Process Utilities

Percent Solids by Mass vs Volume

Mass percent solids (Cw) and volume percent solids (Cv) are not interchangeable. Learn the difference, why mass percent is usually higher for dense solids, and the common mistake of treating 30 wt% as 30 vol%.

TypeEngineering guide — concept explainer

Definition

Percent solids can be reported two ways. Mass percent solids (Cw, or weight percent) is the mass of solids divided by the total slurry mass, ×100. Volume percent solids (Cv) is the volume of solids divided by the total slurry volume, ×100. They describe the same slurry but answer different questions — how much of the mass is solid, versus how much of the volume is solid — and they are equal only when the solids and liquid have the same density.

Why it matters

Engineers must not interchange Cw and Cv. Assays, plant balances, and Marcy-cup readings are usually mass-based (Cw). But slurry density-from-volume, pump deposition velocity, and many pipeline correlations are volume-based (Cv). Quoting the wrong basis silently corrupts pump sizing, pipe velocity checks, thickener targets, and reagent dosing. For dense minerals the gap is large: 30 wt% quartz solids is only about 14 vol%, so confusing the two more than doubles the apparent solids volume.

Formula

Mass percent solids

Cw = (mass solids / mass slurry) × 100

Volume percent solids

Cv = (volume solids / volume slurry) × 100

Cv from Cw (Xs = Cw/100)

Cv = (Xs / ρ_S) / (Xs / ρ_S + (1 − Xs) / ρ_L)

Cw from Cv

Xs = (Cv × ρ_S) / (Cv × ρ_S + (1 − Cv) × ρ_L)

Units involved

•Cw — mass percent solids (0–100), a.k.a. weight percent
•Cv — volume percent solids (0–100)
•Xs — solids mass fraction (Cw / 100)
•ρ_S, ρ_L — solids and liquid densities, kg/m³

Concept diagram

Worked example

Water (ρ_L = 1000 kg/m³) carries quartz-like solids (ρ_S = 2650 kg/m³) at 30% by mass. What is the volume percent solids?

01Xs = 30 / 100 = 0.30
02Solids volume term = Xs / ρ_S = 0.30 / 2650 = 0.0001132
03Liquid volume term = (1 − Xs) / ρ_L = 0.70 / 1000 = 0.0007000
04Cv = 0.0001132 / (0.0001132 + 0.0007000)
05Cv = 0.0001132 / 0.0008132 ≈ 0.139

Result

30% solids by mass is only about 13.9% solids by volume — because quartz is ~2.65× denser than water.

Common mistakes

•Treating 30 wt% as 30 vol% — the single most common slurry error. For dense minerals the volume fraction is roughly half the mass fraction.
•Converting between Cw and Cv without the densities — the conversion is not a fixed factor; it needs both ρ_S and ρ_L.
•Mixing bases inside one calculation — e.g. taking a mass-based assay into a volume-based pipeline correlation.
•Assuming mass percent is always higher — it is higher only when solids are denser than the liquid (the usual case); for light solids the relationship reverses.
•Reporting a percent solids without stating the basis — always label it Cw (by mass) or Cv (by volume).

When to use the calculator

Use the Slurry Density Calculator to convert between mass percent and volume percent (it returns both fractions from either basis) and to get the slurry density. Use the Slurry Mass Balance Calculator when you have a volumetric flow and need solids/liquid mass flows and the volume-basis percent.

Percent Solids Mass ↔ Volume Calculator →Slurry Density Calculator →Slurry Mass Balance Calculator →Slurry Solids Calculator →

FAQ

Why is mass percent usually higher than volume percent?

Because mineral solids are denser than water. A given mass of dense solid occupies a small volume, so it contributes a large share of the mass but a small share of the volume. The denser the solid relative to the liquid, the bigger the gap.

Is there a quick rule of thumb for the conversion?

Only loosely. For quartz-like solids in water, volume percent is roughly mass percent divided by ~2.2 at low loadings, but it is not linear and shifts with concentration. Always do the proper conversion with the densities — do not rely on a single factor.

Which basis do plant instruments report?

Marcy density cups and most field density measurements give SG / mass percent (Cw). Some come scaled directly in Cw for a specific solids SG. Pipeline and pump volumetric concentration work is typically Cv. Confirm before using a reading.

When are Cw and Cv equal?

Only when the solids density equals the liquid density. That essentially never happens for mineral slurries, so for practical purposes the two are always different and must be tracked separately.