HomeCalculatorsPhysicsStatics & StrengthYoung's Modulus Calculator
Physics calculator

Young's Modulus Calculator

Y = (F/A) / (ΔL/L₀). Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · 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 (youngs, invalid-domain) · Matrix
Known limitations
  • Linear elastic isotropic
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Y = (F/A) / (ΔL/L₀)
Scope
Documented on page
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · 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
1/1 property · digest 4a5b888fc08c
Legacy regression
3/3 tests · Production surface contract 6/6
Trust layers
Verification VERIFIED · Production CURRENT · overall VERIFIED
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 · 1/1 CVP boundary · 1/1 invalid · 1/1 property · 1/1 cross-interface · 4/4 CVP contract · Manifest
Sources
  • Intro physics / NIST units — standard relations
  • Materials science / linear elasticity texts — Young's modulus
Sources
Evidence
1 legacy golden · 1 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 1/1 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

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

Formulas

Core equations used by this calculator.

PrimaryY = (F/A) / (dL/L0)
iSI units unless noted.

How to use

1

Enter known values

Leave the unknown for the API mode to solve.

2

Confirm units

Use SI units unless noted.

3

Read the result

Y = (F/A) / (ΔL/L₀)

Example calculations

Common configurations with formula and result.

ϟ

Example

validation

—
F=1000 N, A=1e-4 m², L0=1 m, ΔL=1e-4 m → Y=1e11 Pa

Young's Modulus calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Y = (F/A) / (ΔL/L₀)
What it calculates
Y = (F/A) / (ΔL/L₀)
Inputs
  • see form
Outputs
  • see API
Formula
see formulas
Assumptions
  • Documented on page
Units
  • SI
Boundary conditions
  • coded hard errors
Example
F=1000 N, A=1e-4 m², L0=1 m, ΔL=1e-4 m → Y=1e11 Pa
Validation cases

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

  • see suite → see suite
Sources
  • Intro physics / NIST units — standard relations
    Supports: engine formulas
  • Materials science / linear elasticity texts — Young's modulus
    Supports: Y = (F/A) / (ΔL/L0)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Y = (F/A) / (ΔL/L₀)

Supported and not supported

Supported — API physics.materials.youngs

Not supported — Plastic yield, anisotropic materials

Agent / API notes

Capability id: physics.materials.youngs · tool id: youngs · pin 1.0.0.

Other calculators in this family: Angled Pull Calculator, Angled Pull on an Incline Calculator, Area Moment Calculator, Beam Deflection Calculator, Bending Stress Calculator, Cantilever Deflection Calculator, Circular Plastic Modulus Calculator, Circular Section Calculator . Explore all Statics & Strength.

→ Angled Pull Calculator Pull at an angle above the horizontal that puts a block on a level surface at impending slip. The normal is W − P sinα. Runs locally. › → Angled Pull on an Incline Calculator The pull at an angle above the horizontal that puts a block on an incline at impending slip. α = 0 is horizontal. α = θ is parallel to the plane. Runs locally. › → Area Moment Calculator Second moment of composite plane areas about the composite centroid. Supply each part's centroidal Ix and Iy. Runs locally. Not a section modulus and not a beam calculator. › → Beam Deflection Calculator Midspan deflection of a simply supported span with one concentrated load. δ = P L³/(48 E I). I is an input. Runs locally. › → Bending Stress Calculator Elastic bending stress from a moment and a section modulus. S can also be formed from Ix and c. Runs locally. › → Cantilever Deflection Calculator Free-end deflection of a cantilever with one concentrated load at the tip. δ = P L³/(3 E I). I is an input. Runs locally. › → Circular Plastic Modulus Calculator Plastic modulus and shape factor of a solid circle. The elastic modulus comes from the circular-section engine. Runs locally. › → Circular Section Calculator Centroidal Ix, Iy, and elastic section moduli of a solid circle from its radius. Runs locally. ›
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Frequently asked questions

Key distinctions behind the calculation.

What does the API reject?

Hard validation errors such as missing inputs or out-of-range values.