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Process Design

Percent Solids Mass ↔ Volume Calculator

This calculator converts between percent solids by mass (Cw) and percent solids by volume (Cv) using the liquid density and the solids density, and returns the slurry density, specific gravity and phase fractions for an ideal two-phase mixture.

Percent solids by mass (Cw) and percent solids by volume (Cv) describe the same slurry but are not interchangeable — for dense minerals they differ by more than 2×. This standalone converter takes the liquid density, the solids (dry particle) density, and the solids loading on either basis, then returns the other basis along with the slurry density, slurry specific gravity, and the solids/liquid mass and volume fractions. It is a preliminary two-phase (liquid + solid) calculation: it does not model entrained air, dissolved species, rheology, settling, or particle size.

TypeInteractive engineering calculator

Calculator

Water ≈ 1000 kg/m³; use the measured liquor density if dissolved salts are present.

Dry particle density. Quartz ≈ 2650, hematite ≈ 5200 kg/m³.

0–100 % — mass of solids ÷ total slurry mass

Result
Percent solids by mass (Cw)30 %
Percent solids by volume (Cv)13.9211 %
Slurry density1229.7 kg/m³
Slurry specific gravity1.2297
Solids mass fraction0.3
Liquid mass fraction0.7
Solids volume fraction0.139211
Liquid volume fraction0.860789
Dilution ratio (mass liquid : solids)2.33333 : 1
Volume ratio (liquid : solids)6.18333 : 1
  • !Preliminary two-phase (liquid + solid) estimate only. Assumes representative densities, no entrained air, and no dissolved species unless a corrected liquid density is entered. Does not model rheology, settling, segregation, or pressure drop. Use lab measurements for design work.

Formulas

Volume fraction from mass fraction Xs
Cv = (Xs / ρ_solids) / (Xs / ρ_solids + (1 − Xs) / ρ_liquid)
Slurry density from mass fraction Xs
ρ_slurry = 1 / (Xs / ρ_solids + (1 − Xs) / ρ_liquid)
Slurry density from volume fraction Cv
ρ_slurry = Cv × ρ_solids + (1 − Cv) × ρ_liquid
Mass fraction from volume fraction Cv
Xs = (Cv × ρ_solids) / ρ_slurry
Slurry specific gravity
SG = ρ_slurry / 1000

Diagram

Percent Solids by Mass vs by Volumeby mass (Cw)30% solids70% liquidby volume (Cv)14%86% liquidsame slurry — denser solids occupy less volume

Worked example

A quartz-like slurry has a liquid (water) density of 1000 kg/m³ and a solids density of 2650 kg/m³ at 30% solids by mass. What is the percent solids by volume and the slurry density?

  1. 01Xs = 0.30 (mass fraction)
  2. 02ρ_slurry = 1 / (0.30 / 2650 + 0.70 / 1000) = 1 / 0.0008132 ≈ 1229.6 kg/m³
  3. 03Cv = (0.30 / 2650) / 0.0008132 ≈ 0.139
Result

Percent solids by volume ≈ 13.9% (Cv), slurry density ≈ 1229.6 kg/m³ — versus 30% by mass.

FAQ

Why are Cw and Cv so different for the same slurry?
Because the solids are denser than the liquid. A given mass of dense solid occupies relatively little volume, so the volume percent is much lower than the mass percent. For quartz-like solids (2650 kg/m³) in water, 30% by mass is only about 14% by volume. They only coincide when the solids and liquid have the same density.
Which basis does my data use?
Plant assays and Marcy-cup readings are usually mass-based (Cw). Some pumping, pipeline, and deposition-velocity calculations use volume-based (Cv). Always confirm the basis before using a number — treating 30 wt% as 30 vol% is a common and large error.
How does this differ from the Slurry Density Calculator?
The Slurry Density Calculator is the hub: it also handles g/L solids concentration and a target-density lab-prep mode. This page is the focused Cw ↔ Cv converter that every other slurry page links to when the only question is the mass-vs-volume basis conversion.
Does this account for dissolved salts, air, or rheology?
No. Dissolved species are only captured if you enter a corrected (measured) liquid density instead of 1000 kg/m³. Entrained air, foaming, yield stress, viscosity, settling, and particle size are all out of scope. This is a clean two-phase basis conversion for preliminary work only.

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