What is the difference between fiber volume fraction and fiber weight fraction?

Volume fraction is the fraction of the cured ply volume occupied by fiber; weight fraction is the fraction of its mass. They are converted through the densities: Wf = fiber density x Vf / composite density. Since fiber is denser than resin, the weight fraction is always the larger number, for example 60% by volume in carbon/epoxy is roughly 69% by weight. Stiffness and strength models use volume fraction, so check which one a datasheet is quoting before using it.

Why does fiber areal weight not depend on the resin?

FAW is defined as the mass of dry fiber per unit area, so only the fiber density, the fiber volume fraction and the ply thickness enter it. Resin density and resin content affect the cured ply mass and density, and therefore the weight fractions and the coupon calculations, but not the FAW to thickness relationship itself.

How do I estimate void content from a cured panel?

Compute the theoretical density from your design fiber and resin densities and fiber volume fraction by the rule of mixtures, measure the actual density of a coupon from its mass, area and thickness, and take the relative shortfall: void content = (theoretical - measured) / theoretical. Voids add volume without adding mass, so porosity shows up as a density deficit. A negative result means the inputs are wrong, most often the coupon thickness or the assumed design fiber volume fraction.

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Ply Calculator: FAW, Fiber Volume Fraction and Cured Ply Thickness

Three numbers that describe a ply, tied together by one equation, plus how to recover the same numbers from a cured coupon you can put on a scale.

Fiber areal weight, fiber volume fraction and ply thickness

A ply is usually described by whichever quantity the supplier or the process happens to quote. The reinforcement is sold by fiber areal weight (FAW), the mass of dry fiber per unit area, in g/m², the number a fabric datasheet quotes as gsm. The layup is analysed at a given fiber volume fraction (V_f), the fraction of the cured ply volume occupied by fiber. The part is drawn and machined to a cured ply thickness (t), in mm. Those three are not independent: fix any two and the third follows.

F A W = ρ_{f} V_{f} t \times 1000

The reasoning is short: per unit area, the ply occupies a volume equal to its thickness, of which the fraction V_f is fiber, and that fiber volume times the fiber density ρ_f is the fiber mass. The factor 1000 is nothing but unit bookkeeping, taking g/cm³ times mm into g/m². Get that factor wrong and every number downstream is off by a power of ten, which is the single most common arithmetic slip in ply bookkeeping.

Note what the equation does not contain: the resin. FAW is a dry-fiber quantity, so the resin density and the resin content never enter it. They matter for the mass and density of the cured ply, covered below, but not for the fiber-thickness relationship itself.

Solving for areal weight, volume fraction or ply thickness

The same relation, rearranged, answers the three questions that actually come up in design:

F A W = ρ_{f} V_{f} t \times 1000 (what areal weight do I need to order?)

V_{f} = \frac{F A W}{ρ _{f} t \times 1000} (what V_{f} does my process actually achieve?)

t = \frac{F A W}{ρ _{f} V _{f} \times 1000} (how thick will one ply cure out?)

The middle one is the reality check on a process. You know the fabric you bought and you can measure the cured thickness of a panel, so V_f is not a number you get to choose, it is a number your layup and cure hand back to you. A hand layup landing near 40% and a cured prepreg part near 60% is the usual spread, and if the arithmetic returns 75% for a wet layup then the thickness measurement, not the material, is what needs revisiting.

The third one is what turns a stacking sequence into a part thickness, and it is where the laminate analysis starts: ply thickness is a direct input to the ABD matrix, so an assumed V_f that never gets checked against a real panel propagates straight into every stiffness number you report.

Composite density and fiber weight fraction

Once V_f is fixed, the cured ply's density follows from the rule of mixtures¹, on the assumption that fiber and resin fill the volume between them and no voids are left:

ρ_{c} = ρ_{f} V_{f} + ρ_{m} (1 - V_{f})

That composite density is what converts volume fractions into weight fractions. Volume is what stiffness and strength models care about, because load is carried by cross-section; weight is what the shop floor works in, because resin is mixed and parts are weighed. The two are related through the densities:

W_{f} = \frac{ρ _{f} V _{f}}{ρ _{c}} W_{m} = \frac{ρ _{m} ( 1 - V _{f} )}{ρ _{c}}

Because carbon fiber is roughly 1.8 g/cm³ against a resin near 1.2 g/cm³, the weight fraction always exceeds the volume fraction: 60% fiber by volume is about 69% fiber by weight. Reading a datasheet's "60% fiber" as a volume fraction when it was quoted by weight (or the reverse) shifts predicted stiffness by several percent, so it is worth checking which one a number is before feeding it into micromechanics.

