Calculate Volume Solids from Weight Solids

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Calculate Volume Solids from Weight Solids

Convert paint weight specifications to practical volumetric coverage metrics

Understanding the relationship between weight solids and volume solids is crucial for accurate coating estimations, film thickness control, and cost analysis. Use the calculator below to instantly calculate volume solids from weight solids using density parameters.

The percentage of solid material by weight (from SDS or technical data sheet).
Please enter a valid percentage between 0 and 100.
Specific Gravity of the total liquid paint (e.g., 1.25 g/mL).
Please enter a valid positive density.
Density of the solvent portion (Typical range: 0.80 – 1.00).
Please enter a valid positive density.
Calculated Volume Solids 0.00%
Logic: We calculate the volume occupied by the volatile components first, then subtract from total volume to find solids volume.
Volatile Content (Volume) 0.00%
Theoretical Coverage (at 25 microns) 0.0 m²/L
Weight of Solids (per L) 0.00 kg
Figure 1: Volumetric distribution of paint components (Solids vs. Solvents)
Metric Value Unit
Table 1: Detailed breakdown of physical properties derived from inputs.
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What is Calculate Volume Solids from Weight Solids?

When you calculate volume solids from weight solids, you are converting the mass-based specification of a coating into a volumetric utility metric. In the coatings industry, "Weight Solids" ($S_w$) refers to the percentage of the paint that remains after the solvent has evaporated, measured by mass. However, paint is bought by volume (liters or gallons) and applied to cover an area (square meters or feet).

Therefore, the "Volume Solids" ($S_v$)—the volume of paint that remains on the surface to form the protective film—is the critical number for determining coverage rates and dry film thickness (DFT). Misunderstanding this conversion often leads to ordering too little paint or incorrectly estimating project costs.

Volume Solids Formula and Mathematical Explanation

The formula to calculate volume solids from weight solids requires knowing the specific gravity (density) of the liquid coating and the specific gravity of the volatile components (solvents/water).

$$S_v = 100 \times \left( 1 – \frac{\rho_{mix} \times (100 – S_w)}{100 \times \rho_{solvent}} \right)$$

The derivation works by calculating the volume of the volatile portion and subtracting it from the total volume.

Variables Table

Variable Meaning Unit Typical Range
$S_v$ Volume Solids % 30% – 98%
$S_w$ Weight Solids % 40% – 99%
$\rho_{mix}$ Density of Liquid Paint g/mL (SG) 0.9 – 2.5
$\rho_{solvent}$ Density of Solvent g/mL (SG) 0.78 – 1.0 (Water)
Table 2: Key variables required for the calculation logic.

Practical Examples (Real-World Use Cases)

Example 1: Industrial Primer

A contractor has a zinc-rich primer with 85% Weight Solids. The technical data sheet states the liquid density is 2.4 g/mL due to heavy zinc content. The solvent is Xylene (density approx 0.87 g/mL).

  • Weight of Volatiles: $100 – 85 = 15$ grams (per 100g paint)
  • Volume of Volatiles: Using the formula logic, the high density of the paint means those 15 grams occupy a significant portion of volume relative to the heavy zinc.
  • Result: The calculation reveals Volume Solids of approximately 58.6%.

Interpretation: Even though it is 85% solids by weight, barely 60% of the volume in the can remains on the steel.

Example 2: Water-Based Architectural Paint

Consider a standard latex wall paint with 50% Weight Solids. The density is 1.3 g/mL, and the solvent is water (1.0 g/mL).

  • Input: $S_w = 50$, $\rho_{mix} = 1.3$, $\rho_{solvent} = 1.0$.
  • Calculation: Volume of water = $1.3 \times 0.5 / 1.0 = 0.65$ mL per 1 mL of paint.
  • Result: Volume Solids = $1.0 – 0.65 = 35\%$.

Interpretation: This low volume solid count explains why multiple coats are often needed for architectural paints compared to high-build industrial epoxies.

How to Use This Calculator

  1. Locate the Technical Data Sheet (TDS): Find the section listing Physical Properties.
  2. Enter Weight Solids: Input the percentage value (e.g., 65).
  3. Enter Liquid Density: Usually listed as "Specific Gravity" or "Density". If listed in lbs/gal, divide by 8.345 to get Specific Gravity.
  4. Enter Solvent Density: If unknown, use 1.0 for water-based coatings or 0.87 for standard solvent-based (alkyd/epoxy) coatings.
  5. Review Results: The primary result shows the actual volume of film-forming material. Use the "Theoretical Coverage" to estimate how many liters you need.

