Authoritative Data Source and Methodology

Primary reference: ASTM International, “ASTM C136/C136M-19: Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates,” 2019. Direct standard page. Secondary reference for grading limits: ASTM International, “ASTM C33/C33M-18: Standard Specification for Concrete Aggregates,” 2018. Direct standard page.

All calculations are strictly based on the formulas and data provided by this source.

The Formulas Explained

1. Percent retained on sieve i: P_i = \\frac{w_i}{\\sum_{k=1}^{n} w_k}\\times 100
2. Cumulative percent retained up to sieve i: C_i = \\sum_{j=1}^{i} P_j
3. Percent passing on sieve i: F_i = 100 - C_i
4. Fineness Modulus (fine aggregate): FM = \\frac{\\sum C_{\\#4,\\#8,\\#16,\\#30,\\#50,\\#100}}{100}
5. Particle sizes at fraction passing (log interpolation): \\log_{10}(D_p) = \\log_{10}(d_1) + (\\log_{10}(d_2)-\\log_{10}(d_1))\\cdot \\frac{p-F_1}{F_2-F_1}
6. Uniformity and Curvature Coefficients: C_u = \\frac{D_{60}}{D_{10}}, \\quad C_c = \\frac{D_{30}^2}{D_{10}\\cdot D_{60}}

Glossary of Variables

  • w_i: mass retained on sieve i (g or kg)
  • P_i: percent retained on sieve i
  • C_i: cumulative percent retained through sieve i
  • F_i: percent passing sieve i
  • D10, D30, D60: particle sizes at 10%, 30%, 60% passing (mm)
  • C_u, C_c: coefficients describing gradation uniformity and curvature
  • FM: Fineness Modulus for fine aggregate

How It Works: A Step-by-Step Example

Example: Select “Fine Aggregate (ASTM C33)”. Suppose you test a 1000 g oven-dry sand with the following masses retained: No. 4: 20 g, No. 8: 80 g, No. 16: 180 g, No. 30: 260 g, No. 50: 240 g, No. 100: 170 g, Pan: 50 g.

  1. Total mass W = 20+80+180+260+240+170+50 = 1000 g.
  2. Percent retained P_i = w_i / W × 100. For No. 30: 260/1000 × 100 = 26%.
  3. Cumulative retained C_i is the running total. If through No. 30 the sum is 54%, then F_30 = 100−54 = 46% passing.
  4. FM = (C_#4 + C_#8 + C_#16 + C_#30 + C_#50 + C_#100) / 100. If the sum is 270, FM = 2.70.
  5. Interpolate D10, D30, D60 on the % passing curve using log spacing of sieve openings.

The tool performs these steps automatically and flags any result outside ASTM C33 limits.

Frequently Asked Questions (FAQ)

Do I need to use the exact ASTM sieves?

No. You can add or remove rows and enter any sieve openings you used. Compliance checks only apply to supported templates.

What if my sample was wet?

Use the moisture correction field to normalize to oven-dry mass. If you already corrected to dry mass, leave it at 0%.

My percent retained doesn’t sum to 100%. Is that a problem?

The tool shows the sum. Small rounding discrepancies (±0.5%) are typical; large gaps may indicate weighing or data-entry errors.

How accurate are D10, D30, D60?

They are interpolated linearly between adjacent points on a log-size axis, which is standard for gradation curves.

What FM range is acceptable?

Most concretes use fine aggregates with FM roughly 2.3–3.1. Mix design and workability may dictate narrower targets.

Does this tool replace laboratory procedures?

No. It complements ASTM-compliant lab testing by accelerating calculations and documentation.

Tool developed by Ugo Candido. Content verified by CalcDomain Editorial Team.
Last reviewed for accuracy on: .