Calculate maximum bending moment, shear force, reactions and deflection for simply supported or cantilever beams.
On the Bending Moment & Shear tab, choose whether your beam is simply supported (resting on two supports) or a cantilever (fixed at one end, free at the other), and whether it carries a point load or a uniformly distributed load. Enter the span and load to get maximum bending moment, shear force, and support reactions. On the Deflection tab, choose the same beam and load type, select a material (or enter a custom modulus of elasticity), and enter your beam's moment of inertia to estimate maximum deflection and how it compares to common serviceability guides.
For a point load P at distance a from the left support (with b as the remaining distance to the right support), the support reactions and maximum bending moment are:
For a uniformly distributed load w (force per unit length) across the full span L:
A cantilever is fixed at one end and completely free at the other, so all of the load is carried by the single fixed support.
Deflection depends on the load, span, the beam material's stiffness (modulus of elasticity, E), and the beam cross-section's resistance to bending (moment of inertia, I).
For an off-centre point load on a simply supported beam, the calculator solves the full elastic curve rather than the centred-load formula above, since maximum deflection then occurs slightly off from directly under the load — entering a centred position (a = L/2) still reduces to the formula shown.
Moment of inertia depends entirely on your beam's specific cross-sectional shape and size. For a solid or hollow rectangle or circle, the Deflection tab's built-in cross-section calculator works it out from your dimensions automatically; for other or manufactured sections, get it from a manufacturer's datasheet or a structural section property table (like an AISC steel manual for I-beams, or a lumber/LVL manufacturer's span table).
The Deflection tab includes approximate reference values for common materials: steel (~200 GPa / 29,000,000 psi), aluminum (~69 GPa / 10,000,000 psi), timber/softwood (~11 GPa / 1,600,000 psi), and reinforced concrete (~25 GPa / 3,600,000 psi). These are typical, widely published approximate figures - actual E depends on the specific material, grade, species, alloy, concrete mix, condition and relevant engineering assumptions. Selecting a material here estimates deflection only; it does not by itself make the result suitable for structural design. Use a custom value from your material's datasheet for a more precise result.
A beam can be strong enough not to break under load, yet still deflect (bend or sag) enough to cause problems - visible sag, cracked plaster or drywall, doors and windows that stick, or an uncomfortable "bouncy" floor feel. Because of this, building codes typically set separate deflection limits alongside strength requirements, commonly expressed as a fraction of the span. Span/360 is a commonly cited limit for live loads on floors supporting brittle finishes; span/240 is commonly cited for total load or roof members. This calculator shows your beam's deflection ratio against both as a general reference comparison only, not a building-code compliance determination - always confirm the specific limit that applies to your project and jurisdiction.
Example 1 — Simply supported, point load. A 4m beam with a 10 kN point load at 2m (center): reactions are 5 kN each, max bending moment is 10 kN·m, max shear is 5 kN.
Example 2 — Simply supported, off-center load. The same 4m beam with the same 10 kN load at 1m from the left support: reactions are 7.5 kN and 2.5 kN, max bending moment is 7.5 kN·m (at the load point), max shear is 7.5 kN.
Example 3 — Cantilever, uniform load. A 2m cantilever beam with a 5 kN/m uniform load: the fixed-end reaction is 10 kN, max bending moment is 10 kN·m, max shear is 10 kN.
A common mistake is confusing simply supported and cantilever formulas - a cantilever's maximum moment and deflection are both several times larger than a simply supported beam of the same span and load, because all the bending is concentrated at a single fixed end rather than shared and reduced by two supports. Another mistake is using an incorrect or estimated moment of inertia - since deflection is inversely proportional to I, even a modest error in your section's I value produces a proportional error in the deflection result. It's also easy to overlook that strength (will it break?) and deflection (will it sag too much?) are two separate checks - a beam can easily pass one and fail the other.
This calculator uses standard engineering-mechanics formulas for idealized, uniform, elastic beams under a single static point load or uniform distributed load, with simple support or cantilever end conditions. It does not perform member strength/capacity design, bending or shear stress capacity checks, lateral-torsional or local buckling checks, bearing checks, connection design, continuous/multi-span analysis, combined or multiple-load analysis, dynamic/impact analysis, load combinations, safety/load factors, code compliance checks, or manufacturer span-table verification - and it does not include manufacturer-specific steel, LVL or glulam section dimension and span tables. A calculated bending moment or deflection result does not mean the selected beam is structurally adequate. This tool is for general reference only and is not a substitute for a licensed structural engineer's design and calculations on any real project.
This depends on the beam type (simply supported or cantilever), load type (point load or uniformly distributed load), span, and load magnitude. Use the Bending Moment & Shear tab above with your beam's details for an automatic result.
For a cantilever with a point load at the free end, deflection equals PL³÷(3EI); for a uniformly distributed load, it's wL⁴÷(8EI), where E is the modulus of elasticity and I is the beam's moment of inertia. Use the Deflection tab above with your beam's details for an automatic result.
For a point load P at distance a from the left support (b = span − a), the reactions are Pb÷L and Pa÷L, and the maximum bending moment is Pab÷L, occurring at the load point. Use the Bending Moment & Shear tab above for an automatic result.
Deflection is how much a beam bends or sags under load. Excessive deflection can cause visible sag, cracked finishes, or doors/windows that stick, even if the beam isn't at risk of breaking - which is why building codes set separate deflection limits (often expressed as span/360 or span/240) alongside strength requirements.
Span/360 (deflection no more than 1/360th of the span) is a commonly cited limit for live loads on floors supporting brittle finishes, and span/240 is commonly cited for total load or roof members - but actual limits depend on your application and local building code. Use the Deflection tab above to compare your beam's ratio to these general guides.
A simply supported beam rests on two supports (typically one at each end) and can rotate freely at both; a cantilever beam is fixed rigidly at one end and completely free at the other, with no support at all at the free end. These different support conditions produce very different bending moment, shear and deflection patterns.
For a simply supported beam under a uniformly distributed load, maximum shear occurs at the supports and equals half the total load. For a cantilever, maximum shear occurs at the fixed end and equals the full applied load. Use the Bending Moment & Shear tab above for an automatic result.
The modulus of elasticity (E) measures a material's stiffness - how much it resists bending under load. It's a key input to every beam deflection formula. This calculator provides typical reference values for common materials (steel, aluminum, timber, concrete) on the Deflection tab, or you can enter a custom value from your specific material's datasheet.
Moment of inertia (I) measures how a beam's cross-sectional shape resists bending - a deeper or wider section generally has a higher moment of inertia and deflects less. For a solid or hollow rectangle or circle, the Deflection tab's built-in cross-section calculator works it out from your dimensions automatically; for other or manufactured sections, get it from a manufacturer's datasheet or a structural section property table.
No - it calculates bending moment, shear, reactions and deflection from the span, load and section properties you provide. It does not include manufacturer-specific I-beam, LVL or glulam dimension and span tables, since those vary by product and should come from the manufacturer's or code body's official span tables.
No - it provides general engineering-mechanics estimates for simple, idealized beam and load conditions. Real structures often have more complex loading, continuous spans, dynamic loads, or code-specific safety factors that require a licensed structural engineer's design and sign-off.