From a cured coupon back to fiber volume fraction

Everything above is design intent. The other direction, working from a panel you have already made, needs nothing but a scale and a caliper. Cut a coupon, measure its mass and its area, and its total areal weight is immediate:

T A W = \frac{m}{A} \times 1 0^{6} P A W = \frac{T A W}{n} M A W = P A W - F A W

TAW covers the whole laminate, so dividing by the ply count n gives the per-ply areal weight PAW, cured resin included. Subtract the dry FAW you started with and what is left, the matrix areal weight MAW, is the resin that actually stayed in the part. MAW / PAW is then the resin content by weight, measured rather than assumed. A negative MAW is not a subtle result: the panel weighs less than its own dry fiber, so either the ply count or the FAW being assumed is wrong.

Add a thickness measurement and the coupon gives up its density, and with it V_f:

ρ_{m e a s u r e d} = \frac{m}{A t _{co u p o n}} \times 1000 V_{f} = \frac{ρ _{m e a s u r e d} - ρ _{m}}{ρ _{f} - ρ _{m}}

The second expression is just the rule-of-mixtures density solved for V_f, so it inherits the same no-voids assumption. That assumption is exactly what you can now test, by comparing the density the design intent predicts against the density the coupon reports:

V_{v} = \frac{ρ _{t h eor e t i c a l} - ρ _{m e a s u r e d}}{ρ _{t h eor e t i c a l}}

Voids displace mass without displacing volume, so a panel full of porosity comes out lighter than the mixture rule says it should, and the shortfall in density is the void volume fraction. Autoclaved aerospace laminates typically sit under 1%, while vacuum-bag and wet layup parts commonly run a few percent. A negative V_v means the measured density beat the theoretical one, which is physically impossible for a two-phase mixture and points at the inputs: usually the coupon thickness (measured over a resin-rich surface, or over peel-ply texture) or the assumed design V_f.

This mass-and-caliper route is a quick shop-floor estimate, not a substitute for a standardised test. Where a certified constituent content or void content is required, matrix digestion or burn off per ASTM D3171² and void content per ASTM D2734³ use these same relations under controlled conditions.

In the ABD Composites dashboard

The Ply Calculator has two tabs that mirror the two directions above. Design Values works forward from densities: pick which of FAW, V_f or ply thickness you want to solve for, enter the other two, and the chosen field turns read-only and fills itself in. The results panel adds the quantities that follow from that solve, matrix volume fraction, composite density, fiber weight fraction and matrix content by weight, so the volume-to-weight conversion is done for you rather than on a napkin. Give it a ply count as well and it reports the laminate thickness, or works backwards from a target laminate thickness to the per-ply value.

$ABD Composites Ply Calculator showing FAW, fiber volume fraction and ply thickness inputs with derived composite density and weight fractions$

Measured Coupon is the reverse pass. Enter the coupon mass and its dimensions, rectangular (length and width) or circular (diameter), plus the number of plies, and it reports area, TAW, PAW, MAW and the measured resin content. Add the optional coupon thickness and it also reports measured density, V_f back-calculated from that density, and the void content against the design values on the other tab. Fiber and matrix densities can be pulled straight from your material library instead of typed, and the results flag the physically impossible cases (V_f outside 0-100%, negative MAW, negative void content) rather than quietly displaying them.

The V_f you settle on here is the number the rest of the workflow runs on: it drives every micromechanics prediction of ply stiffness and strength, and the ply thickness it pairs with is a direct input to the ABD matrix.

References

Jones, R.M. Mechanics of Composite Materials, 2nd ed., Taylor & Francis, 1999.
ASTM D3171, Standard Test Methods for Constituent Content of Composite Materials, ASTM International.
ASTM D2734, Standard Test Methods for Void Content of Reinforced Plastics, ASTM International.

Frequently Asked Questions

Run the numbers on your own layup

The dashboard's Ply Calculator solves for FAW, V_f or ply thickness, and back-calculates V_f and void content from a measured coupon. Create a free account to get started.

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