 2%, 2.36 mm = 10%, 1.18 mm = 25%, 0.60 mm = 50%, 0.30 mm = 80%, 0.15 mm = 90%.

Sum = 0 + 0 + 0 + 2 + 10 + 25 + 50 + 80 + 90 = 257, so FM = 257 / 100 = 2.57.