Practical tools for measured work
Shelf Sag & Deflection Calculator
Estimate center deflection of a shelf under a uniform or center point load from span, dimensions and modulus of elasticity.
Enter a value appropriate to the actual material, direction, grade and moisture condition.
Uniform mode spreads this total across the full span.
Planning estimate only. It does not approve a shelf, load, connection or support; verify material properties and structural requirements for the actual installation.
How it works
Direct answer. This estimates the elastic center deflection of a rectangular shelf simply supported at both ends under either a full-span uniform load or one center point load.
Method. The section property is I = b h^3 / 12. Uniform-load deflection is 5wL^4/(384EI); center-point deflection is PL^3/(48EI). The entered modulus E must match the real product and grain/panel direction.
Worked example. An 800 x 300 x 18 mm shelf with E = 3,000 MPa and a 200 N uniformly distributed total load has about 3.05 mm predicted center deflection.
Current-input example
The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.
- Units
- mm, N, MPa
- Idealized load
- Uniformly distributed total load
- Clear shelf span
- 800
- Shelf width
- 300
- Shelf thickness
- 18
- Modulus of elasticity
- 3000
- Total applied load
- 200
Primary result: Maximum center deflection: 3.048 mm.
Before using the result
- Measure from the datum or reference edge described by this tool, and do not mix inside, outside and centerline dimensions.
- Keep inputs in the displayed units and preserve more precision than the final cutting or purchasing tolerance requires.
- When the result is close to a limit, verify it with a test piece, field measurement, manufacturer drawing or qualified project professional.
Limitations
This small-deflection beam model excludes shelf self-weight, creep, humidity, joints, edge strips, wall anchorage, local damage and material variability. Wood Handbook data show that wood and panel properties vary with species, grade, direction and moisture. Use measured or supplier engineering data and qualified structural guidance where failure could harm people or property.
Frequently asked questions
Why does thickness matter so much?
Bending stiffness contains thickness cubed, so a modest thickness change has a large effect in this ideal model.
Can I use an average material value?
Only for rough exploration. Final work needs a value appropriate to the actual product, orientation and conditions.
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