The Beam Load Calculator computes reactions, maximum bending moment, and allowable load for simply supported and cantilever beams. Performs both strength and serviceability checks — the two independent criteria that govern structural beam design in any material and code system.
6.2208
in
0.4
in
23.1
L/x
1,555.2
%
22,500
lb-ft
3,000
lb
6.2208
in
0.4
in
23.1
L/x
1,555.2
%
22,500
lb-ft
3,000
lb
A beam must satisfy two independent structural requirements: it must be strong enough that the material does not yield under the maximum bending moment, and stiff enough that it does not deflect beyond the code-specified serviceability limit. These two requirements often lead to different controlling beam sizes — stiffness governs in long-span low-load situations; strength governs in short-span high-load cases. The calculator for beam loads solves both checks simultaneously, identifying the controlling condition and the maximum allowable load or required beam depth for any configuration.
Maximum bending moment M_max and support reactions for common beam configurations:
Simply supported, central point load P:
M_max = P × L / 4 (at midspan); Reaction each end = P/2
Simply supported, uniformly distributed load w (per unit length):
M_max = w × L² / 8 (at midspan); Reaction each end = w × L / 2
Cantilever, point load P at free end:
M_max = P × L (at fixed support); Reaction at support = P; Moment reaction = P × L
Fixed-fixed beam, central point load P:
M_max = P × L / 8 (at midspan, versus P×L/6 for fixed ends — fixed beam is 33% more efficient than simply supported). Use this online calculator for any of these configurations. The beam deflection calculator focuses specifically on the displacement side of this analysis.
The required section modulus S determines whether a cross-section can resist the applied bending moment within allowable stress:
S_required = M_max / f_allow
where f_allow is the allowable bending stress for the material: 0.6 × F_y for steel (AISC ASD); F_b from NDS Supplement for dimension lumber (varies by species and grade). Section modulus for common shapes: rectangle: S = b×h²/6; W-shape: tabulated values (W12×50 has S = 64.7 in³). The section modulus doubles when height doubles — deeper beams are far more moment-efficient than wider ones. The Young's modulus calculator and materials science calculators provide material property reference values.
Every beam must pass two independent checks:
For typical steel floor beams, the deflection check governs for spans above approximately 20–25 ft; strength governs for shorter spans with heavy loads. For wood floor beams, deflection governs at nearly all practical spans in residential construction — the L/360 requirement typically requires a deeper section than the bending stress check alone.
A beam continuous over multiple spans has significantly lower bending moments than a series of simple spans. For a two-span continuous beam with equal spans L and uniform load w, the maximum positive moment is only 0.07×w×L² (vs. 0.125×w×L² for a simply supported beam) — a 44% reduction in bending demand. This is why multi-span continuous construction is structurally more efficient than simply supported framing, and why interior supports (columns, bearing walls) dramatically reduce beam size requirements compared to open-span designs of the same total length.
Enter the required input values in the fields provided. The calculator uses established formulas and mathematical relationships to compute the results in real-time. All calculations are performed client-side for instant feedback.
The Beam Load Calculator applies standard beam & column formulas to deliver accurate results. Adjust any input value to see how it affects the output.
Inputs
Results
An 800 lb/ft (including self-weight) distributed load on a 16-ft simply supported beam produces a maximum moment of 25,600 ft-lbs at midspan and reactions of 6,400 lbs at each end. A 3.5×11.25 LVL (I ≈ 288 in⁴, E = 1,600,000 psi) deflects 0.59 inches — slightly over the L/360 limit of 0.53 inches. Upgrading to a 3.5×14 LVL (I ≈ 570 in⁴) brings deflection to 0.30 inches, well within limits.
Inputs
Results
A 2,000 lb point load at the tip of a 6-ft steel cantilever produces a maximum fixed-end moment of 12,000 ft-lbs (12 kip-ft). A W6×15 steel section (I ≈ 29.1 in⁴) would be overstressed; a W8×24 (I ≈ 82.7 in⁴) satisfies both moment capacity and the L/180 = 0.40-inch deflection limit with margin.
The Beam Load Calculator uses precise mathematical formulas and provides results with up to 6 decimal places of precision. The accuracy depends on the precision of your input values.
The calculator uses standard units commonly used in beam & column calculations. Each input and output field displays its unit for clarity.
Yes, the Beam Load Calculator is fully responsive and works on all devices including smartphones, tablets, and desktop computers.
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