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Beam Deflection Calculator

Estimate maximum deflection, slope, flexural rigidity, and section properties for common Euler-Bernoulli beam cases.

Beam Deflection inputs

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.

Calculation mode

Display precision

Material properties

Material property mode

Material preset

Young's modulus

Young's modulus unit

Shear modulus

Shear modulus unit

Yield strength

Yield strength unit

Ultimate strength

Ultimate strength unit

Generic steel values. Use grade-, standard-, temperature-, and process-specific data for real design.

Beam geometry and loading

Beam load case

Section mode

Beam length

Beam length unit

Point load

Point load unit

Distributed load

Distributed load unit

Second moment of area

Second moment of area unit

Length output unit

Stress output unit

Result section

warningcantilever-end-load

Maximum deflection

1.66667 mm

Secondary results

Maximum slope: 0.00125 rad
Maximum slope: 0.0716197 deg
Flexural rigidity EI: 1.60000e+6 N*m^2
Second moment of area: 8.00000e-6 m^4
Section area: 0.01 m^2
Point load: 1,000 N
Distributed load: 1,000 N/m

Unit conversion summary

Unit-normalization summary: 2 m; 2.00000e+11 Pa; 8.00000e-6 m^4

Warnings

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.
Material properties vary with grade, condition, temperature, manufacturing process, loading direction, heat treatment, applicable standard, and data source. Verify all properties for the actual material.
These calculations are preliminary scalar mechanics checks and do not certify design adequacy.
No shear deflection, continuous-beam behavior, multiple loads, plasticity, or dynamic response is included.

Assumptions

Small-deflection Euler-Bernoulli beam theory.
Only the selected standard single-load case is evaluated.

Calculation steps

Resolve beam casecantilever-end-load
Resolve section propertiesCustom section properties
Calculate flexural rigidity1.60000e+6 N*m^2
Calculate deflection0.00166667 m

Standard beam deflection formula

delta = C P L^3 / E I or C w L^4 / E I

Cantilever end load: PL^3/(3EI). Cantilever UDL: wL^4/(8EI). Simply supported center load: PL^3/(48EI). Simply supported UDL: 5wL^4/(384EI).

EI = 2.00000e+11 Pa x 8.00000e-6 m^4

Technical visual

Engineering interpretation

Compare calculated deflection with project-specific serviceability limits. This tool does not choose an allowable deflection ratio.

What is the beam deflection calculator?

This calculator evaluates standard closed-form elastic beam deflection cases. It reports maximum deflection, slope, flexural rigidity, section properties, and allowable-deflection comparison where entered.

How to use the beam deflection calculator

Choose the beam load case that matches the hand calculation you want to perform.
Enter geometry, loads, material values, and units from a consistent source.
Review the primary result, secondary values, formula substitution, assumptions, and warnings.
Use the related-tool links only as a workflow aid; verify every transferred value before design use.

Input explanations

Select cantilever or simply supported load case before entering point load or distributed load.
Use custom I when the section property is known from a reliable table or CAD calculation.
Rectangular, circular, hollow circular, and symmetric I-section modes calculate the second moment of area.
Deflection formulas assume Euler-Bernoulli bending and small deflection.

Notation

Formula notation
Symbol	Meaning	Unit
P	Point load	N
w	Uniform distributed load	N/m
EI	Flexural rigidity	N*m^2
delta	Maximum deflection	m
theta	Beam slope	rad

Worked examples

Cantilever end load with P = 1000 N, L = 2 m, E = 200 GPa, and I = 8e-6 m^4 gives deflection 0.0016667 m.

Cantilever UDL with w = 1000 N/m and the same beam gives deflection 0.00125 m.

Simply supported center load with the same beam gives deflection 0.000104167 m.

Cross-tool workflow

The beam deflection workflow complements bending stress, buckling, shaft alignment, and serviceability checks.

Check bending stress Review buckling

Common mistakes

Using area instead of second moment of area.
Mixing point load and distributed load formulas.
Ignoring shear deflection for deep beams or low-shear-modulus materials.
Treating a single-span formula as a continuous-beam solver.

Limitations

Only four standard single-load cases are included.
No continuous beams, multiple loads, shear deflection, large deflection, plasticity, or dynamic response.
Support and load idealizations must match the selected formula.

References

Shigley's Mechanical Engineering Design: Budynas and Nisbett, Shigley's Mechanical Engineering Design.
Roark's Formulas for Stress and Strain: Young, Budynas, and Sadegh, Roark's Formulas for Stress and Strain.
Mechanics of Materials: Common mechanics-of-materials texts covering torsion, beam deflection, column buckling, and elastic stress relationships.
Machinery's Handbook: Machinery's Handbook reference material for machine-element formulas and terminology.

How is beam deflection calculated?

The calculator applies closed-form Euler-Bernoulli formulas for the selected support and load case.

What is flexural rigidity?

Flexural rigidity is E times I and measures resistance to bending curvature.

Does the tool calculate shear deflection?

No. The formulas are Euler-Bernoulli bending formulas and do not include Timoshenko shear deflection.

What does L over 250 mean?

L/250 is a serviceability-style deflection ratio. This tool reports deflection; acceptance limits must come from the applicable context.

Does the tool support multiple loads?

