This is a definitive guide to **Fineness Modulus**.

In this guide, you’ll find everything about fineness modulus that you need to know as a construction professional.

That includes:

- Definition of Fineness Modulus

- Sieve analysis process for finding the FM of both fine and coarse aggregates;

- Fineness Modulus formula and calculation process, and

- Lot more

So, if you want to:

- Choose the correct proportions of aggregates for a workable concrete mix design

- Know the average size of aggregates;

- Evaluate aggregate gradations, and

- Control the properties of concrete…

…Then, you’ll love this easy-to-read guide.

## What Is Fineness Modulus?

In short, the Fineness Modulus (FM) is an empirical value that represents the mean size of particles.

Here is the FM range of various types of sand:

To get FM, a sieve analysis is performed with a specified series of sieves.

And, then calculated by a formula.

So, what is the…

## Fineness Modulus Formula

It’s:

With this, let’s learn the…

## Process Of Sieve Analysis And Fineness Modulus Calculation

This time, you’ll learn the process for finding the…

### Fineness Modulus Of Fine Aggregates

Fine aggregates are the particles that pass through the 4.75 mm sieve.

We generally call it Sand.

To perform the sieve analysis of fine aggregates:

#### First, Prepare A Sample.

For that, take some quantity of sand into a pan.

And, place it in an oven.

Let the sample dry at a temperature of approximately **100°c** to **110°c**.

Once dried, take the sample out and note down its weight.

Let’s say, the weight of the dried sample is **1000 grams**.

#### Next, Put Sieves On A Mechanical Shaker.

And, arrange them in a descending order.

That means the largest one will be on top.

These are the sieves we call a **specified series of sieves** for fine aggregates.

You’ll use this definite series of sieves whenever you want to know the FM of fine aggregates.

#### After That, Pour The Sand Sample Into The Top Sieve.

And, close it with a sieve plate and switch on the mechanical shaker to shake the sand for at least five minutes.

* Note that:* You can perform this task manually too (without a mechanical shaker).

In that case, put the sample into the top sieve and close it.

And then hold the top two sieves by hand.

After that, shake it horizontally and vertically, inwards & outwards.

Again, do it for the 4th & 3rd sieves, and then the remaining sieves.

#### Next, Record The Retained Quantity Of Sand On Each Sieve.

And, write them down in a chart like the image below:

**Look:** In the chart above, the retained aggregate is zero on the 4.75 mm sieve.

That means, our sample is fine aggregates.

So, we can say, fine aggregates will pass through the 4.75 mm sieve.

Okay!

#### Now, Calculate The Cumulative Percentage Of Weight Retained

And, you’ll get this:

#### Finally, Calculate The Fineness Modulus.

And, it is:

So, the fineness modulus of our sample aggregate is **2.75**.

Done!

But:

#### How Can You Determine The Average Particle Size Of Fine Aggregates…

…From the fineness modulus?

Let’s see:

The FM of our sample sand is 2.75.

That means the sand is in between the **2nd** and **3rd** sieve.

And, the size of those two sieves is **0.3** mm and **0.6** mm respectively.

So, we can say that the average size of our sample aggregates is between 0.3 mm and 0.6 mm.

Now that you know the process, let’s perform the test to get the…

### Fineness Modulus Of Coarse Aggregates

The procedure of finding the fineness modulus of coarse aggregates is the same as fine aggregates.

But, with a little variation.

So let’s perform the test and see where it varies.

For that:

#### First, Prepare A Sample.

To do that, take some quantity of coarse aggregates into a pan.

And, place it in an oven.

Let the sample dry at a temperature of approximately **100°c** to **110°c**.

Once dried, take the sample out and note down its weight to the nearest grams.

Let’s say, it’s 5000 grams.

#### Next, Put Sieves On A Mechanical Shaker.

And, arrange them in a descending order.

The largest one should be on top.

(See the Image below:)

As you can see in the above image, we use a series of sieves that starts with an **80 mm** sieve on the top.

And, a **0.15 mm** sieve at the bottom.

In between, there are **8** more sieves.

These are the sieves we call a specified series of sieves for coarse aggregates.

Whenever you want to know the FM of coarse aggregates, you’ll use this definite series of sieves.

[*Note:**Manual testing for coarse aggregates should be avoided due to the large number of sieves involved and the considerable weight of the coarse aggregates.*]

#### After That, Pour The Coarse Aggregates Sample Into The Top Sieve.

And, close it with a sieve plate and switch on the mechanical shaker to shake the aggregates for at least five minutes.

#### Next, Record The Retained Quantity Of Aggregates On Each Sieve.

And, write them in a chart like the image below:

**Look:** In the above chart, no particles passed through the 4.75 mm sieve.

So, we can say, these are coarse aggregates.

In other words, the aggregates which are retained on the 4.75 mm sieve are the coarse aggregates.

From this definition, you may ask, why have we used sieves in this test that are smaller than 4.75 mm?

Because fineness modulus is a value that basically indicates the number of sieves from lower to higher size (Read on).

#### Now, Calculate The Cumulative Percentage Of Weight Retained.

You’ll get this:

#### Finally, Calculate The Fineness Modulus.

And, it is:

So, the fineness modulus of our sample coarse aggregates is **7.17**.

Done!

But,

#### How Can You Determine The Average Size Of Particles Of Coarse Aggregates

Let’s see.

The FM of our sample coarse aggregates is **7.17**.

That means the aggregate is in between the** 7th** and **8th** sieve.

And, the size of those two sieves is **10 **mm and** 20 mm** respectively.

So, we can say that the average size of our sample aggregate is in between those two sieves.

**Here is the range of fineness modulus of coarse aggregates of different sizes:**

So far, you’ve learned about the process of getting FM of fine and coarse aggregates.

But,

## Why Do You Need To Know About Fineness Modulus…

…As a construction professional?

Basically, the fineness modulus is used for concrete mix design.

Duff Abrams, an American materials researcher, defined fineness modulus in **1918** as a way of:

- Characterizing concrete aggregates;

- Simplifying the gradation curve, and

- Estimating the correct proportions to use in the mix design.

He said:

“*Aggregate of the same fineness modulus will require the same quantity of water to produce a mix of the same consistency and give a concrete of the same strength.*”

So, it’s a job for a mix designer to find out the required FM of aggregates and the correct proportion of materials.

And, they specify that in the structural drawing book.

As construction professionals, we need to ensure that we are using aggregates of specified FM.

And, producing concrete with the correct proportions.

That’s it for the fineness modulus.

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