Calculate the weighted arithmetic mean particle size from sieved range data.
Lower Bound (µm/mm)Upper Bound (µm/mm)Retained Mass (g) or %
Calculated Results
Total Sample Mass: 0
0
Weighted Mean Particle Size
function calculateParticleMean() {
var totalMass = 0;
var sumMoment = 0;
var validRows = 0;
// Iterate through fixed 5 rows
for (var i = 1; i <= 5; i++) {
var lowElem = document.getElementById('lower' + i);
var upElem = document.getElementById('upper' + i);
var massElem = document.getElementById('mass' + i);
var low = parseFloat(lowElem.value);
var up = parseFloat(upElem.value);
var mass = parseFloat(massElem.value);
// Check if row has complete data
if (!isNaN(low) && !isNaN(up) && !isNaN(mass)) {
// Calculate bin center (arithmetic mean of bounds)
var center = (low + up) / 2;
// Accumulate mass
totalMass += mass;
// Accumulate moment (mass * center)
sumMoment += (mass * center);
validRows++;
}
}
var resultBox = document.getElementById('result-box');
var meanDisplay = document.getElementById('mean-size-display');
var massDisplay = document.getElementById('total-mass-display');
if (validRows === 0) {
alert("Please enter at least one complete row of data (Lower, Upper, and Mass).");
resultBox.style.display = "none";
return;
}
if (totalMass === 0) {
alert("Total mass cannot be zero.");
resultBox.style.display = "none";
return;
}
var meanSize = sumMoment / totalMass;
// Display results
resultBox.style.display = "block";
massDisplay.innerHTML = totalMass.toFixed(2);
meanDisplay.innerHTML = meanSize.toFixed(4) + " (Units)";
}
How to Calculate Mean Particle Size from Range Bins
Calculating the mean particle size from sieved data or laser diffraction results is a fundamental task in sedimentology, soil mechanics, pharmaceutical manufacturing, and chemical engineering. When data is collected in "range bins" (e.g., 63µm–125µm), you do not have the exact size of every single particle. Instead, you have the total mass or percentage of particles that fall within specific upper and lower boundaries.
To find the average size of the entire sample, you must determine a representative diameter for each bin and weight it by the mass retained in that bin. This calculator uses the arithmetic method to determine the Weighted Mean Particle Size.
The Calculation Method
The process involves three main steps for each size range (bin):
Determine the Bin Center: Calculate the midpoint of the range. For a bin with a lower bound ($L$) and an upper bound ($U$), the center ($d_i$) is usually calculated as the arithmetic mean:
d_i = (Upper + Lower) / 2
Calculate the Moment: Multiply the mass ($m_i$) retained in that bin by the bin center ($d_i$).
Moment_i = m_i × d_i
Sum and Divide: Sum all the moments and divide by the total mass of the sample.
Mathematical Formula
The formula for the Mean Particle Size ($D_{mean}$) is:
D_mean = Σ(m_i × d_i) / Σm_i
Where:
m_i = Mass or Frequency in the i-th bin
d_i = Representative diameter (midpoint) of the i-th bin
Σ = Summation across all bins
Calculation Example
Imagine you have sieved a sand sample and have the following data:
Bin Range (µm)
Bin Center (d_i)
Mass Retained (m_i)
Moment (m_i × d_i)
100 – 200
150
10g
1,500
200 – 300
250
20g
5,000
300 – 400
350
5g
1,750
Totals
–
35g
8,250
Step 1: Calculate Total Mass = 10 + 20 + 5 = 35g.
Step 2: Calculate Total Moment = 1500 + 5000 + 1750 = 8250.
Flowability: In powder technology, mean size affects how easily a powder flows.
Reactivity: Smaller mean sizes often indicate higher surface area and reactivity in chemical processes.
Permeability: In soil science, the mean grain size correlates with the soil's ability to drain water.
Filter Efficiency: Determining the correct filter grade based on contaminant particle size distribution.
Note: This calculator assumes a uniform distribution within each bin (Arithmetic Mean). For log-normal distributions or very wide bins, a geometric mean of the bounds might be more appropriate, though the arithmetic mean is the standard approximation for sieve analysis.