Percent passing in sieve analysis is calculated by subtracting the cumulative percent retained on each sieve from 100. The process starts with weighing the material retained on every sieve after shaking, converting each retained weight into a percentage of the total sample, accumulating those percentages from the coarsest sieve down, and then subtracting from 100 at each level. The math itself is straightforward arithmetic, but getting reliable numbers depends on understanding how the data flows from raw weights to the final gradation curve, and where small errors can cascade into misleading results.
From Raw Weights to Percent Passing
After you run a sieve analysis, you end up with a stack of sieves, each holding some amount of material, plus whatever fell through to the bottom pan. The first step is to weigh the material on each sieve individually. Record these as your “mass retained” values. Then add up every retained mass, including the pan, to get the total. This total should be close to the original sample weight you recorded before shaking. If the two differ by more than about 1–2%, something went wrong during the test, and the results may not be trustworthy.
Once you have all retained masses and the total, you calculate percent retained for each sieve by dividing the mass retained on that sieve by the total mass and multiplying by 100. Then you work down from the largest opening to the smallest, adding each percent retained to the running total above it. That running total is the cumulative percent retained. Finally, for each sieve, you subtract the cumulative percent retained from 100. The result is your percent passing, sometimes called percent finer. It tells you what fraction of the total sample was small enough to pass through that particular opening size.
Here is the sequence laid out as discrete steps:
- Weigh each fraction: Record the mass retained on every sieve and the bottom pan. Sum them to get the total recovered mass.
- Percent retained: For each sieve, divide mass retained by total mass, then multiply by 100.
- Cumulative percent retained: Starting at the coarsest sieve, add each sieve’s percent retained to the sum of all coarser sieves above it.
- Percent passing: Subtract the cumulative percent retained from 100 at each sieve.
The bottom pan should always show 100% cumulative retained (and therefore 0% passing), because nothing passes through solid metal. If your cumulative retained at the pan does not reach 100%, the individual percent-retained values do not add up correctly, and you should recheck your arithmetic or your weighing.
A Worked Example
Suppose you sieve 500 grams of sand through five sieves and a pan, and record the following retained masses: 4.75 mm sieve holds 35 g, 2.36 mm holds 85 g, 1.18 mm holds 140 g, 600 µm holds 120 g, 300 µm holds 80 g, and the pan holds 40 g. The total is 500 g, matching the original sample.
Percent retained on the 4.75 mm sieve is 35 ÷ 500 × 100 = 7.0%. On the 2.36 mm sieve it is 85 ÷ 500 × 100 = 17.0%. The cumulative percent retained at the 4.75 mm sieve is just 7.0% (nothing is coarser), so the percent passing at that sieve is 100 − 7.0 = 93.0%. At the 2.36 mm sieve, cumulative retained is 7.0 + 17.0 = 24.0%, so percent passing is 76.0%. You continue that pattern all the way down. At the pan, cumulative retained reaches 100% and percent passing is 0%.
That percent-passing column is what you ultimately report and plot. Every specification limit you will ever see for aggregate, soil, pharmaceutical powder, or any other granular material is written in terms of percent passing at specific sieve sizes.
Plotting the Gradation Curve
Numbers in a table are useful, but most engineers and geologists convert percent passing into a gradation curve, also called a particle-size distribution curve. You plot sieve opening size on the horizontal axis (using a logarithmic scale, because sieve sizes span orders of magnitude) and percent passing on the vertical axis (using a standard linear scale). Each sieve’s data point goes on the chart, and you connect them with a smooth line.
The shape of this curve reveals a lot. A steep, nearly vertical curve means most particles are about the same size. A gently sloping curve that stretches across many sieve sizes means a wide spread of particle dimensions. In geology, grain-size distribution is a fundamental tool for interpreting sedimentary units within depositional systems, because different transport mechanisms sort grains into recognizable patterns.1Sedimentology. A comparison of grain‐size analysis methods for sand‐dominated fluvial sediments In civil engineering, the curve is compared against specification envelopes to confirm that an aggregate meets design requirements.
Researchers studying the Wasia Formation sandstone in Saudi Arabia, for example, used dry-sieving procedures on fourteen representative samples and found unimodal distributions centered on particular phi values depending on whether the sample came from the upper or lower section of the formation, with a couple of beds showing bimodal distributions.2Sustainability. Grain-Size Analysis of Middle Cretaceous Sandstone Reservoirs, the Wasia Formation, Riyadh Province, Saudi Arabia Those distribution shapes tell geologists something about the energy of the environment where the sediment was deposited. The gradation curve makes that story visible at a glance.
