Elastic Beam Deflection Calculator

Input parameters

Unit system Metric (m, kN, GPa, cm⁺) Imperial (ft, kips, ksi, in⁺)

Inputs are converted to SI units internally for consistent calculations.

Span length L (m or ft)

Clear span between supports or fixed-end to free-end.

Elastic modulus E (GPa or ksi)

For steel ≈ 200–210 GPa or ≈ 29,000 ksi.

Second moment of area I (cm⁺ or in⁺)

Section inertia about the bending axis from section tables.

Load case Simply supported – central point load Simply supported – full-span uniform load Cantilever – free-end point load Cantilever – full-span uniform load

Point load P (kN or kips)

Used for point load cases only.

Uniform load w (kN/m or kips/ft)

Used for uniform load cases only.

Allowable deflection ratio L/x

Typical serviceability limits include L/240, L/360, or L/480.

Calculate deflection

The following examples illustrate typical beam configurations and resulting maximum deflections using the same formulas implemented in this calculator.

Consider a metric steel beam that is simply supported with a central point load:

• Unit system: Metric
• Load case: Simply supported – central point load
• Span length: L = 6.0 m
• Elastic modulus: E = 200 GPa
• Section inertia: I = 8000 cm⁺
• Point load: P = 50 kN at midspan
• Allowable deflection ratio: L/360

Using the formula δmax = P L³ / (48 E I), the calculator converts all inputs to SI units and returns:

• Maximum deflection ≈ 0.0141 m (14.06 mm)
• Span/deflection ratio ≈ 427
• Allowable deflection for L/360 ≈ 16.67 mm
• Utilization ≈ 84 % of the allowable limit
• Status: Within limit

Entering these values in the interface will reproduce the numbers shown, matching Example 1 in the data table for quick verification.

Each input controls stiffness or applied action on the beam. Understanding how they interact helps you quickly test alternatives during design checks.

• Span length L: Longer spans produce significantly larger deflections.
• Elastic modulus E: Stiffer materials (higher E) reduce deflection.
• Second moment of area I: Deeper or optimized sections greatly cut deflection.
• Loads P and w: Higher loads increase both bending moments and deflections.
• Load case selection: Boundary conditions strongly shape deflection response.

The calculator reports absolute deflection values and a span ratio so you can compare actual response against commonly used serviceability limits and code guidance.

• Max deflection: Reported in metres, millimetres, and inches.
• Span/deflection ratio: Higher ratios indicate stiffer performance.
• Allowable ratio L/x: User-defined limit such as L/240 or L/360.
• Utilization percentage: Ratio of actual to allowable deflection.
• Status flag: Quickly highlights whether the limit is exceeded.

Use realistic stiffness and inertia values to obtain meaningful deflection predictions. These are indicative ranges only; always verify against manufacturer or code tables.

• Structural steel: E ≈ 200–210 GPa or ≈ 29,000 ksi.
• Reinforced concrete: E ≈ 25–35 GPa depending on mix and age.
• Engineered timber: E varies widely by species and grade.
• Cold-formed steel: Similar E to hot-rolled, different I values.
• Section inertia I: Take from steel, concrete, or manufacturer tables.

This calculator is ideal for quick what-if studies or educational use. Combine numerical results with engineering judgement and relevant code provisions.

• Check both strength and serviceability; this tool covers deflection only.
• Try alternative spans or sections to see sensitivity of deflection.
• Use realistic long-term loads when checking flexible floor systems.
• Consider cracking, creep, and composite action where relevant.
• Document assumptions when exporting CSV or PDF for project records.

The calculator assumes linear elastic behavior, small deflections, and prismatic beams with constant stiffness along the span. Deflection is computed using classic Euler–Bernoulli theory.

• Simply supported, central point load P: δmax = P L³ / (48 E I), θsupport = P L² / (16 E I)
• Simply supported, uniform load w: δmax = 5 w L&sup4; / (384 E I), θsupport = w L³ / (24 E I)
• Cantilever, free-end point load P: δmax = P L³ / (3 E I), θfixed = P L² / (2 E I)
• Cantilever, full-span uniform load w: δmax = w L&sup4; / (8 E I), θfixed = w L³ / (6 E I)

Units: P in N, w in N/m, L in m, E in Pa, I in m⁺. Metric and imperial inputs are converted to these units internally.

1. What assumptions does this beam deflection calculator make?

It assumes linear elastic material, small deflections, prismatic beam, idealized supports, and loads applied statically; not suitable for large deformations, dynamic loading, or highly cracked or nonlinear members.

2. Can I use these results directly for code compliance?

No, use them as a quick check alongside governing design standards. Always verify load combinations, serviceability limits, reduction factors, and special provisions in your building, bridge, industrial, or local jurisdictional code.

3. Which unit system should I choose?

Choose metric when your project data are in metres, kilonewtons, and gigapascals. Choose imperial when drawings and supplier tables use feet, kips, ksi, and inch-based section properties or traditional imperial design documentation.

4. How accurate are the reported deflections?

Accuracy mainly depends on how realistic your stiffness, loading, and support assumptions are. For typical beams within the elastic range, results closely match textbook solutions and hand calculations using the same standard formulas.

5. Can this calculator handle multiple spans or continuous beams?

No, it is limited to single-span simply supported or cantilever configurations. For continuous, fixed–fixed, indeterminate, or complex framing, use structural analysis software or appropriate frame formulas and redistribution methods.

6. What if my beam experiences long-term effects like creep?

Short-term elastic deflections can be estimated here, but long-term effects require modification factors or more advanced models. Check your concrete, timber, or composite design standard for multipliers or serviceability procedures.

7. How should I document these calculations for project files?

After running the calculation, export CSV or PDF, then store them with drawings and design notes. Include load cases, assumptions, version date, and any manual checks or peer review you performed for traceability.

1. Select the unit system matching your input data.
2. Choose the appropriate load case for your beam configuration.
3. Enter span length, elastic modulus, section inertia, and relevant load values.
4. Specify an allowable deflection ratio if you want an automatic check.
5. Click Calculate deflection to view deflection, slope, ratios, and status.
6. Export the results as CSV or PDF for design documentation if required.

Always verify assumptions, boundary conditions, and formula applicability against the design standards governing your project and jurisdiction.