Size Distribution Calculator
Cumulative curve, D10–D90 and Cu/Cc from masses retained per sieve.
Calculator
Retained masses per sieve
Theory & method
Sieve analysis determines the particle-size distribution of a granular material by shaking a dried sample through a stack of sieves with decreasing apertures and weighing the mass retained on each. The cumulative passing curve — % of mass finer than each aperture, plotted against aperture on a logarithmic axis — is the standard representation defined in ISO 9276-1.
Characteristic diameters (D-values) are read from the curve: D10, D30, D50 (median), D60 and D90 are the sizes below which 10%, 30%, 50%, 60% and 90% of the mass lies. This calculator interpolates them log-linearly between measured points and never extrapolates beyond the measured curve — a percentile outside the tested range is reported as unavailable rather than guessed.
Two coefficients summarize the shape of the curve per ASTM D2487: the coefficient of uniformity Cu = D60/D10 and the coefficient of curvature Cc = D30²/(D10·D60). Together with the gravel, sand and fines fractions (sieves No. 4 and No. 200), they drive the Unified Soil Classification System (USCS): a sand with Cu ≥ 6 and 1 ≤ Cc ≤ 3 is well graded (SW), otherwise poorly graded (SP); for gravel the Cu threshold is 4 (GW/GP).
Sieving alone yields a definitive USCS symbol only when fines are below 5%. Between 5% and 12% a dual symbol applies, and above 12% the second letter (M for silt, C for clay) depends on the Atterberg limits of the fines — information a sieve test cannot provide. This calculator states that limitation explicitly instead of guessing. The test itself is validated by the mass-loss criterion of ASTM C136 §9.2: more than 0.3% difference between initial and recovered mass invalidates the run.
How to use
- 01Enter the aperture (µm) and dry retained mass (g) for each sieve in the stack. Use the series selector to add standard ASTM E11 sieves, and 0 g for sieves that retained nothing.
- 02Enter the mass collected in the pan and, optionally, the initial dry sample mass to validate the 0.3% mass-loss criterion.
- 03Read the cumulative passing curve, the D-values with Cu and Cc, and the USCS classification with its gravel/sand/fines split.
- 04If the classification requires Atterberg limits (fines ≥ 5%), the possible symbols are listed and the required complementary test is indicated.
Frequently asked questions
How are D10, D50 and D90 calculated?
By log-linear interpolation on the cumulative passing curve (linear in log-aperture vs. % passing), following the representation of ISO 9276-1. Percentiles outside the measured curve are not extrapolated — extend the sieve stack or complement with sedimentation if you need them.
What do Cu and Cc mean?
Cu = D60/D10 measures how spread out the grading is; Cc = D30²/(D10·D60) measures the shape of the curve between D10 and D60. ASTM D2487 uses both: well-graded sand requires Cu ≥ 6 and 1 ≤ Cc ≤ 3; well-graded gravel requires Cu ≥ 4 and 1 ≤ Cc ≤ 3.
Why doesn't the calculator always give a single USCS symbol?
Because the standard doesn't allow it. With 5–12% fines, ASTM D2487 assigns a dual symbol whose second half (e.g. SP-SM vs. SP-SC) depends on the plasticity of the fines, and above 12% the M/C distinction requires Atterberg limits. The calculator lists the possible symbols and tells you which complementary test decides.
What invalidates a sieve analysis?
Per ASTM C136 §9.2 (and NBR NM 248), a difference greater than 0.3% between the initial dry mass and the sum of retained masses plus pan invalidates the test. A non-monotonic cumulative curve — % passing decreasing with size — is physically impossible and is rejected as an input error.
Normative references
- ISO 9276-1:1998 — Representation of results of particle size analysis — Graphical representation.
- ISO 9276-2:2014 — Calculation of average particle sizes/diameters and moments from particle size distributions.
- ASTM D2487-17 — Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System).
- ASTM C136/C136M-19 — Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates.