Fineness Modulus of Sand: Formula, Ranges and Example

The fineness modulus of sand is a single number that sums up how coarse or fine a sand is. You get it from an ordinary sieve analysis: add up the cumulative percent retained on a standard stack of sieves and divide by 100. A bigger number means a coarser sand. Concrete producers, ready-mix plants and state labs use it to accept sand, to keep an eye on a pit or quarry from one load to the next, and to decide how much stone goes into a concrete mix. This guide covers the formula, a worked example, a shortcut that works from percent passing, the usual ranges and what the number does and does not tell you.

The short answer

Formula: FM = (sum of cumulative percent retained on the No. 100, 50, 30, 16, 8 and 4 sieves, plus 3/8 inch and larger) ÷ 100. The No. 200 sieve is left out.
Concrete sand limits: ASTM C33 asks for a fineness modulus between 2.3 and 3.1 for fine aggregate in concrete.
Consistency rule: under C33, ongoing shipments from one source should stay within 0.20 of that source’s usual (base) value.
Typical values: sands tend to fall roughly between 2 and 4, while coarse aggregate usually lands somewhere around 6.5 to 8.

What fineness modulus measures

A full gradation lists a percentage for every sieve, which is a lot to compare when you are checking dozens of deliveries. The fineness modulus folds that table into one index. Each sieve in the standard series has an opening about twice the size of the one below it (150 µm, 300 µm, 600 µm, 1.18 mm, 2.36 mm, 4.75 mm, 9.5 mm and so on), so the sum works out to something like the average sieve a particle is held on. Coarse grains get held on many sieves and push the total up. Fine grains slip through most of them and keep it low.

The idea goes back to Duff Abrams, who in 1918 proposed proportioning concrete from the fineness modulus of the combined aggregate. That exact method has largely faded, but the index stuck because it is quick to compute and easy to track over time. The U.S. Army Corps of Engineers still keeps a short method sheet for it, CRD-C 104, and ASTM C136 / AASHTO T 27 sieve results are the usual input.

The sieves used

For sand, the sieves that count are the No. 100 (150 µm), No. 50 (300 µm), No. 30 (600 µm), No. 16 (1.18 mm), No. 8 (2.36 mm), No. 4 (4.75 mm) and 3/8 inch (9.5 mm). For coarse aggregate you keep going with the 3/4 inch, 1-1/2 inch and larger sizes in the same doubling pattern. Sizes outside that series, such as the 1/2 inch or the No. 200, are not part of the sum even if you ran them in the test. If you have not run the test before, our step-by-step sieve analysis of aggregate guide shows how to get cumulative percent retained from the weights on each sieve.

Worked example: a concrete sand

Here is a made-up sample, with cumulative percent retained already worked out from the sieve weights:

Sieve	Cumulative % retained	% passing
3/8 in (9.5 mm)	0	100
No. 4 (4.75 mm)	3	97
No. 8 (2.36 mm)	14	86
No. 16 (1.18 mm)	33	67
No. 30 (600 µm)	57	43
No. 50 (300 µm)	80	20
No. 100 (150 µm)	95	5

Add the retained column: 0 + 3 + 14 + 33 + 57 + 80 + 95 = 282. Divide by 100 and the fineness modulus is 2.82. That sits inside the 2.3 to 3.1 window, and every percent passing value in the table also falls inside the ASTM C33 grading band for fine aggregate (100 passing the 3/8 inch, 95 to 100 the No. 4, 80 to 100 the No. 8, 50 to 85 the No. 16, 25 to 60 the No. 30, 5 to 30 the No. 50 and 0 to 10 the No. 100).

Shortcut when you only have percent passing

Supplier sheets and specs usually list percent passing, not retained. You do not need to convert every line. CRD-C 104 gives a shortcut:

FM = (N × 100 − sum of percent passing) ÷ 100

N is the number of sieves in the sum, counted from the largest one you include down to the No. 100. For the example above, N is 7 (3/8 inch through No. 100) and the passing values add to 100 + 97 + 86 + 67 + 43 + 20 + 5 = 418. So FM = (700 − 418) ÷ 100 = 2.82, the same answer. Start the count at a sieve that passes 100 percent, and make sure you include each standard size in between.

What counts as fine, medium or coarse sand?

There is no single national scale, but a common rule of thumb, used for example in a North Carolina DOT concrete training manual, is:

Fine sand: about 2.3 to 2.5
Medium sand: about 2.5 to 2.8
Coarse sand: about 2.8 to 3.1

Sands used for mortar and plaster are usually finer than concrete sand, which is one reason the two are sold separately. Our comparison of mason sand vs concrete sand covers the practical differences.

