Differential size measurement captures how particles, cells, or grains are distributed across a range of sizes, showing the proportion that falls within each size interval rather than a running total. It’s the difference between knowing “30% of your particles are between 10 and 20 micrometers” (differential) and “70% of your particles are smaller than 20 micrometers” (cumulative). The method you use depends on what you’re measuring and how small it is, from sand grains visible to the naked eye down to nanoparticles a thousand times thinner than a human hair.
Differential vs. Cumulative Distribution
These two ways of presenting size data answer different questions. A differential distribution plots the amount of material in each size bin, producing peaks that show you where most of your sample clusters. A cumulative distribution adds up all the material below (or above) a given size, producing an S-shaped curve that’s useful when you care about a specific cutoff, like the fraction of particles smaller than 1 micrometer.
Some techniques produce one type of data natively. Sieve analysis, for example, generates cumulative data because each sieve catches everything above its opening size. You can convert cumulative data into a differential distribution by taking the mathematical derivative of the curve, but this step introduces additional error compared to measuring the differential distribution directly. When possible, choosing a technique that gives you differential data from the start yields cleaner results.
On a differential plot, a single sharp peak means your sample is uniform in size. Two distinct peaks (a bimodal distribution) indicate two separate populations, which could signal contamination, incomplete processing, or an intentional blend. The width of each peak tells you how much size variation exists within that population.
Sieve Analysis for Coarse Materials
Sieve analysis is the most straightforward way to measure differential size for powders, soils, aggregates, and food products with particles larger than about 50 micrometers. You stack 5 to 10 sieves in descending aperture size, place your sample on the top sieve, cap it, and shake the stack for up to 30 minutes. Each sieve traps particles too large to pass through its mesh, while smaller particles fall to the next level.
After shaking, you weigh the material retained on each sieve. The mass on each sieve, expressed as a percentage of the total sample mass, gives you the differential size distribution directly. A typical run uses around 200 grams of material to ensure that even fine fractions at the bottom of the stack contain enough to weigh accurately. Plotting these mass percentages as columns against particle size produces a histogram showing where most of your material sits. You can also plot undersize and oversize curves against particle size to find the median diameter (d0.5) at their intersection.
Laser Diffraction for Micron-Scale Particles
Laser diffraction is the workhorse technique for particles roughly in the 0.1 to 3,000 micrometer range. The principle is simple: particles passing through a laser beam scatter light at angles that relate directly to their size. Smaller particles scatter light at wider angles, larger particles at narrower angles. A ring of detectors captures this scattered light pattern, and software uses Mie theory (a set of equations describing how spheres interact with electromagnetic waves) to back-calculate the size distribution.
The result is a volume-weighted differential distribution, typically plotted as the percentage of total volume in each size bin. Because the measurement happens on thousands of particles simultaneously as they flow through the beam, you get statistically robust data in seconds. Samples can be dispersed in liquid or measured as dry powders blown through the sensing zone. This speed and versatility make laser diffraction the default choice in pharmaceutical, chemical, and materials industries when particles are too small for sieves but too large for nanoscale techniques.
Dynamic Light Scattering for Nanoparticles
When particles shrink below about 1 micrometer, laser diffraction loses resolution. Dynamic light scattering (DLS) picks up where it leaves off, measuring particles from below 1 nanometer up to a few micrometers. Instead of measuring the angle of scattered light, DLS measures how fast the scattered light intensity fluctuates over time. Small particles jitter around quickly due to random collisions with solvent molecules, while larger particles move more slowly.
The instrument tracks these fluctuations and calculates a diffusion speed for each particle population. That diffusion speed converts to a particle size through the Stokes-Einstein equation, which relates how fast a sphere drifts through a fluid of known viscosity at a known temperature to the sphere’s radius. The output is an intensity-weighted differential distribution showing peaks at each distinct size population in your sample. DLS is especially common for characterizing nanoparticles, protein aggregates, and emulsions, though it struggles to resolve populations that are close together in size since the technique has lower resolution than laser diffraction.
Electrical Sensing for Cells and Particles
The Coulter principle, named after its inventor, measures individual particles one at a time as they pass through a tiny opening between two electrodes. A steady electrical current flows through the opening. When a particle enters, it displaces conducting fluid and briefly changes the electrical resistance across the gap. This produces a voltage pulse whose height is proportional to the particle’s volume.
By counting and sizing thousands of these pulses, the instrument builds a differential size distribution with exceptional resolution. Each particle is measured individually, so there’s no mathematical deconvolution or modeling involved. This makes Coulter-based instruments particularly accurate for samples with narrow size distributions or multiple closely spaced populations. The technique is widely used in hematology labs to measure blood cell sizes and in industrial settings for quality control of toners, abrasives, and other precision powders. The measurable range depends on the orifice diameter, but instruments can cover roughly 0.4 to 1,600 micrometers using different tube sizes.
Red Cell Distribution Width in Blood Tests
If your search relates to medical lab results, “differential size” in blood work most commonly refers to the red cell distribution width (RDW). This value quantifies how much your red blood cells vary in size. A normal RDW falls between 11.5% and 14.0%, and this range holds across age groups. A value above 14.0% means your red blood cells are more varied in size than expected, which can point to iron deficiency, vitamin B12 deficiency, or other conditions affecting how your body produces red blood cells.
The RDW is calculated automatically by hematology analyzers that use the same Coulter principle described above. As each red blood cell passes through the sensing zone, the instrument records its volume. The RDW is essentially the coefficient of variation of that volume distribution: the standard deviation of red blood cell volumes divided by the mean volume, expressed as a percentage. A higher number means a wider spread of sizes in the differential distribution.
Choosing the Right Technique
Your choice comes down to particle size range, sample type, and what kind of answer you need.
- Above 50 micrometers: Sieve analysis is cheap, intuitive, and requires no specialized instruments. It works well for powders, soils, and granular materials.
- 0.1 to 3,000 micrometers: Laser diffraction provides fast, high-resolution differential distributions for wet or dry samples. It’s the most versatile option for this range.
- 1 nanometer to a few micrometers: Dynamic light scattering handles nanoparticles and macromolecules in solution, though with lower resolution than other methods.
- 0.4 to 1,600 micrometers (individual counting needed): Coulter counters measure each particle separately, giving the most accurate differential distributions when you need to distinguish closely spaced size populations.
Some applications overlap between techniques, and labs often cross-check results using two methods. The key is matching your instrument’s range and resolution to the actual sizes in your sample. Running a quick estimate of your expected size range before selecting a method saves time and avoids data that’s clipped at the edges of an instrument’s capability.