Cantilever Moment Deflection Calculator
Free-end deflection of a cantilever with one concentrated moment. δ = M L²/(2 E I). I is an input. Runs locally.
Trust summary CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance
- Input interpretation
- Enter values to calculate.
- Result
- —
- Assurance
- Engineering
- Declared partition coverage
- PASS · 2/2 declared partitions (domain, invalid-domain) · Matrix
- Known limitations
- Physics L1 gap capability
- Core CVP does not include live graph, viewport, or pointer interaction.
- Model
- Free-end deflection of a cantilever with one concentrated moment at the free end.
- Scope
- Calculation runs locally in the browser; values are not uploaded.
- Verification
- Engine tested · Source checked · v1.0.0 · CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
- Versions
- Calculation 1.0.0 · CVP protocol 1.0.0-proposed
- CVP identity
- 0/0 property · digest b308e6edc1c9
- Legacy regression
- 4/4 tests · Production surface contract 6/6
- Trust layers
- Verification VERIFIED · Production STALE · overall VERIFIED_STALE
- CVP status
- STALE · Capability production binding: STALE · Site report: STALE · Evidence changed after the last successful production attestation. Re-attestation required.
- Reference
- O1 model · O2 expected_values · O2 numerical_behavior
- Interfaces
- PASS · UI (SSR) / REST / MCP
- Supplemental domain review
- Not performed
- Named expert review
- Not performed
- CVP suite
- 1/1 golden · 2/2 CVP boundary · 2/2 invalid · 1/1 cross-interface · 6/6 CVP contract · Manifest
- Sources
- Hibbeler, Mechanics of Materials
- Gere and Goodno, Mechanics of Materials
- Evidence
- 2 legacy golden · 2 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 2/2 invalid · Artifact integrity PASS
- Semantic contract
- PASS
Full verification
Formulas
Core equations used by this calculator.
How to use
Enter the moment, the length, the modulus, and the area moment
L, E, and I must be positive. M may be negative. Positive M is the positive deflection direction. M, L, E, and I share one unit system, and δ then has the unit of L.
Read the free-end deflection
δ = M L²/(2 E I). The sign of M is the sign of δ.
Example calculations
Common configurations with formula and result.
Length 2
M = 4, L = 2, E = 1, I = 1, in one consistent unit system
Twice the moment
M = 8, L = 2, E = 1, I = 1
Cantilever Moment Deflection calculator specification
Version 1.0.0 · Engine tested
- Engine tested 4/4 tests · Production surface contract 6/6
- Named expert review Not performed
- Calculation version 1.0.0
- Definition
- A cantilever of length L is fixed at one end and carries one concentrated moment M at the free end. The deflection at the moment is δ = M L² / (2 E I). E is the elastic modulus. I is the centroidal area moment, typed in.
- What it calculates
- Free-end deflection of a cantilever with one concentrated moment at the free end.
- Inputs
- M
- L
- E
- I
- Outputs
- delta
- M
- L
- E
- I
- Formula
δ = M L² / (2 E I).- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- I comes from a section page. This page does not rebuild a rectangle, a circle, or a hollow circle. A point load and a uniform load are their own pages.
- Units
- M, L, E, and I set the deflection unit. δ has the unit of length when those four are consistent.
- Boundary conditions
- missing M, L, E, or I → MISSING_REQUIRED_INPUT
- L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
- Example
- M=4 L=2 E=1 I=1 → δ=8
- Validation cases
3 published on this page · 4/4 tests · Production surface contract 6/6 · View evidence
- M=4 L=2 E=1 I=1 → δ=8
- M=-4 L=2 E=1 I=1 → δ=-8
- L=0 → VALUE_MUST_BE_POSITIVE
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — cantilever with a concentrated moment at the free endSupports: The free-end deflection is M L² / (2 E I) when the moment sits at the tip of a cantilever.
- Gere and Goodno, Mechanics of Materials — Deflection of beams — cantilever with a concentrated moment at the free endSupports: Supports the page formula: δ = M L² / (2 E I)
- Hibbeler, Mechanics of Materials — Deflection of beams — cantilever with a concentrated moment at the free end
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the free-end deflection of a cantilever with one concentrated moment at the free end.
Supported and not supported
Supported: δ = M L²/(2 E I). Positive M is the positive deflection direction. Aliases are moment, couple, span, length, youngs, modulus, Ix, and inertia.
Not supported: a point load, a uniform load, a simply supported span, a point between the support and the tip, and rebuilding I from a section. /calc/mechanical is not open.
Agent / API notes
Capability id: mechanical.statics.cantilever_moment_deflection · tool id: cantilever-moment-deflection · pin 1.0.0.
{ "M": 4, "L": 2, "E": 1, "I": 1 }
Share the link with M, L, E, and I. The result is not written into the link.
Related tools
Other calculators in this family: Angled Pull Calculator, Angled Pull on an Incline Calculator, Area Moment Calculator, Beam Deflection Calculator, Beam Moment Deflection Calculator, Beam Moment Maximum Deflection Calculator, Bending Stress Calculator, Cantilever Deflection Calculator . Explore all Statics & Strength.
Frequently asked questions
Key distinctions behind the calculation.
Where is the deflection reported?
At the free end, where the moment is applied. A point between the support and the tip is not this page.
Does this rebuild the area moment?
No. I is an input. A rectangle, a circle, and a hollow circle stay on their section pages.
Is a point load or a uniform load included?
No. A concentrated force and a uniform load are their own pages.