No. It supports one load case at a time.

Can I enter a custom section property?

Yes. Use custom I when it is known from a reliable source.

Does this calculate bending stress?

No. Use the beam bending stress calculator for stress.

Professional support from ScholarEase Consultancy Services LLP

Professional FEA, simulation setup, solid-mechanics calculations, mechanical-design review, technical documentation, and research support are available through the connected services website. These calculators remain free to use without purchasing services.

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Engineering disclaimer

This tool is intended for educational, estimation, and preliminary engineering use. It does not certify designs or replace applicable codes, standards, validated software, physical testing, or qualified professional engineering judgment.

Need Professional Support?

ScholarTool is powered by ScholarEase Consultancy Services LLP. Professional engineering, simulation, research, and technical documentation support is available through the connected services website.

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Last reviewed: 2026-06-30

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Beam Deflection inputs

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.

Calculation mode

Display precision

Material properties

Material property mode

Material preset

Young's modulus

Young's modulus unit

Shear modulus

Shear modulus unit

Yield strength

Yield strength unit

Ultimate strength

Ultimate strength unit

Generic steel values. Use grade-, standard-, temperature-, and process-specific data for real design.

Beam geometry and loading

Beam load case

Section mode

Beam length

Beam length unit

Point load

Point load unit

Distributed load

Distributed load unit

Second moment of area

Second moment of area unit

Length output unit

Stress output unit

Result section

warningcantilever-end-load

Maximum deflection

1.66667 mm

Secondary results

Maximum slope: 0.00125 rad
Maximum slope: 0.0716197 deg
Flexural rigidity EI: 1.60000e+6 N*m^2
Second moment of area: 8.00000e-6 m^4
Section area: 0.01 m^2
Point load: 1,000 N
Distributed load: 1,000 N/m

Unit conversion summary

Unit-normalization summary: 2 m; 2.00000e+11 Pa; 8.00000e-6 m^4

Warnings

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.
Material properties vary with grade, condition, temperature, manufacturing process, loading direction, heat treatment, applicable standard, and data source. Verify all properties for the actual material.
These calculations are preliminary scalar mechanics checks and do not certify design adequacy.
No shear deflection, continuous-beam behavior, multiple loads, plasticity, or dynamic response is included.

Assumptions

Small-deflection Euler-Bernoulli beam theory.
Only the selected standard single-load case is evaluated.

Calculation steps

Resolve beam casecantilever-end-load
Resolve section propertiesCustom section properties
Calculate flexural rigidity1.60000e+6 N*m^2
Calculate deflection0.00166667 m

Standard beam deflection formula

delta = C P L^3 / E I or C w L^4 / E I

Cantilever end load: PL^3/(3EI). Cantilever UDL: wL^4/(8EI). Simply supported center load: PL^3/(48EI). Simply supported UDL: 5wL^4/(384EI).

EI = 2.00000e+11 Pa x 8.00000e-6 m^4

How to use the beam deflection calculator

Choose the beam load case that matches the hand calculation you want to perform.
Enter geometry, loads, material values, and units from a consistent source.
Review the primary result, secondary values, formula substitution, assumptions, and warnings.
Use the related-tool links only as a workflow aid; verify every transferred value before design use.

Input explanations

Select cantilever or simply supported load case before entering point load or distributed load.
Use custom I when the section property is known from a reliable table or CAD calculation.
Rectangular, circular, hollow circular, and symmetric I-section modes calculate the second moment of area.
Deflection formulas assume Euler-Bernoulli bending and small deflection.

Symbol

Meaning

Unit

Point load

Uniform distributed load

N/m

Flexural rigidity

N*m^2

delta

Maximum deflection

theta

Beam slope

rad

References

Shigley's Mechanical Engineering Design: Budynas and Nisbett, Shigley's Mechanical Engineering Design.

Roark's Formulas for Stress and Strain: Young, Budynas, and Sadegh, Roark's Formulas for Stress and Strain.

Mechanics of Materials: Common mechanics-of-materials texts covering torsion, beam deflection, column buckling, and elastic stress relationships.

Machinery's Handbook: Machinery's Handbook reference material for machine-element formulas and terminology.

Beam Deflection inputs

Calculation mode

Material properties

Beam geometry and loading

Result section

Secondary results

Unit conversion summary

Warnings

Assumptions

Calculation steps

Standard beam deflection formula

Technical visual

Engineering interpretation

What is the beam deflection calculator?

How to use the beam deflection calculator

Input explanations

Notation

Worked examples

Cross-tool workflow

Common mistakes

Limitations

References

Related tools

Professional support from ScholarEase Consultancy Services LLP

Print summary

Engineering disclaimer

Need Professional Support?

Beam Deflection inputs

Calculation mode

Material properties

Beam geometry and loading

Result section

Secondary results

Unit conversion summary

Warnings

Assumptions

Calculation steps

Standard beam deflection formula

Technical visual

Engineering interpretation

What is the beam deflection calculator?

How to use the beam deflection calculator

Input explanations

Notation

Worked examples

Cross-tool workflow

Common mistakes

Limitations

References

Related tools

Professional support from ScholarEase Consultancy Services LLP

Print summary

Engineering disclaimer

Need Professional Support?