HomeCalculatorsPhysicsStatics & StrengthUniform Load Deflection Calculator
Physics calculator

Uniform Load Deflection Calculator

Midspan deflection of a simply supported span with a uniform load. δ = 5 w L⁴/(384 E I). I is an input. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
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
Midspan deflection of a simply supported span with a uniform load over the whole span.
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 6c2d3eb00242
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 — ui-ssr is query-result HTML, not a live browser session.
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 — Deflection of beams — simply supported beam with a uniform load
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — simply supported beam with a uniform load
Sources
Evidence
2 legacy golden · 2 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 2/2 invalid · Artifact integrity PASS
STALE · Build schema 1.0.0 ready · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Midspan deflectionδ = 5 w L⁴ / (384 E I)
iI comes from a section page. This page does not rebuild a rectangle, a circle, or a hollow circle. A cantilever and a concentrated load are their own pages.

How to use

1

Enter the load intensity, the span, the modulus, and the area moment

L, E, and I must be positive. w may be negative. Positive w is the positive deflection direction. w, L, E, and I share one unit system, and δ then has the unit of L.

2

Read the midspan deflection

δ = 5 w L⁴/(384 E I). The sign of w is the sign of δ.

Example calculations

Common configurations with formula and result.

ϟ

Span 2

w = 24, L = 2, E = 1, I = 1, in one consistent unit system

δ = 5 × 24 × 2⁴ / (384 × 1 × 1)
δ = 5
ϟ

Same total load as a midspan point load

w L = 48. That point load on the beam-deflection page is δ = 8.

δ_uniform / δ_point = 5/8
δ = 5 here, δ = 8 on the point-load page

Uniform Load Deflection calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A simply supported span of length L carries a uniform load w over the whole span. The midspan deflection is δ = 5 w L⁴ / (384 E I). E is the elastic modulus. I is the centroidal area moment, typed in.
What it calculates
Midspan deflection of a simply supported span with a uniform load over the whole span.
Inputs
  • w
  • L
  • E
  • I
Outputs
  • delta
  • w
  • L
  • E
  • I
Formula
δ = 5 w L⁴ / (384 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 cantilever and a concentrated load are their own pages.
Units
  • w, L, E, and I set the deflection unit. δ has the unit of length when those four are consistent.
Boundary conditions
  • missing w, L, E, or I → MISSING_REQUIRED_INPUT
  • L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
Example
w=24 L=2 E=1 I=1 → δ=5
Validation cases

3 published on this page · 4/4 tests · Production surface contract 6/6 · View evidence

  • w=24 L=2 E=1 I=1 → δ=5
  • w=-24 L=2 E=1 I=1 → δ=-5
  • L=0 → VALUE_MUST_BE_POSITIVE
Sources
  • Hibbeler, Mechanics of Materials — Deflection of beams — simply supported beam with a uniform load
    Supports: The midspan deflection is 5 w L⁴ / (384 E I) when a uniform load covers a simply supported span.
  • Gere and Goodno, Mechanics of Materials — Deflection of beams — simply supported beam with a uniform load
    Supports: Supports the page formula: δ = 5 w L⁴ / (384 E I)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the midspan deflection of a simply supported span with a uniform load over the whole span.

Supported and not supported

Supported: δ = 5 w L⁴/(384 E I). Positive w is the positive deflection direction. Aliases are intensity, omega, q, span, length, youngs, modulus, Ix, and inertia.

Not supported: a cantilever, a concentrated load, a load that covers only part of the span, a deflection away from midspan, and rebuilding I from a section. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.uniform_load_deflection · tool id: uniform-load-deflection · pin 1.0.0.

{ "w": 24, "L": 2, "E": 1, "I": 1 }

Share the link with w, L, E, and I. The result is not written into the link.

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.

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Frequently asked questions

Key distinctions behind the calculation.

Where is the deflection reported?

At midspan. A point elsewhere on the span 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 cantilever or a point load included?

No. A cantilever and a concentrated load are their own pages.