Introduction
This free beam calculator solves beams in seconds. Type in your beam length, add supports, and add loads. Press Calculate. You get support reactions, shear force, bending moment, slope, deflection, and stress — all in one place.
The tool draws your beam as you build it, so you can see if the model looks right. It also draws the shear force diagram (SFD), bending moment diagram (BMD), and deflection curve, with the max and min values marked for you.
You can pick a beam type with one click: simply supported, cantilever, fixed–fixed, overhanging, or continuous. Add point loads, moments, uniform loads (UDL), or triangular and trapezoidal loads. Pin, roller, fixed, spring, and internal hinge supports are all supported.
Work in metric or imperial units. Choose a steel, wood, aluminum, or concrete section from the library, build a shape, or type your own A, I, and E values. Load cases and code combinations (ASCE 7, ACI 318, Eurocode, AS/NZS, NBCC) are built in.
Every answer comes with step-by-step hand calculations, so you can check the math or show your work. When you are done, export your results to CSV, Word, or PDF with your name, project, and logo on it.
This calculator is made for students, engineers, and builders who need fast, clear beam results without heavy software. If you only need sag numbers, the Beam Deflection Calculator is a quicker option, and the Section Modulus Calculator helps you size the cross-section first.
How to use our Beam Calculator
Enter your beam length, supports, loads, and cross-section, then press Calculate. The tool gives you support reactions, shear force, bending moment, slope, deflection, and stress diagrams, plus step-by-step hand calculations.
Unit system: Pick Metric or Imperial. All boxes, tables, and charts switch right away. Handy converters: mm to inches, meters to feet, and kg to lbs.
Length unit: Choose the unit for spans and positions, like m, mm, ft, or in.
Force unit: Choose the unit for loads and reactions, like kN, N, kip, or lbf. See the Force Calculator if you need to work a load out from mass and acceleration.
Moment sign convention: Pick if a positive moment means sagging (tension at the bottom) or hogging (tension at the top).
Example presets: Click one button to load a ready-made beam, such as a simply supported beam with a point load. This replaces your current model.
Beam description: Type your beam in plain English, then press Generate Beam. Check the summary and click Apply.
Beam length (span): Type the total length of the beam. It must be more than zero.
Beam type: Pick Simply Supported, Cantilever, or Fixed–Fixed to place supports for you. Pick Overhanging / Continuous to set your own supports.
Canvas label size: Choose how big the text on the beam drawing is.
Show load labels / dimension labels: Tick these to show or hide load values and span marks on the drawing. Use the zoom buttons, scroll, or drag to move the view.
Support type: Choose Pin, Roller, Fixed (wall), Spring, or Internal hinge. For spring supports, the Spring Force Calculator helps you find a stiffness value.
Position preset: Put the support at the left end, right end, or a custom spot you type in.
Position from left: Type how far the support sits from the left end of the beam.
Roller angle: For rollers only. Type the angle from the beam axis. Use 90° for a normal vertical reaction.
Spring stiffness k: For springs only. Type how stiff the spring support is.
Add Support: Click to save the support. Use the pencil to edit or the bin to delete it in the table.
Load type: Choose Point load, Applied moment, UDL (even spread load), or Trapezoidal / triangular.
Position: For point loads and moments, type the distance from the left end.
Start and end position: For spread loads, type where the load starts and stops. The end must be past the start.
Magnitude: Type the load size. Point loads use force units, UDLs use force per length, moments use force × length. The Torque Calculator is useful for turning a force and lever arm into a moment.
Start and end magnitude: For trapezoidal loads, type the load value at each end of the range.
Angle: For point loads, type the angle from the beam axis. Use 90° for straight down.
Direction: Pick Downward or Upward for the load. Trapezoidal loads have one pick for each end.
Rotation: For applied moments, pick Clockwise or Counter-clockwise.
Load case: Tag the load as Dead, Live, Wind, Snow, Seismic, or your own case. This lets load factors work. For lateral pressures, try the Wind Load Calculator.
Add Load: Click to save the load. Edit or delete it later from the load table.
Include beam self-weight: Turn this on to add the beam's own weight as a UDL from its density and area. You can cross-check it with the Steel Weight Calculator or the Metal Weight Calculator.
New load case: Type a name and click Add case to make your own load group.
Section source: Pick Library for standard steel shapes, Custom to type your own numbers, or Shape builder to work them out from sizes.
Section name: Give the section a name so you can spot it in the tables.
Segment start and end: Type the part of the beam this section covers. Sections should cover the full span.
Region, Category, Section: In Library mode, pick the code region, the shape family, and the exact section. Area and inertia fill in for you.
Primitive shape and sizes: In Shape builder mode, pick a shape like rectangle, pipe, or I-beam, type the widths and thicknesses, then click Derive properties. For hollow shapes you may also like the Tube Weight Calculator and the Square Tube Weight Calculator.
Material preset: Pick steel, aluminum, wood, concrete, and more. This fills E, density, and strength values. See the Density Calculator if you are working with a custom material.
Young's modulus E: Type the stiffness of the material. It must be more than zero.
Density: Type the material density. This is used for self-weight.
Yield strength Fy and Ultimate strength Fu: Type the material strengths used for the stress checks.
Area A: Type the cross-section area. It is used for axial and shear stress. The Area Calculator can help with odd shapes.
Moment of inertia Iz: Type the second moment of area about the bending axis. See the Moment of Inertia Calculator for common shapes.
y-top and y-bottom: Type the distance from the neutral axis to the top and bottom fibres. The tool works out the section modulus S.
Add Section: Click to save the section to the segment table.
Design code: Pick a code like ASCE 7, ACI 318, Eurocode, AS/NZS, or NBCC, or leave it as None.
