Beam Deflection Calculator
Calculate the maximum elastic deflection of a simply supported or cantilever beam under a uniform distributed load, a center/end point load, or both — with the span-to-deflection ratio checked against common L/360 and L/240 serviceability limits.
Input
Sets the elastic modulus E. Pick Custom to enter your own value.
mm⁴ — the section's second moment of area about the bending axis.
Meters. For a cantilever, this is the length from the fixed support to the free end.
kN/m, spread across the full span. Leave blank for none.
kN, applied at mid-span (simply supported) or at the free end (cantilever). Leave blank for none.
Output
| Metric | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/beam-deflection-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"beamType": "simply-supported",
"material": "structural-steel",
"elasticModulus": "",
"momentOfInertia": "8360000",
"span": "3",
"udl": "5",
"pointLoad": "10"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `beam-deflection-calculator` tool (Beam Deflection Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
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src="https://iotools.cloud/embed/beam-deflection-calculator/"
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<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
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Guides
Estimate the maximum elastic deflection of a beam under a uniform distributed load, a point load, or both — for either a simply supported beam or a cantilever. Enter the section's moment of inertia, the span, and the load, and the calculator reports the sag in millimeters and inches, plus a plain-English read on whether that sag falls within the span-to-deflection ratios most codes reference for serviceability.
How to use it
- Pick the beam type — simply supported (resisted at both ends) or cantilever (fixed at one end, free at the other).
- Choose the material, which fills in the elastic modulus E for you, or select Custom to enter your own.
- Enter the section's moment of inertia (I) and the span (L).
- Enter a distributed load (w), a point load (P), or both — leave either blank to skip it.
Results update as you type: the deflection contributed by each load, the total maximum deflection, and the span-to-deflection ratio with a verdict against common limits.
The formulas
For a simply supported beam:
- Uniform distributed load: δ = 5wL⁴ / (384EI)
- Center point load: δ = PL³ / (48EI)
For a cantilever:
- Uniform distributed load: δ = wL⁴ / (8EI)
- Point load at the free end: δ = PL³ / (3EI)
When both a distributed load and a point load are present, the two deflections are added together (superposition) — valid because both are linear-elastic responses to independent loads on the same beam.
Why the span-to-deflection ratio matters
A raw deflection number in millimeters doesn't tell you much on its own — 10 mm of sag is trivial on a 20-meter span and alarming on a 1-meter one. Structural codes instead express a limit as a fraction of the span: L/360 is a common ceiling for live-load deflection on floors and roofs (where excessive sag cracks finishes or feels bouncy), and L/240 is a common total-load limit. The calculator divides your span by the computed deflection and tells you where the result falls against those two thresholds — a starting point for a serviceability check, not a substitute for the specific limit your governing code actually requires.
Limits
This is a preliminary stiffness check, not a design tool. It assumes a prismatic (constant cross-section) beam, ignores shear deformation, and covers only the two loading cases above — it doesn't handle multiple point loads, partial-span distributed loads, or multi-span (continuous) beams. Verify results against your code's actual serviceability requirements, and check bending and shear capacity separately — a beam can pass a deflection check and still fail in bending.
Privacy
Everything runs in your browser — no dimensions or load data are sent anywhere.
Related tools
To find the reactions at each support before checking deflection, use the Beam Reaction Calculator. For a spring or fastener elsewhere in the same assembly, the Spring Rate Calculator and Bolt Torque Calculator cover those calculations.