Reading Useful Numbers Off the Curve
Once you have the gradation curve, you can pull specific values from it that engineers and soil scientists use constantly. The most common are D10, D30, and D60, which are the particle diameters at which 10%, 30%, and 60% of the sample (by mass) is finer. You read these directly off the curve by finding the desired percent passing on the vertical axis and tracing horizontally to the curve, then dropping down to the horizontal axis to read the particle size.
From these values, two coefficients are widely used. The coefficient of uniformity (Cu) equals D60 divided by D10, and the coefficient of curvature (Cc) equals D30 squared divided by the product of D60 and D10. A soil is generally considered well-graded if Cu is greater than 4 for gravels or greater than 6 for sands, and Cc falls between 1 and 3. If either coefficient falls outside those ranges, the soil is considered poorly graded.3Elsevier. Significance of Cu and Cc in Evaluating Internal Stability with Application to Design of Subbase Gradation in Pavements These classifications matter for real decisions: a well-graded soil compacts more efficiently and drains differently than a poorly graded one, which affects everything from road construction to foundation design.
Common Mistakes That Throw Off Your Numbers
The arithmetic of percent passing is simple enough that most errors do not come from the math itself. They come from the testing procedure, and they show up in your final percentages in ways that can be hard to detect after the fact.
Overloading a sieve is one of the most frequent problems. If you put too much material on a single sieve, particles that should pass through cannot reach the openings because the bed of material is too thick. The result is artificially high retained mass on that sieve and artificially low percent passing at that size. Standards typically specify maximum masses per sieve based on the opening size and sieve diameter. The fix is to split large samples into smaller charges or use larger-diameter sieves.
Insufficient shaking time is related. If you stop the shaker too early, fine particles that have not yet worked their way through the mesh get counted as retained. This inflates the coarser fractions and depresses percent passing on the finer sieves. Many labs run the shaker for a set time and then check whether an additional minute of shaking changes the retained masses by more than a small threshold. If it does, the original time was not long enough.
Not accounting for material loss is another pitfall. If the total recovered mass is noticeably less than the starting mass, some material was lost, possibly blown out by the shaker, stuck in sieve frames, or spilled during transfer. Because every percent-retained value uses the total as its denominator, a low total inflates every percentage. Some labs use the original sample weight as the denominator instead of the recovered total, but this introduces a different kind of error: the “missing” mass is effectively treated as finer than the finest sieve, which skews the pan fraction.
Wet Sieving Versus Dry Sieving
Most routine sieve analyses are done dry. You oven-dry the sample, weigh it, pour it onto the top sieve, shake, and weigh each fraction. But some materials clump together when dry, forming agglomerates that behave as if they are much larger than the individual particles. Clays, silts, and certain powders are especially prone to this.
In wet sieving, you wash the sample through the sieves with water, which breaks apart those clumps and lets the true fine particles pass through. The difference can be dramatic. A study comparing wet and dry sieving on 47 limestone samples found that 15 samples showed differences of 5% or more in the percent passing at the No. 40 sieve when the dry samples were not pre-crushed to break agglomerates, and three of those samples differed by more than 15%. Even manually crushing the dry samples with a rubber roller before sieving only reduced the discrepancy by about 3 to 10 percentage points on those 15 problem samples.4Journal of AOAC INTERNATIONAL. Wet Sieve Analysis of Limestone
A 15-percentage-point swing in percent passing at a single sieve is enormous. It can move a material from “within specification” to “rejected” or vice versa. If you are working with any material that tends to clump, wet sieving produces a more accurate picture of the true particle-size distribution. The tradeoff is that wet sieving takes longer and requires drying the retained fractions before weighing, which adds time and introduces its own handling steps.
Why Particle Shape Complicates the Results
Sieves sort particles by whether they can fit through a square opening. A perfectly spherical particle either passes or does not, cleanly. But real particles are rarely spherical. A flat, plate-like particle might be longer than the sieve opening in one dimension but thin enough to slip through on its edge. A long, needle-like particle might pass through at certain orientations and get stuck at others. The result is that sieve analysis does not measure the size of any individual particle in a strict geometric sense; it measures an effective size that is heavily influenced by particle shape.5Engineering Geology. The effect of particle form on sieve analysis: a test by image analysis
For most civil engineering applications, this is actually fine. The sieve-based “size” is what matters for predicting how the material will pack, drain, and compact, because those behaviors are also shape-dependent. Problems arise when you try to compare sieve-analysis results with measurements from a different technique. Laser diffraction, for instance, reports a particle diameter based on how the particle scatters light, which depends on its volume. A flat particle with a large surface area but small volume will register differently on a laser instrument than on a sieve. Research comparing the two methods found that discrepancies were attributable to particle shape factors and varied depending on the size fraction examined, though laser diffraction gave sufficient accuracy when applied to products with a narrow range of particle size.6Powder Technology. Comparison of sieving and laser diffraction for the particle size measurements of raw materials used in foodstuff
The practical takeaway is that percent-passing values from sieve analysis and percent-finer values from laser diffraction are not directly interchangeable, even though both describe particle-size distribution. If a specification was written around sieve analysis, you need to meet it with sieve analysis. Mixing methods without a documented correlation is a recipe for disputes.
