How far can a steel beam span?

It depends on the section, the load and the limit that governs, so the span is found by iteration rather than read off a table. Fix the section and the load in the beam calculator, then raise the beam length until either deflection reaches your serviceability limit or the moment demand reaches the capacity of the section. L/360 and L/240 are the limits most commonly applied to floor and roof members respectively, though the governing value comes from your project requirements.

What size beam do I need for a given span and load?

Sizing is a two-step job: get the demands, then check a section against them. The free beam calculator gives you the first step, returning moment, shear, deflection and reactions for the span and loads you enter. Comparing those demands against the capacity of a candidate section is a design check, which needs a free Calcs.com account and the steel, timber or concrete library to AISC, NDS or ACI 318.

What size beam do I need for a 20 foot span?

Deflection sets the size on a 20 ft span, not strength, so size the section from a stiffness target rather than from the moment. Take a simply supported 20 ft span carrying 1,000 plf. The moment is M = wL2 / 8 = 50 kip-ft, which almost any rolled section covers, but holding deflection to L/360 (0.67 in) needs I of at least 5wL4 / 384E-delta = 186 in4. A W12x26 at I = 204 in4 clears that; the W14x68 loaded by default in the beam calculator is far stiffer at 722 in4, deflecting 0.17 in or L/1,396. Change the span, the load or the limit and the required I moves with them, which is what the calculator is for. Confirming a section also needs a strength and lateral-torsional buckling check against AISC, NDS or ACI 318, which is a design check rather than an analysis output.

How do you calculate a beam?

Four steps: define the geometry, restrain it, load it, then read the demands. Set the span and the section stiffness (E, A and Ix). Place the supports, since their type and position decide whether the beam is determinate or continuous. Apply the point and distributed loads. The solver then returns the reactions, the shear force and bending moment diagrams and the deflected shape along the full length. For standard cases you can shortcut this with closed-form results, M = wL2 / 8 and delta = 5wL4 / 384EI for a simply supported uniform load, but those only hold for textbook support and load arrangements. Anything continuous, cantilevered or unevenly loaded needs the general solution, which is why this calculator uses a finite element stiffness method instead.

How do you calculate beam deflection?

For a simply supported span under a uniform load, δ = 5wL⁴ / 384EI, where w is the load per unit length, L the span, E the elastic modulus and I the second moment of area. A W14x68 carrying 1,000 plf over 20 ft deflects 0.17 in, or L/1,396. Closed-form results like this only hold for standard support and load cases, which is why the calculator solves the general case with a finite element method instead.

How do you get bending stress from the moment?

Divide the moment by the elastic section modulus: σ = M / S, where S is the second moment of area I_x divided by the distance c from the neutral axis to the extreme fiber. The beam calculator returns the moment demand M*, so the stress follows directly once you know S for your section. Checking that stress against an allowable or factored value is a design check rather than an analysis output.

What types of beams can this calculator analyze?

Simply supported, cantilever, continuous multi-span, propped cantilever and overhanging beams, with any number of spans. Supports take fixed, pinned or roller restraint and sit at any position along the beam, so a support placed away from an end produces a cantilever without a separate mode.

What sign conventions does the beam calculator use?

Two, and both catch people out. In the Calcs.com beam calculator a positive deflection value is downward and a negative value is upward. Distributed and point loads both act perpendicular to the beam, so a downward load on a simply supported span returns a positive mid-span deflection. For bending moment, Calcs.com reports tension along the top of the beam as negative. Some published worked examples use the opposite sign, so when you check against a textbook expect the sign to differ while the magnitude matches.

Is the beam calculator free to use?

Yes, completely free with no sign-up required. The calculator runs in your browser and solves any number of spans, supports and loads. A free Calcs.com account adds saved calculations, PDF export, the built-in section library and the full steel, timber and concrete design library to AISC, NDS and ACI 318.

What is locked behind a Calcs.com account?

The free tool covers fixed, pinned and roller supports plus point, uniform, partial and linearly varying distributed loads. Axial, moment, linked and oriented loads, internal hinges, spring and continuous supports, inclined beams, the built-in section library, saved calculations and PDF export need a free Calcs.com account, which also opens the full steel, timber and concrete library to AISC, NDS and ACI 318.

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Model bending moment, shear force, and deflection for any beam - no sign-up required.

How to use the free beam calculator

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[ 01 ]
Enter beam geometry
Set the span length L in ft, elastic modulus E in psi, second moment of area I_x in in⁴, and cross-sectional area A in in². Defaults are 10 ft and a W14x68 at 29,000,000 psi.
[ 02 ]
Set your supports
Add fixed, pinned or roller supports at any position along the beam. A support set away from the ends creates a cantilever, so overhanging and propped beams are entered the same way.
[ 03 ]
Apply loads
Add point loads in lb and distributed loads in plf. Unequal start and end magnitudes give a linearly varying load, and locations inside the span give a partial load.
[ 04 ]
Read the diagrams
Moment in lb·ft, shear in lb and deflection in in update instantly. Per-span moments and per-support reactions are tabulated below the diagrams.

About this calculator

Solve simple, continuous, cantilever and propped beams in imperial units. Enter the span, section stiffness, supports and loads, and a finite element solver returns bending moment, shear force and deflection along the full length, with per-span and per-support demands underneath. The analysis is code independent, so the same model holds whichever standard you design to.

Simply supported, uniform load: M = wL² / 8

Simply supported, uniform load: V = wL / 2

Simply supported, uniform load: δ = 5wL⁴ / 384EI

Simply supported, central point load: M = PL / 4

Simply supported, central point load: δ = PL³ / 48EI

Bending stress from moment: σ = M / S, where S = I_x / c

Validated against:

Connor (2013), Fundamentals of Structural Engineering, Example 3.13: a two-span beam with an internal hinge under opposing triangular loads. Solver moment agrees to within 0.3%, shear and support reactions match exactly.

Last reviewed August 28, 2026

Inside the calculator

The Calcs.com beam calculator takes the geometry and loading of a beam and returns bending moment, shear and deflection diagrams, plus maximum demands, from a finite element analysis engine. Results update as you type. This page loads the calculator in imperial units.

The solver works from the section stiffness you enter rather than a section type, so it handles any prismatic member: a rolled steel I-beam or RSJ, a timber joist, a concrete beam, or a built-up shape. Enter the area and second moment of area and the analysis is the same.

The analysis itself is code independent: it solves statics and stiffness, so the same model holds under AS, NZS, Eurocode, CSA and US standards. Design checks against a specific standard need a Calcs.com account, which adds design in steel, concrete and wood to AISC 360, ACI 318 and the NDS.

Inputs and outputs at a glance

Quantity	Symbol	Unit	Default
Length of beam	L	ft	10 ft
Young's modulus	E	psi	29,000,000 psi
Area of cross-section	A	in²	20 in²
Second moment of area	I_x	in⁴	722 in⁴
Point load	P	lb	none
Distributed load	w	plf	100 plf rising to 1,000 plf
Moment demand	M*	lb·ft	calculated
Shear demand	V*	lb	calculated
Deflection	δ	in	calculated
Maximum reaction	R*	lb	calculated

Frequently asked questions

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