How to use this calculator

Enter the fiber volume fraction, then pick a fiber and a matrix to fill in typical properties, or type your own from a datasheet. The graph shows how stiffness along and across the fibers changes as you add more fiber.

Formulas

Along the fibers (equal strain, upper bound)E_L = V_fE_f + V_mE_m

Across the fibers (equal stress, lower bound)1E_T = V_fE_f + V_mE_m

Density, weight fraction and strengthρ_c = V_fρ_f + V_mρ_m W_f = V_fρ_fρ_c σ_L ≈ V_fσ_f + V_mσ′_m

V_m = 1 − V_f (assuming no voids). σ′_m is the stress in the matrix at the strain where the fibers break.

Worked example

60% E-glass in epoxy (the default)

E_L = 0.6 × 72.5 + 0.4 × 3.1 = 44.7 GPa.
E_T = 1/(0.6/72.5 + 0.4/3.1) = 7.28 GPa, about 6 times less stiff across the fibers.
ρ_c = 0.6 × 2.58 + 0.4 × 1.2 = 2.03 g/cm³, and the fibers are 76% of the weight.
Strength along the fibers is about 0.6 × 3450 + 0.4 × 70 = 2.1 GPa as an ideal upper estimate.

Why direction matters so much

Unidirectional composites are extremely stiff and strong along the fibers and little better than plain resin across them. That is why real parts stack plies at 0°, ±45° and 90°: a quasi-isotropic carbon laminate gives up about two thirds of the 0° stiffness in exchange for similar properties in every direction.

Assumptions and limits

Continuous, straight, aligned fibers perfectly bonded to the matrix, with no voids.
The transverse formula is a lower bound; measured transverse moduli are usually somewhat higher. The Halpin–Tsai equations give a closer estimate.
Strength depends on defects, fiber waviness and the interface, so real values are typically 60–90% of the rule-of-mixtures estimate.

Frequently asked questions

What fiber volume fraction is typical?

Hand lay-up gives about 30–40%, vacuum infusion 50–55%, and autoclave-cured prepreg 55–65%.

What about chopped or short fibers?

Short, randomly oriented fibers are much less efficient. A common estimate multiplies the fiber term by an efficiency factor of about 0.375 for random in-plane fibers.

Why is carbon fiber used when it costs so much?

Its stiffness per unit weight. Unidirectional carbon/epoxy is about twice as stiff as aluminum along the fibers at roughly 60% of its density, and high-modulus grades go further still.