How Specifications Use Percent Passing
Nearly every industry that handles granular materials sets specifications in terms of percent passing at designated sieve sizes. In road construction, state and national standards define upper and lower limits for aggregate gradation, creating an envelope on the gradation curve. Your plotted curve must fall inside that envelope at every specified sieve size for the material to be accepted. Falling outside even at a single sieve size can mean rejecting an entire stockpile.
In geotechnical work, the percent-passing values feed directly into soil classification systems. A soil where more than 50% passes the No. 200 sieve (75 µm opening) is classified as fine-grained, and the testing shifts to methods like hydrometer analysis for the portion below that threshold, because particles that fine cannot be mechanically sieved. A soil where less than 50% passes the No. 200 sieve is coarse-grained, and the gradation curve from sieve analysis becomes the primary classification tool.
In food processing and pharmaceuticals, particle-size specifications control how powders dissolve, compress, and flow. A flour that is too coarse will not hydrate properly; a pharmaceutical excipient with the wrong gradation will not form uniform tablets. The percent-passing calculation is identical in these fields. The sieve sizes and target ranges differ, but the math and the curve do not change.
Applications Beyond Engineering
Sieve analysis and the percent-passing framework show up in environmental science and geology for reasons that have nothing to do with meeting a construction specification. In glacial and fluvial settings, grain-size distribution of sediment transported by rivers and streams tells researchers about the energy of the water, the distance the sediment has traveled, and the stage of development of the riverbed itself. Studies of bedload transport in glaciated catchments have used grain-size distribution to compare how riverbeds in polar regions evolve over time.7Water. Grain Size Distribution of Bedload Transport in a Glaciated Catchment (Baranowski Glacier, King George Island, Western Antarctica)
In these contexts, the percent-passing curve is not being compared against a specification envelope. Instead, the shape of the curve, the sorting, the skewness, and the kurtosis of the distribution are being used to infer something about the natural processes that created that sediment deposit. A well-sorted, narrow distribution in a riverbed suggests consistent flow energy. A bimodal distribution might suggest two different sediment sources mixing together, or two distinct transport events. The calculation of percent passing is the same as in any engineering lab; the interpretive framework built on top of it is what changes.
Handling Very Fine Material
Standard sieve analysis works well for particles down to about 75 µm (the No. 200 sieve). Below that, mechanical sieving becomes unreliable. Particles that fine tend to clump from static electricity, stick to the mesh, or simply take extremely long to pass through. Wet sieving helps push the practical limit a bit lower, but at some point you need to switch to a different measurement technique entirely.
For soils, the traditional method for sub-75 µm material is the hydrometer test, which measures how fast particles settle in a water column and uses settling velocity to infer diameter. For industrial powders, laser diffraction instruments are common. In either case, the results are reported in the same format: percent finer than a given size. If you need a complete particle-size distribution from gravel down to clay, you splice the sieve data (for the coarser portion) with the hydrometer or laser data (for the finer portion) at the No. 200 sieve, making sure the two curves agree reasonably well at the overlap point.
The splicing step is where inconsistencies creep in. If the sieve analysis says 18% passes the No. 200 sieve, but the hydrometer analysis, when extrapolated back to 75 µm, implies 22%, you have a mismatch that needs to be resolved before the combined curve is trustworthy. Some practitioners normalize the hydrometer curve to match the sieve’s percent passing at 75 µm; others accept a small discontinuity and note it in the report. There is no single universal convention, so if you are submitting results to someone else, confirm which approach they expect.
Checking Your Work
A few quick sanity checks can catch most errors before they make it into a report. First, confirm that the sum of all individual percent-retained values equals 100% (or very close to it). If it does not, you have either a weighing error or a data-entry error. Second, verify that percent passing decreases monotonically from the coarsest sieve to the pan. If percent passing jumps up at any sieve, something is wrong, because it is physically impossible for more material to pass through a finer sieve than a coarser one above it in the stack. Third, compare the total recovered mass with the original sample weight. A discrepancy of more than 1–2% is a flag.
If you are running replicate tests on the same material, the percent-passing values at each sieve should be reproducible within a few percentage points. Large scatter between replicates usually points to inconsistent sample splitting, variable shaking time, or degradation of the sieve mesh. Worn or damaged sieves with stretched or torn openings will pass more material than their nominal size suggests, inflating percent passing on the finer sieves below. Periodic inspection and replacement of sieves is a mundane but real source of data quality.