What beam formulas does this use?

For a simply supported beam, a central point load P gives Mmax = PL/4, Vmax = P/2, and deflection = PL³ / (48EI). A uniform load w gives Mmax = wL²/8, Vmax = wL/2, and deflection = 5wL⁴ / (384EI). Cantilever cases use their own standard formulas.

What is the deflection limit for a beam?

A common serviceability limit is span over 360 (L/360) for floors under live load, or L/240 for total load. The tool reports the actual deflection; compare it to L/360 in the same units to see whether the beam is stiff enough.

What is EI and why does it matter?

EI is flexural rigidity: E is the modulus of elasticity of the material and I is the moment of inertia of the cross-section. Deflection is inversely proportional to EI, so a stiffer material or a deeper section reduces sag dramatically because I grows with depth cubed.

Does this size a beam for me?

No. It computes the demands — moment, shear, and deflection — for a given beam and load. Comparing those against a material's allowable stress and your deflection limit is the engineer's job. Treat this as a fast check, not a substitute for stamped design.

What units does the calculator use?

Inputs are span in feet, point load in pounds, and uniform load in pounds per foot. Outputs are moment in foot-pounds, shear in pounds, and deflection in inches, using consistent unit conversions internally so the numbers are directly comparable to code limits.

Simple Beam Load & Deflection Calculator

Checking a beam comes down to three demands: how much it bends (moment), how much it shears at the supports, and how far it sags (deflection). This calculator applies the textbook closed-form formulas for the most common loading cases on simply supported and cantilever beams, with a section lookup so you can get a real deflection number, not just the forces.

How it works

Each support-and-load combination has an exact closed-form result. With span L, point load P, uniform load w, modulus of elasticity E, and moment of inertia I:

Simply supported, central point load P:
  Mmax = P·L / 4      Vmax = P / 2      δmax = P·L³ / (48·E·I)

Simply supported, uniform load w:
  Mmax = w·L² / 8     Vmax = w·L / 2    δmax = 5·w·L⁴ / (384·E·I)

Cantilever, point load P at the free end:
  Mmax = P·L          Vmax = P          δmax = P·L³ / (3·E·I)

Cantilever, uniform load w:
  Mmax = w·L² / 2     Vmax = w·L        δmax = w·L⁴ / (8·E·I)

Lengths are converted to inches for the deflection terms so the result comes out in inches, while moments are reported in foot-pounds.

Example and tips

A 16 ft simply supported steel W10×22 (I = 118 in⁴, E = 29,000,000 psi) under a uniform 200 lb/ft load carries Mmax = 200 × 16² / 8 = 6,400 ft-lb, a shear of 1,600 lb, and deflects about 0.28 in — well inside an L/360 limit of 0.53 in. Always check all three demands: a beam can pass on strength yet fail on deflection, especially long, shallow members where the depth-cubed term in I works against you. This is a screening tool — final sizing needs a qualified engineer.