Sieve Analysis & Gradation Calculator
Percent passing = 100 − cumulative percent retained, the running total of mass retained ÷ total sample mass × 100. Fineness modulus is the sum of cumulative percent retained on the eight sieves from ¾ in to No. 100, ÷ 100. The 1,000 g example gives 60% passing No. 4 and FM 4.71. See the Aggregate Specific Gravity Calculator.
How it's calculated: Cumulative % retained = running total of mass retained ÷ total sample mass × 100; % passing = 100 − cumulative % retained; fineness modulus = sum of cumulative % retained on the ¾ in to No. 100 sieves ÷ 100.
Result appears here
Fill in the fields and press Calculate.
Formula, calculation, assumptions and sources
Cumulative % retained (at a sieve) = running total of mass retained down to that sieve ÷ total sample mass × 100
% passing = 100 − cumulative % retained
Fineness modulus = (sum of cumulative % retained on ¾ in, 3/8 in, No. 4, 8, 16, 30, 50, 100) ÷ 100
Run the calculation to see each step with your own numbers.
A 1,000 g combined aggregate sample sieved down to No. 200, aggregate mode.
Cumulative retained builds: 0, 150, 400, 600, 750, 870, 950, 990, 1000 g
% passing: ¾in 100%, 3/8in 85%, No.4 60%, No.8 40%, No.16 25%, No.30 13%, No.50 5%, No.100 1%, No.200 0%
Fineness modulus = (99+95+87+75+60+40+15+0) ÷ 100 = 4.71
- Dry sieving of a single representative sample; washing loss (material finer than No. 200 lost during a wash sieve analysis) is not separately accounted for.
- The 9 sieves listed are a standard combined series — a specific project spec may call for a different or additional set.
- Fineness modulus uses the 8-sieve ASTM C125 definition (¾ in down to No. 100); it does not include the No. 200 sieve or pan.
- Sieve masses should sum to the total sample mass; a shortfall (material lost to the pan/dust) is normal and shows as % passing the No. 200 sieve.
- What's fineness modulus used for?
- It's a single index number for how coarse or fine an aggregate is — higher means coarser. Fine aggregate (sand) for concrete typically runs 2.3–3.1; a combined or coarse aggregate sample, like the worked example, runs much higher. Mix designers use it to check an aggregate source stays consistent batch to batch.
- Why does this cover both aggregate and soil?
- ASTM C136 (aggregate) and the sieving portion of ASTM D6913 (soil) use the identical percent-retained/percent-passing arithmetic on the same standard sieve series — only the interpretation and specification differ. One calculator avoids near-duplicate pages for the same math.
- My retained weights don't add up to the total mass — is that a problem?
- A small shortfall is normal — it's material finer than your last sieve or lost as dust, and shows up as material passing the finest sieve. A shortfall of more than a percent or two suggests a scale or transcription error worth double-checking.
- How do you calculate percent passing in a sieve analysis?
- Add up the mass retained on that sieve and every coarser one, divide by the total sample mass and multiply by 100, then subtract from 100. With 150 g on the ⅜ in sieve and 250 g on the No. 4, 400 g of 1,000 g is retained — 60% passes the No. 4.
- How is fineness modulus calculated?
- Add the cumulative percent retained on the eight sieves from ¾ in down to No. 100 and divide by 100. In the example that is (0 + 15 + 40 + 60 + 75 + 87 + 95 + 99) ÷ 100 = 4.71. The No. 200 sieve and the pan are not counted.
Aggregate sieve analysis
ASTM C136/C136M, 'Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates'.
Soil sieve analysis
ASTM D6913/D6913M, 'Standard Test Methods for Particle-Size Distribution (Gradation) of Soils Using Sieve Analysis'.
Fineness modulus
ASTM C125, 'Standard Terminology Relating to Concrete and Concrete Aggregates' — fineness modulus definition (sum of cumulative percentages retained on the 8 standard sieves, divided by 100).
About the Sieve Analysis & Gradation Calculator
The Sieve Analysis & Gradation Calculator turns a lab sieve-stack worksheet — the weight of sample retained on each standard sieve — into percent passing at every sieve and the fineness modulus, the same arithmetic ASTM C136 (aggregates) and ASTM D6913 (soil, sieve portion) both use. Enter the total dry sample mass and the mass retained on each sieve from largest to smallest; leave any sieve you skipped at 0. This tool covers sieving only, not hydrometer analysis of the fraction passing the No. 200 sieve.
What you enter
- Sample type
- Total dry sample mass — The dry mass of the whole sample before sieving.
- ¾ in (19.0 mm) retained
- 3/8 in (9.5 mm) retained
- No. 4 (4.75 mm) retained
- No. 8 (2.36 mm) retained
- No. 16 (1.18 mm) retained
- No. 30 (600 µm) retained
- No. 50 (300 µm) retained
- No. 100 (150 µm) retained
- No. 200 (75 µm) retained
What you get back
- % passing ¾ in (19.0 mm) — %
- % passing 3/8 in (9.5 mm) — %
- % passing No. 4 (4.75 mm) — %
- % passing No. 8 (2.36 mm) — %
- % passing No. 16 (1.18 mm) — %
- % passing No. 30 (600 µm) — %
- % passing No. 50 (300 µm) — %
- % passing No. 100 (150 µm) — %
- % passing No. 200 (75 µm) — %
- Fineness modulus — ASTM C125 — sum of cumulative % retained on the 8 standard FM sieves (¾ in through No. 100) ÷ 100.
The formula, a worked example, the assumptions behind it and the sources are shown in full below the calculator.
Related calculators
- Los Angeles Abrasion Value Calculator — Percent loss (LA abrasion value) of a coarse aggregate sample from its mass before and after the Los Angeles abrasion test.
- Aggregate Specific Gravity & Water Absorption Calculator — Bulk (oven-dry and SSD), apparent specific gravity and water absorption of a coarse aggregate sample from its oven-dry, SSD and submerged mass.
- Gravel Calculator — Gravel by volume and by delivered weight for driveways, paths and fill.
- Crushed Stone Calculator — Crushed stone by volume and weight. Shares the density question with the Gravel Calculator.
Related articles
- What Is Aggregate and Why Does Gradation Matter? — Aggregate is the sand and crushed stone in concrete, asphalt and base layers — and its gradation (the mix of particle sizes) matters as much as its size.
- Sieve Analysis Explained for Construction Materials — Sieve analysis shows up across concrete mix design, asphalt production, and base-material specifications — it's one of the most common material tests.
Part of the Materials calculators.