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Calcimator

Beam Load Calculator

Calculate maximum shear, bending moment, and deflection for simply supported and cantilever beams under uniform or point loads.

About this calculator

This calculator solves the four classic statically-determinate beam cases every structural engineer learns first: a simply supported or cantilevered beam carrying either a uniformly distributed load or a single point load at midspan (or at the tip, for the cantilever). For a simply supported beam under uniform load w, it applies the standard results wL/2 for max shear, wL²/8 for max moment, and the deflection formula 5wL⁴/(384EI); under a center point load P, the formulas become P/2, PL/4, and PL³/(48EI). The cantilever cases use wL, wL²/2, and wL⁴/(8EI) for uniform load, or P, PL, and PL³/(3EI) for a tip point load — note the cantilever moment and deflection formulas don't carry the fractional divisors of the simply-supported case because the fixed end resists the full load at a single point rather than sharing it across two supports. Deflection is computed in inches by converting span length from feet to inches and working in the beam's elastic modulus (E, in ksi) and moment of inertia (I, in in⁴), so getting those two section-property values right matters as much as the load itself — a beam sized only for strength (moment) can still fail a serviceability (deflection) check.

The elastic modulus default of 29,000 ksi is AISC 360's specified value for structural steel; for wood, the American Wood Council's National Design Specification (NDS) publishes E by species and grade — Douglas Fir-Larch No. 2 around 1,600 ksi, laminated veneer lumber (LVL) around 1,900 ksi — so switching material means switching which standard governs the number you enter. This tool only covers single-span, single-load-case scenarios: it doesn't handle multiple point loads, partial uniform loads, continuous multi-span beams, or combined loading, so treat it as a quick check for simple framing members rather than a substitute for a full structural analysis on anything with mixed or multiple loads.

Inputs

lb or lb/ft
ft

Results

Maximum Shear

5,000 lb

≈ 5 grand pianos

Maximum Bending Moment

25,000 ft·lb

Maximum Deflection0.62 in

Figures current as of 2018. Sources: American Wood Council, National Design Specification (NDS) for Wood Construction, 2018 Edition, Chapter 2 (Design Values for Structural Members), American Institute of Steel Construction, AISC 360, Specification for Structural Steel Buildings

How to Use This Calculator
  1. Select load type (uniform distributed load or point load at center).
  2. Enter load magnitude and span length.
  3. Choose support type (simply supported or cantilever).
  4. Review maximum moment, shear, and deflection results for structural sizing.

How the result changes with Load Magnitude

Load MagnitudeMaximum ShearMaximum Bending Moment
2502,500 lb12,500 ft·lb
3753,750 lb18,750 ft·lb
7507,500 lb37,500 ft·lb
1,25012,500 lb62,500 ft·lb

What each input means

Load Type
Select whether the beam carries a distributed uniform load or a single concentrated point load at midspan.
Load Magnitude
For uniform load enter lb/ft; for point load enter total lb.
Span Length
Clear span length of the beam between supports.
Support Type
Simply supported has pins at both ends; cantilever is fixed at one end and free at the other.
Elastic Modulus (E)
Modulus of elasticity of the beam material per AISC 360 and NDS. Steel: 29,000 ksi; aluminum: 10,000 ksi; Douglas fir: 1,600 ksi; LVL: 1,900 ksi.
Moment of Inertia (I)
Second moment of area of the beam cross-section per AISC Steel Construction Manual. W8×31: I=110 in⁴; W12×50: I=394 in⁴; W16×67: I=954 in⁴. For wood joists, calculate bh³/12.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Load Type = 1, Load Magnitude = 500, Span Length = 20, Support Type = 1 = 6 input(s) provided
  2. Calculate Maximum Shear
    Maximum Shear
    5000 = 5000
  3. Calculate Maximum Bending Moment
    Maximum Bending Moment
    25000 = 25000
  4. Calculate Maximum Deflection
    Maximum Deflection = abs(maxDeflection)
    0.6207 = 0.6207

Figures and sources

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why don't the cantilever formulas have the same fractions (like /2 or /8) as the simply supported ones?

A simply supported beam shares the load between two end supports, so the peak moment and deflection get divided down by factors like 4 or 8 depending on load type. A cantilever is fixed at only one end, which must resist the entire load and its full moment arm by itself with nothing shared at the free end — that's why the cantilever formulas here (wL²/2 for moment vs. wL²/8 for simply supported) come out several times larger for the same load and span.

Why does deflection depend on elastic modulus and moment of inertia, when shear and moment don't?

Maximum shear and moment are statics results — they only depend on the load and how it's supported, not on what the beam is made of or its cross-section shape. Deflection, however, describes how much the beam actually bends, which depends on stiffness: EI, the product of the material's elastic modulus (E) and the cross-section's moment of inertia (I). That's why this calculator's deflection formulas (like 5wL⁴/(384EI)) divide by EI while the shear and moment formulas don't reference either value. The elastic modulus itself comes from a governing standard, not a lab test on your specific beam — AISC 360 fixes E at 29,000 ksi for structural steel, while the American Wood Council's NDS publishes species-specific values for wood (Douglas Fir-Larch No. 2 around 1,600 ksi, LVL around 1,900 ksi), so picking the right material standard matters before you even get to the deflection math.

How does choosing a point load instead of a uniform load change the results?

A uniform load spreads the same total weight evenly across the whole span, while a point load concentrates it at a single location (center for simply supported, tip for cantilever). For the same total load, this generally produces different peak values — for example, a simply supported beam's max moment is wL²/8 under uniform load but PL/4 under a center point load — because concentrating force at one spot changes how the internal bending moment builds up along the span.

Can this calculator handle a beam with more than one load or more than one span?

No — it only solves the four single-span, single-load-case scenarios described above (simply supported or cantilever, under one uniform or one point load). It can't combine multiple point loads, partial-length uniform loads, continuous multi-span beams, or mixed loading types, so for anything beyond a simple framing member with one load case you'd need a full structural analysis rather than this quick-check tool.

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