ASTM C33 rules that go with it

ASTM C33, the common U.S. spec for concrete aggregate, uses the fineness modulus in three ways for sand:

A window: not less than 2.3 and not more than 3.1.
A consistency check: for continuing shipments from a source, the value should not drift more than 0.20 from that source’s base fineness modulus. A sand that tests 2.70 most of the time should stay between 2.50 and 2.90.
A shape check on the gradation: no more than 45 percent may pass one sieve and be retained on the next one down, so a sand that is all one size fails even if its FM looks fine.

Those numbers sit alongside other C33 limits, such as caps on material finer than the No. 200 sieve and on clay lumps. State DOT specs often copy C33 with local changes, so the job spec is the one that rules.

Why concrete mix design cares

The main use of fineness modulus in a mix is choosing how much coarse aggregate to put in. In the ACI 211.1 proportioning method, a table tells you how much dry-rodded stone, as a fraction of each cubic yard or cubic metre of concrete, to use based on the maximum stone size and the sand’s fineness modulus. A finer sand (lower FM) has more surface area to coat with paste, so the table calls for more stone and less sand to keep water demand in check. A coarser sand gets a bit less stone. That is why a change of a couple of tenths in a sand’s FM can be enough for a ready-mix plant to adjust its batch weights.

Most homeowners never see this directly. If you are figuring bags or yards for a slab, our concrete calculator and the concrete mix ratio guide are the practical starting points.

Coarse aggregate and combined fineness modulus

The same math works for stone; you simply include the larger sieves. Because nearly all of a stone sample is held on the No. 4 and everything below it, its fineness modulus comes out much higher, usually in the 6.5 to 8 range when everything passes the 1-1/2 inch sieve.

For a blend of sand and stone, the combined fineness modulus is close to the weighted average of the two. Say a mix uses 40 percent sand at FM 2.82 and 60 percent stone at FM 7.10 by weight: 0.40 × 2.82 + 0.60 × 7.10 = 1.13 + 4.26 = about 5.39. Some agencies and contractors track combined FM to keep blends steady, though limits are far more often set on the sand alone.

What the number cannot tell you

Different gradings can share one value. CRD-C 104 points out that several particle-size distributions can give the same fineness modulus. Two sands at 2.75 can still behave differently, so it never replaces the full gradation.
It ignores dust. The No. 200 sieve is not in the sum, so clay and silt content has to be checked separately.
It says nothing about shape or quality. Rounded river sand and crushed manufactured sand at the same FM can need different water, and things like soundness or organic impurities are separate tests.
Asphalt specs lean on the gradation itself. Hot mix asphalt designs, including Superpave, usually control aggregate with sieve-by-sieve limits rather than a fineness modulus, though the sieve analysis behind it is the same.

Common mistakes when calculating it

Using percent passing in the retained formula. Summing passing values and dividing by 100 gives a meaningless number. Either convert to retained or use the shortcut above.
Adding non-standard sieves. Including a 1/2 inch, No. 40 or No. 200 result inflates the total.
Skipping a sieve with zero retained. A standard size with 0 percent retained still belongs in the list, and in the shortcut it still counts toward N.
Mixing up the sample. The test must be run on a properly split, dried sample. A poor sample gives a precise-looking number that does not describe the stockpile.

Questions people ask

What is the fineness modulus of sand?

It is an index of how coarse a sand is. Total up the cumulative percentages held on each standard sieve, from the No. 100 through the 3/8 inch and larger, and divide that total by 100. Higher values mean coarser sand.

What is a good fineness modulus for concrete sand?

ASTM C33 calls for fine aggregate with a fineness modulus from 2.3 to 3.1. Many producers aim for the middle of that range, and the job or state spec may set its own limits.

Which sieves are used to calculate fineness modulus?

The No. 100, No. 50, No. 30, No. 16, No. 8 and No. 4 sieves, plus 3/8 inch, 3/4 inch, 1-1/2 inch and larger sizes in the same doubling series. The No. 200 sieve is not included.

Can you calculate fineness modulus from percent passing?

Yes. Use FM = (N x 100 - sum of percent passing) / 100, where N is the number of standard sieves counted from the largest one included down to the No. 100.

What does a fineness modulus of 2.5 mean?

It points to a fairly fine sand, near the line many references draw between fine and medium sand. It is inside the ASTM C33 range for concrete sand, but the full gradation still has to meet the spec.

What is the fineness modulus of coarse aggregate?

Stone uses the same calculation with the larger sieves included. Values usually fall somewhere around 6.5 to 8 when all of the material passes the 1-1/2 inch sieve.

Related guides

Open the sand calculator →

As an Amazon Associate, AsphaltTons.com earns from qualifying purchases. Product links below are sponsored.