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.
How do you calculate a particle size distribution from a sieve analysis?
Weigh the mass retained on each sieve and on the pan, divide each by the total recovered mass to get the percentage retained, then accumulate from the pan upwards to get the percentage passing at each aperture. Plotting that passing percentage against aperture on a logarithmic axis gives the distribution, in the representation defined by ISO 9276-1. D50 is simply the aperture at which the curve crosses 50% passing — read by interpolation, not by picking the nearest sieve.
What is the difference between the retained curve and the cumulative passing curve?
The retained curve shows how much mass stayed on each individual sieve — it is a histogram, and its shape depends on which apertures you happened to stack. The cumulative passing curve shows how much of the sample is finer than each aperture; it always rises monotonically and is comparable between labs using different sieve sets. D-values, Cu and Cc are all read from the cumulative curve, never from the retained one.
Can I compute D10, D50 and D90 in a spreadsheet instead?
Yes, but the common mistake is interpolating linearly on a linear size axis, which biases every D-value. Bracket the target percentile P between the two measured points (d1, P1) and (d2, P2), then interpolate on the logarithm of the aperture: D = EXP(LN(d1) + (P − P1)/(P2 − P1) × (LN(d2) − LN(d1))). And never extrapolate past your coarsest or finest measured point — a D90 outside the tested range is not a result.
How do I plot the grain size distribution curve?
Aperture on the horizontal axis, on a logarithmic scale, running coarse to fine from left to right; cumulative percentage passing on the vertical axis, linear from 0 to 100. The log axis is not cosmetic — sieve series are geometric progressions, so on a linear axis the fine end collapses into the origin and the curve cannot be read. This calculator plots that chart directly and exports it with the underlying table.
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.