What does this calculator compute?

The calculator runs a full Classical Lamination Theory (CLT) analysis on your stacking sequence. It outputs the ABD stiffness matrix (A for in-plane, B for coupling, D for bending), effective engineering constants (Ex, Ey, Gxy, vxy in-plane; Efx, Efy, Gfxy for bending), ply-level stresses and strains in both material (1-2) and laminate (x-y) coordinates, thermal stress resultants, and the standard laminate shorthand notation.

Do I need an account to use it?

None needed. It runs entirely in your browser. Sign up free to unlock custom materials, saved laminates, failure criteria, micromechanics, fabric lamina, and structural analysis (beam, sandwich, plate, cylinder).

Which failure criteria are included?

Nine criteria are available in the full dashboard: Maximum Stress, Maximum Strain, Tsai-Hill, Tsai-Wu, Hashin, Puck, Cuntze, Sun, and Edge. All but Tsai-Hill and Tsai-Wu distinguish fiber from matrix failure modes, which is what progressive damage analysis needs. Sign up free to access them.

How accurate are the results?

CLT is an exact analytical solution for thin laminates under plane stress, not an approximation. The free calculator uses standard floating-point math, which is adequate for most engineering checks. The full dashboard uses 64-digit BigNumber arithmetic and lets you control the number of decimal places displayed.

Where can I learn the theory behind the calculations?

The CLT theory guide covers what the ABD matrix represents, how the engineering constants come out of inverting [A] and [D], and where CLT stops applying. It also lists the textbooks the full derivations come from, starting with Jones, Mechanics of Composite Materials.

Free Composite Laminate Calculator

Build stacking sequences and compute ABD stiffness matrices and engineering constants in real-time. Results are verified against textbook reference cases by an automated test suite that runs on every release. Learn more about CLT theory.

Take Your Analysis Further

The calculator above runs on one material and up to 12 layers. A free account adds custom materials, micromechanics models, failure analysis, structural tools, and laminates saved to your account.

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How the Classical Lamination Theory Calculator Works

Classical Lamination Theory in five steps: the theory behind the numbers on screen.

It turns plies into a plate

Classical Lamination Theory takes what you know about a single ply (E₁, E₂, G₁₂, v₁₂, its thickness and its angle) and predicts how the whole stack behaves. It has been the workhorse of composite design since the 1960s, and it rests on three assumptions: the laminate is thin compared to its width, out-of-plane stresses are negligible (plane stress), and the plies are perfectly bonded so strain runs continuously through the thickness.

Every ply gets rotated into a shared frame

A ply is stiff along its fibers (the 1 direction) and soft across them (the 2 direction). The laminate, though, is loaded in its own x-y axes. So each ply's stiffness matrix is rotated from material coordinates into laminate coordinates through its angle. Two identical plies at 0 and 45 degrees contribute completely different stiffness to the same laminate.

The stack becomes the ABD matrix

Sum the rotated plies through the thickness and you get one 6x6 matrix relating the forces and moments you apply to the strains and curvatures you get. It splits into three blocks:

[A], extensional: in-plane force to in-plane strain. How stiff the laminate is when you pull on it.
[B], coupling: pull on it and it bends. Zero for symmetric laminates, which is why symmetry is the default in practice.
[D], bending: moment to curvature. Weighted by the cube of distance from the midplane, so plies on the outside dominate.

That z-cubed weighting in [D] is the single most useful thing to internalise: where a ply sits matters as much as how many of them you have. The default layup on this page is quasi-isotropic in plane, E_x = E_y = 60.5 GPa, and yet its bending stiffness is E_fx = 96.8 GPa against E_fy = 29.7 GPa, purely because the 0 degree plies happen to be on the outside.

Invert it for engineering constants

Engineers rarely want raw stiffness terms; they want moduli they can compare to a datasheet. Inverting [A] gives the membrane constants E_x, E_y, G_xy, v_xy, and inverting [D] gives the flexural set E_fx, E_fy, G_fxy. Both are on screen behind the engineering constants toggle.

Know where it stops

CLT is exact within its assumptions, not an approximation, but the assumptions are real limits. Thick laminates need shear deformation theory, and free edges, holes, bolted joints and ply drops need 3D analysis, because that is where interlaminar stresses drive delamination and CLT cannot see them.

That is the outline. The full reference works through the coordinate systems, every individual term of [A], [B] and [D], laminate classification, and standard layup notation.

Read the full CLT theory guide Browse all docs

What Engineers Use This Calculator For

Four workflows the free calculator handles without an account.

Layup trade studies

Compare candidate stacking sequences before committing to detailed analysis. Change a ply angle, flip the symmetry toggle, or adjust ply thickness and watch E_x, G_xy and the bending stiffness react immediately. Because everything recalculates as you type, screening a handful of layup variants takes minutes, not a modeling session.

Verifying hand calculations and spreadsheets

CLT by hand means transformation matrices, per-ply Q̄ terms, and z-coordinate bookkeeping, with plenty of places for a sign slip or a unit error to hide. Enter the same lamina properties and stacking sequence here and compare ABD terms directly against your own numbers. The same goes for the departmental spreadsheet nobody dares touch: an independent implementation is the fastest way to find out whether it still computes what everyone assumes it does.

Preparing and checking FEA inputs

Shell elements want laminate stiffness, either as a layup definition or as homogenized engineering constants. Compute the membrane constants (E_x, E_y, G_xy, v_xy) and the flexural set (E_fx, E_fy, G_fxy) for your laminate, feed them to the model, and sanity-check the model's global response against the CLT prediction before trusting the detailed results.

Coursework and teaching

The default case is a [0/45/-45/90]_s quasi-isotropic carbon/epoxy laminate, the same configuration most textbooks use. Students can verify homework against it, and it makes the classic CLT lessons visible: why the [B] matrix vanishes for symmetric layups, why in-plane stiffness is direction-independent for quasi-isotropic laminates while bending stiffness is not, and how the z-cubed weighting makes outer plies dominate [D].

When the analysis needs more than stiffness (failure criteria, micromechanics from fiber and matrix data, fabric plies, or beam and sandwich panel analysis), create a free account to unlock the full dashboard.

Frequently Asked Questions

Learn the theory in the CLT reference guide or create a free account to unlock the full toolset.