Physics calculator

Composite Wall Calculator

Compute plane composite-wall resistance from a layer list. R_i = L_i/(k_i A), optional films 1/(h A), R = R_in + ΣR_i + R_out. Optional Q=ΔT/R. Runs locally. Not Fourier/Newton Q, not a lumped R-network, and not heatsink θ.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Plane wall R = Σ L_i/(k_i A), optional films 1/(h A), optional Q = ΔT/R, + O3 mpmath tabulated resistance.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Plane wall R = Σ L_i/(k_i A), optional films 1/(h A), optional Q = ΔT/R, + O3 mpmath tabulated resistance.
Assurance: Engineering
Declared partition coverage: PASS · 7/7 declared partitions (films, alias, layers, heat, awkward, default, invalid-domain) · Matrix
Deferred: Not a lumped R-network, not cylindrical, and not radiation.
Numerical scope: O2: plane composite wall vs a separate-module identity (≤2 ULP). Not a lumped R-network and not cylindrical. ≤2 ULP vs O3 applies only to the published tabulated composite-wall vectors. Not radiation and not a heatsink.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: Plane composite-wall resistance from a layer list. Optional films and optional heat rate Q=ΔT/R.
Scope: Plane composite wall; 1-D; shared A; R_i = L_i/(k_i A)
Verification: Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Plane wall R = Σ L_i/(k_i A), optional films 1/(h A), optional Q = ΔT/R, + O3 mpmath tabulated resistance.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-25.o2-o3
Verification revision: 2026-09-25.o2-o3 · 1/1 property · digest d63c309b6b4c
Legacy regression: 14/14 tests · Production surface contract 6/6
Trust layers: Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review: Not performed
Named expert review: Not performed
CVP suite: 3/3 golden · 7/7 CVP boundary · 7/7 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources: Incropera, F.P. and DeWitt, D.P. Fundamentals of Heat and Mass Transfer — Composite walls
ISO 80000-5 — Thermodynamics — Heat rate and temperature difference
Sources
Evidence: 1 legacy golden · 8 legacy boundary · legacy regression suite · 3/3 oracle-backed golden · 7/7 invalid · Artifact integrity PASS
Semantic contract: PASS

Full verification

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

Formulas

Core equations used by this calculator.

LayerR_i = L_i / (k_i A)

FilmR = 1 / (h A)

WallR = R_in + Σ R_i + R_out

Heat rateQ = ΔT / R

iSI K/W. Shared area A. Plane 1-D series only. This page is not Fourier/Newton Q, not a lumped R-network of already-computed R, not package heatsink θJC/θSA, not steam, and not cylindrical.

How to use

Enter at least two layers

Each solid layer needs k and L. A single slab belongs on the thermal-resistance page.

Enter shared area A

All layers use the same face area. Optional inner/outer films use h_in and h_out.

Optionally enter ΔT

If ΔT is given, Q = ΔT/R. Leave blank to report R only.

Read R (and Q)

R is in K/W. Q is in W when ΔT is given.

Example calculations

Common configurations with formula and result.

Two slabs

A=2 m², k1=1 W/(m·K), L1=0.5 m, k2=0.5 W/(m·K), L2=0.2 m

R = 0.5/(1·2) + 0.2/(0.5·2)

R = 0.45 K/W

With films

same wall, h_in=10 W/(m²·K), h_out=20 W/(m²·K)

R = 1/(10·2) + 0.45 + 1/(20·2)

R = 0.525 K/W

Composite Wall calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 14/14 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: Each layer R_i = L_i/(k_i A). Optional films R = 1/(h A). Total R = R_in + Σ R_i + R_out. Optional Q = ΔT/R.
What it calculates: Plane composite-wall resistance from a layer list. Optional films and optional heat rate Q=ΔT/R.
Inputs: k1,L1,k2,L2… | layers[]
A
h_in?
h_out?
dT?
Outputs: R
layers
Q?
dT?
mode
Formula: R_i = L_i/(k_i A); R = R_in + Σ R_i + R_out
Assumptions: Plane composite wall; 1-D; shared A; R_i = L_i/(k_i A)
Optional films R = 1/(h A); series only; Q=ΔT/R
Not Fourier/Newton Q pages
Not lumped R-network, not heatsink θ, not steam, not cylindrical
Units: SI; R in K/W; Q in W; k in W/(m·K); h in W/(m²·K)
Boundary conditions: fewer than two layers → MISSING_REQUIRED_INPUT
k, L, A, or h ≤ 0 → VALUE_MUST_BE_POSITIVE
layers[] with k1/L1, or k/L, or R1, or h → MIXED_INPUT_ENCODING
heat-transfer, heatsink, radiation, steam, series, or cylindrical as mode → INVALID_MODE
Example: k1=1 L1=0.5 k2=0.5 L2=0.2 A=2 → R=0.45 K/W
Validation cases: 3 published on this page · 14/14 tests · Production surface contract 6/6 · View evidence
k1=1 L1=0.5 k2=0.5 L2=0.2 A=2 → R=0.45
same + h_in=10 h_out=20 → R=0.525
mode=heat-transfer k1=1 L1=0.5 k2=0.5 L2=0.2 A=2 → INVALID_MODE
Sources: Incropera, F.P. and DeWitt, D.P. Fundamentals of Heat and Mass Transfer — Composite walls
Supports: Plane multilayer wall; R_i = L_i/(k_i A); film resistances 1/(h A); series combination; Q = ΔT/R
ISO 80000-5 — Thermodynamics — Heat rate and temperature difference
Supports: Q is heat rate; R relates ΔT to Q
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute plane composite-wall resistance from a layer list.

Supported and not supported

Supported — ≥2 conduction layers sharing A · optional inner/outer films · optional Q=ΔT/R · API physics.thermo.composite_wall

Not supported — Fourier/Newton Q as the primary product, lumped R-network of already-computed R, heatsink θJC/θSA, steam, cylindrical/spherical walls, radiation, transient Zth, CFD

Agent / API notes

Capability id: physics.thermo.composite_wall · tool id: composite-wall · pin 1.0.0.

{ "k1": 1, "L1": 0.5, "k2": 0.5, "L2": 0.2, "A": 2 }

Layers array: { "layers": [{ "k": 1, "L": 0.5 }, { "k": 0.5, "L": 0.2 }], "A": 2 }. Optional "h_in", "h_out", "dT". Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/composite-wall. There is no /calc/thermal.

Other calculators in this family: Boyle's Law Calculator, Charles's Law Calculator, Heat Transfer Calculator, Ideal Gas Law Calculator, Specific Heat Capacity Calculator, Stefan–Boltzmann Calculator, Thermal Resistance Calculator . Explore all Thermodynamics.

Frequently asked questions

Key distinctions behind the calculation.

Is this the heat-transfer calculator?

No. /calc/physics/heat-transfer reports Q = k A ΔT/L or Q = h A ΔT for a single slab or film. This page takes a layer list and reports R. Optional Q uses Q = ΔT/R.

Is this the thermal-resistance calculator?

No. /calc/physics/thermal-resistance computes one conduction or convection R, or composes already-known R in series/parallel. This page takes geometry layers (k, L) that share A.

Can I send a list of R values?

No. That is MIXED_INPUT_ENCODING. Use /calc/physics/thermal-resistance with mode=series.

Where does this run?

Locally in the browser by default. REST and MCP call the same thermal-engine compositeWall wrapper.