Load combination: Pick the combination used for results. Change any factor in the table and it turns into a Custom combination.
Calculate: Press this to run the analysis and refresh all results and diagrams.
Deflection limit L / n: Type the number n, such as 360, to check deflection against L/n.
Allowable bending stress: Type the stress your code allows. The tool shows a Pass or Fail.
Query results at location x: Type any point along the beam to see shear, moment, slope, deflection, and stress there.
Diagram toggles: Tick or untick each diagram to show or hide it. Use Reset zoom to fit the chart again.
Report fields: Add your name, project, and a logo, then pick what goes in the report. Use Export CSV, Export Word, or Print / PDF to save your results.
What Is a Beam?
A beam is a straight structural member that carries loads across a gap. Floor joists, roof rafters, bridge girders, and steel lintels over doors are all beams. When you put weight on a beam, the beam pushes back through its supports, bends a little, and builds up internal forces inside it. Structural engineers check those forces to make sure the beam is strong enough and stiff enough. If you are laying out a floor or roof frame first, the Floor Joist Calculator, Rafter Calculator, and Framing Calculator are good starting points.
Supports
How a beam is held up changes everything about how it behaves. The common support types are:
- Pin: stops up-and-down and side-to-side movement, but lets the beam rotate.
- Roller: stops movement in one direction only. The beam can slide and rotate.
- Fixed (wall): stops movement and rotation. This creates a moment at the support.
- Spring: pushes back based on how far it squashes, like a flexible support.
- Internal hinge: a point inside the beam that can rotate freely, so no moment passes through it.
Common beam types come from these supports: a simply supported beam (pin + roller), a cantilever (fixed at one end, free at the other), a fixed–fixed beam, an overhanging beam, and a continuous beam with three or more supports. For pin-jointed frames instead of solid beams, use the Truss Calculator.
Types of Loads
- Point load: a single force at one spot, like a column sitting on the beam.
- Uniformly distributed load (UDL): the same force spread evenly along a length, like the weight of a floor.
- Trapezoidal or triangular load: a spread load that gets bigger or smaller along the beam, like soil or water pressure. The Hydrostatic Pressure Calculator gives you the pressure profile behind a wall or tank.
- Applied moment: a twisting action at one point.
- Self-weight: the weight of the beam itself, found from its density and area. For concrete members, see the Concrete Weight Calculator.
Shear Force and Bending Moment
Shear force (V) is the sideways sliding force at a cut in the beam. It equals the sum of all up and down forces on one side of that cut. Bending moment (M) is the bending action at that cut. It equals the sum of each force times its distance from the cut.
Engineers plot these along the beam as a shear force diagram (SFD) and a bending moment diagram (BMD). A handy rule: the bending moment is largest where the shear force crosses zero. Sagging (bending down, like a smile) puts the bottom of the beam in tension. Hogging (bending up, over a support) puts the top in tension. This matters a lot for where you place steel bars or bracing — the Rebar Calculator helps with the reinforcement layout.
Stress and Deflection
Bending stress at the outer face of the beam is found with the flexure formula:
σ = M × c / I
Here M is the bending moment, c is the distance from the middle (neutral axis) to the top or bottom face, and I is the moment of inertia of the cross-section. A rough average shear stress is τ = V / A. Bending stress must stay below the allowable stress and the yield strength of the material.
Deflection is how far the beam sags. It depends on the load, the span, and the beam's stiffness EI (Young's modulus times moment of inertia). Deflection grows very fast as span grows, so long beams need deep sections. Two classic results:
- Simply supported beam with a center point load: δ = PL³ / 48EI
- Simply supported beam with a full UDL: δ = 5wL⁴ / 384EI
Codes limit deflection with a span ratio like L/360 for floors or L/240 for roofs. A beam can be plenty strong and still fail this check, which is why both strength and stiffness are tested. To dig into sag alone for these standard cases, open the Beam Deflection Calculator.
Section Properties and Materials
The shape of the cross-section decides how well a beam resists bending. Deeper sections are much stiffer, because I grows with the cube of depth. That is why I-beams, wide flange (W) shapes, IPE, and UB sections put most of their steel in the top and bottom flanges. The section modulus S = I / c is a quick strength measure: bigger S means the beam can carry more moment before the stress limit is reached. The Section Modulus Calculator works this out for many standard shapes.
The material sets the Young's modulus E (stiffness), the yield strength Fy, and the density. Steel is about 200,000 MPa, aluminum about 69,000 MPa, and wood is much lower. Two beams of the same shape but different material will bend by very different amounts. For material take-offs, see the Board Foot Calculator for timber, the Aluminum Weight Calculator, and the Plate Weight Calculator.
Statically Determinate vs. Indeterminate
If a beam has only three unknown reactions, you can solve it with the three equilibrium equations: ΣFx = 0, ΣFy = 0, and ΣM = 0. That beam is statically determinate. Fixed-fixed beams and continuous beams have extra reactions, so statics alone is not enough. These indeterminate beams need a stiffness method that also uses the beam's EI, which is solved with matrix algebra behind the scenes — the Matrix Calculator and System of Equations Calculator show how those solves work. The good news is that extra supports usually lower the peak moment and the deflection.
Load Cases and Combinations
Real buildings must handle dead load (permanent weight), live load (people and furniture), wind, snow, and earthquake. Design codes such as ASCE 7, ACI 318, Eurocode, AS/NZS 1170, and the NBCC multiply each load case by a factor and add them together. For example, 1.2D + 1.6L is a common strength check. Different combinations govern at different times, so several are usually checked. Once the beam is sized, connections matter too — the Bolt Torque Calculator covers the fasteners that hold it all together.