Estimate required section modulus or rectangular beam depth for a simply supported beam under a full-span uniform load or a central point load. Include an optional deflection requirement and use actual section dimensions and adjusted allowable properties.

Preliminary elastic beam requirements. Simply supported, prismatic section; one full-span uniform load or one central point load. Final design requires the remaining material and code checks.

Use the applicable uniform load, including distributed self-weight when known. This case does not add a separate point load.

Use the applicable adjusted allowable stress, not yield or ultimate strength. No generic material property is assumed.

Related Calculators

Beam Size Formula

For a rectangular section, required depth is d = sqrt(12 × 6 × M / (b × Fb)), where M is in lb-ft, b and d in inches, and Fb in psi. The square-section special case below assumes b = h. The factor 12 converts lb-ft to lb-in. When deflection is included, the calculator also solves I = b d³ / 12 and uses the larger required depth. The same entered load is applied to both bending and deflection; check separate total and live-load combinations when the applicable code requires them.

h = (72 × M / Fb)(1 / 3)

Variables:

  • M is the maximum bending moment (pound-feet)
  • h is the required beam height (inches)
  • F_b is the adjusted allowable bending stress (psi), not ultimate or yield strength

What is Beam Size?

Beam size refers to the cross-sectional dimensions of a beam that are required to support a given load over a span without exceeding the material’s allowable stress. The size is typically described by the beam’s height and width, which directly relate to the beam’s strength and ability to resist bending. These calculations cover ideal elastic bending and optional deflection only. Final selection also requires shear, bearing, lateral stability, connections, load combinations and the applicable material/building-code checks.

How to Calculate Beam Size?

The following steps outline how to calculate the Beam Size.

  1. First, determine the uniform line load w in lb/ft over the full span, or the central point load P in pounds-force. In the uniform case, include applicable distributed loads and beam self-weight. The central-point case models only that point load; distributed self-weight requires a separate load case.
  2. Next, determine the span (L) in feet over which the beam will support the load.
  3. Calculate maximum moment M in lb-ft using M = wL² / 8 for uniform load, or M = PL / 4 for a point load at mid-span.
  4. Use S = 12M / Fb, then d = sqrt(6S / b) for a specified actual rectangular width b. If deflection is enabled, also use d = (12I / b)^(1/3); select the larger depth and round up to an available actual section.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Uniform line load w = 1000 lb/ft; adjusted allowable bending stress Fb = 1200 psi; actual rectangular width b = 3.5 in.

Span L = 10 ft. M = 12,500 lb-ft; S = 125 in³; bending-only rectangular depth = sqrt(6 × 125 / 3.5) = 14.6385 in. Round up and complete the remaining design checks.