Key Factors That Affect Results

Several financial and physical factors influence the accuracy of trying to calculate volume solids from weight solids:

  • Pigment Density: High-density pigments (like Zinc or Titanium Dioxide) increase the weight solids significantly without adding proportional volume, creating a large gap between weight and volume percentages.
  • Solvent Selection: A lighter solvent (lower density) occupies more volume for the same weight. Changing thinners can alter the wet-to-dry calculation.
  • Temperature Expansion: Volume changes with temperature, while weight does not. Standard calculations assume 25°C.
  • Air Entrainment: If the density is measured incorrectly due to trapped air in the sample, the volume solids calculation will be artificially high.
  • Cost Implications: Purchasing based on weight solids ($/kg) is misleading. A paint with 80% weight solids but only 50% volume solids may be more expensive per square meter of coverage than a 60% volume solid alternative.
  • Waste Regulation: Higher solvent volume means higher VOC (Volatile Organic Compounds) emissions, which may incur environmental taxes or disposal fees.

Frequently Asked Questions (FAQ)

Why is Volume Solids always lower than Weight Solids?

Because the solid components (resins, pigments) are almost always denser than the solvents. Therefore, they contribute more to the total weight than they do to the total volume.

Can I use this for 100% Solids Epoxy?

Yes. If you enter 100% Weight Solids, the result should be 100% Volume Solids, assuming no volatile loss occurs.

How does this relate to Wet Film Thickness (WFT)?

To achieve a specific Dry Film Thickness (DFT), you must apply a specific WFT calculated as: $WFT = DFT / (Volume Solids \%) \times 100$.

Does this calculator account for thinner addition?

No. This calculator assumes the paint is "as supplied." If you add thinner, you are reducing the volume solids percentage further. You can estimate this by adjusting the "Total Volume" in your manual calculations.

What is the typical density of Paint Thinner?

Common mineral spirits and xylene range from 0.78 to 0.88 g/mL. Acetone is roughly 0.79 g/mL.

Why is the result negative?

If the result is negative, check your inputs. It is mathematically impossible unless the input density values are incorrect (e.g., assuming a paint density lower than the solvent density with high solids).

Is this accurate for powder coatings?

No, powder coatings are 100% solids but behave differently regarding specific gravity and coverage efficiency (transfer efficiency).

Which metric determines the price?

Paint is sold by the liter (volume), so Volume Solids is the only accurate metric for value-for-money analysis.

© 2023 Coatings Engineering Tools. All rights reserved.
Disclaimer: This calculator provides theoretical estimates. Always verify with official manufacturer data sheets.

// Main Calculation Logic function calculate() { // 1. Get Inputs using var var weightSolidsInput = document.getElementById('weightSolids'); var paintDensityInput = document.getElementById('paintDensity'); var solventDensityInput = document.getElementById('solventDensity'); var Sw = parseFloat(weightSolidsInput.value); var RhoMix = parseFloat(paintDensityInput.value); var RhoSolvent = parseFloat(solventDensityInput.value); // 2. Validation var errorWeight = document.getElementById('error-weight'); var errorPaint = document.getElementById('error-paint'); var errorSolvent = document.getElementById('error-solvent'); var isValid = true; // Reset errors errorWeight.style.display = 'none'; errorPaint.style.display = 'none'; errorSolvent.style.display = 'none'; if (isNaN(Sw) || Sw 100) { errorWeight.style.display = 'block'; isValid = false; } if (isNaN(RhoMix) || RhoMix <= 0) { errorPaint.style.display = 'block'; isValid = false; } if (isNaN(RhoSolvent) || RhoSolvent <= 0) { errorSolvent.style.display = 'block'; isValid = false; } if (!isValid) return; // 3. Calculation Formula // Sv = 100 * (1 – (RhoMix * (100 – Sw)) / (100 * RhoSolvent)) var weightVolatiles = 100 – Sw; // g per 100g paint // This logic calculates volume of volatiles per 100g of paint // But we need volume per volume. // Let's take 1 Liter of paint. // Mass of 1 Liter = RhoMix * 1000 (if Rho is g/mL, then kg/L is same value) var massPaintPerLiter = RhoMix; // kg var massSolidsPerLiter = massPaintPerLiter * (Sw / 100); var massVolatilesPerLiter = massPaintPerLiter * ((100 – Sw) / 100); // Volume of Volatiles (Liters) = Mass (kg) / Density (kg/L) // Note: Density in g/mL is same as kg/L var volVolatilesPerLiter = massVolatilesPerLiter / RhoSolvent; // Volume of Solids (Liters) = Total Volume (1.0) – Volume Volatiles var volSolidsPerLiter = 1.0 – volVolatilesPerLiter; // Convert to Percentage var Sv = volSolidsPerLiter * 100; // Clamp result (physically impossible to be 100 usually, but formula can drift if inputs clash) if (Sv 100) Sv = 100; // 4. Update UI document.getElementById('resultVolumeSolids').innerText = Sv.toFixed(2) + '%'; document.getElementById('resultVolatileVolume').innerText = (100 – Sv).toFixed(2) + '%'; // Theoretical Coverage: at 25 microns (1 mil approx) // 1 Liter at 100% solids covers 40 m² at 25 microns? No. // 1 Liter = 1000 cm³. 25 microns = 0.0025 cm. // Area = 1000 / 0.0025 = 400,000 cm² = 40 m². // So coverage = 40 * (Sv / 100) var coverage = 40 * (Sv / 100); document.getElementById('resultCoverage').innerText = coverage.toFixed(1) + ' m²/L'; document.getElementById('resultSolidWeight').innerText = massSolidsPerLiter.toFixed(2) + ' kg'; // Update Table var tableBody = document.getElementById('resultTableBody'); tableBody.innerHTML = 'Weight Solids' + Sw.toFixed(1) + '%' + 'Volume Solids' + Sv.toFixed(2) + '%' + 'Volatile Content' + (100 – Sv).toFixed(2) + '% by Vol' + 'Paint Density' + RhoMix.toFixed(2) + 'g/mL' + 'Solvent Density' + RhoSolvent.toFixed(2) + 'g/mL'; // 5. Draw Chart drawChart(Sv, 100 – Sv); } // Chart Logic (Canvas) function drawChart(solids, volatiles) { var canvas = document.getElementById('solidsChart'); var ctx = canvas.getContext('2d'); // Reset canvas size for retina var rect = canvas.parentNode.getBoundingClientRect(); canvas.width = rect.width; canvas.height = rect.height; var centerX = canvas.width / 2; var centerY = canvas.height / 2; var radius = Math.min(centerX, centerY) – 20; var total = solids + volatiles; var startAngle = 0; // Draw Solids Arc var sliceAngle = (solids / total) * 2 * Math.PI; ctx.beginPath(); ctx.moveTo(centerX, centerY); ctx.arc(centerX, centerY, radius, startAngle, startAngle + sliceAngle); ctx.fillStyle = '#004a99'; // Brand Blue ctx.fill(); // Draw Text for Solids if (solids > 10) { var midAngle = startAngle + sliceAngle / 2; var textX = centerX + (radius * 0.6) * Math.cos(midAngle); var textY = centerY + (radius * 0.6) * Math.sin(midAngle); ctx.fillStyle = 'white'; ctx.font = 'bold 16px Arial'; ctx.textAlign = 'center'; ctx.fillText('Solids', textX, textY); ctx.fillText(Math.round(solids) + '%', textX, textY + 20); } startAngle += sliceAngle; // Draw Volatiles Arc sliceAngle = (volatiles / total) * 2 * Math.PI; ctx.beginPath(); ctx.moveTo(centerX, centerY); ctx.arc(centerX, centerY, radius, startAngle, startAngle + sliceAngle); ctx.fillStyle = '#e9ecef'; // Light Gray ctx.fill(); // Draw Text for Volatiles if (volatiles > 10) { var midAngle = startAngle + sliceAngle / 2; var textX = centerX + (radius * 0.6) * Math.cos(midAngle); var textY = centerY + (radius * 0.6) * Math.sin(midAngle); ctx.fillStyle = '#333'; ctx.font = 'bold 16px Arial'; ctx.textAlign = 'center'; ctx.fillText('Solvents', textX, textY); ctx.fillText(Math.round(volatiles) + '%', textX, textY + 20); } } function resetCalc() { document.getElementById('weightSolids').value = 65; document.getElementById('paintDensity').value = 1.25; document.getElementById('solventDensity').value = 0.87; calculate(); } function copyResults() { var sv = document.getElementById('resultVolumeSolids').innerText; var cov = document.getElementById('resultCoverage').innerText; var sw = document.getElementById('weightSolids').value; var rho = document.getElementById('paintDensity').value; var text = "Volume Solids Calculation Summary:\n" + "——————————–\n" + "Input Weight Solids: " + sw + "%\n" + "Input Paint Density: " + rho + " g/mL\n" + "——————————–\n" + "Calculated Volume Solids: " + sv + "\n" + "Theoretical Coverage: " + cov + " @ 25 microns\n"; var textArea = document.createElement("textarea"); textArea.value = text; document.body.appendChild(textArea); textArea.select(); document.execCommand("Copy"); textArea.remove(); var feedback = document.getElementById('copy-feedback'); feedback.style.opacity = 1; setTimeout(function(){ feedback.style.opacity = 0; }, 2000); } // Init window.onload = function() { calculate(); }; // Resize listener for chart window.onresize = function() { calculate(); }

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