Physics calculator

Thermal Resistance Calculator

Compute lumped thermal resistance. Conduction R=L/(k A), convection R=1/(h A), series ΣR, parallel 1/R=Σ1/R_i. Optional Q=ΔT/R. Runs locally. Not Fourier/Newton Q, not heatsink θ, and not steam.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Conduction R=L/(k A), convection R=1/(h A), series and parallel networks, optional Q=ΔT/R, + O3 mpmath tabulated resistance.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Conduction R=L/(k A), convection R=1/(h A), series and parallel networks, optional Q=ΔT/R, + O3 mpmath tabulated resistance.
Assurance: Engineering
Declared partition coverage: PASS · 7/7 declared partitions (alias, convection, network, heat, awkward, default, invalid-domain) · Matrix
Deferred: Not radiation, not a heatsink, and not a composite wall.
Numerical scope: O2: lumped thermal resistance vs a separate-module identity (≤2 ULP). Not radiation and not a heatsink. ≤2 ULP vs O3 applies only to the published tabulated thermal-resistance vectors. Not radiation and not a heatsink.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: Lumped thermal resistance from geometry or series/parallel networks. Optional heat rate Q=ΔT/R.
Scope: Lumped thermal resistances; SI K/W
Verification: Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Conduction R=L/(k A), convection R=1/(h A), series and parallel networks, 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 d06114969238
Legacy regression: 16/16 tests · Production surface contract 5/5
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: 4/4 golden · 8/8 CVP boundary · 7/7 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 CVP contract · Manifest
Sources: Incropera, F.P. and DeWitt, D.P. Fundamentals of Heat and Mass Transfer — Thermal resistance networks
ISO 80000-5 — Thermodynamics — Heat rate and temperature difference
Sources
Evidence: 1 legacy golden · 9 legacy boundary · legacy regression suite · 4/4 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.

ConductionR = L / (k A)

ConvectionR = 1 / (h A)

SeriesR = Σ R_i

Parallel1/R = Σ 1/R_i

Heat rateQ = ΔT / R

iSI K/W. A composite wall is a series of conduction R. This page is not Fourier/Newton Q, not package heatsink θJC/θSA, not steam, and not radiation.

How to use

Choose conduction, convection, series, or parallel

Geometry modes compute R. Series and parallel compose existing R. This is not the heat-transfer Q page.

Enter geometry or resistances

Conduction needs k, A, L. Convection needs h and A. Networks need at least two R > 0.

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.

Slab

k=1 W/(m·K), A=2 m², L=0.5 m

R = 0.5 / (1·2)

R = 0.25 K/W

Film

h=10 W/(m²·K), A=2 m²

R = 1/(10·2)

R = 0.05 K/W

Series wall + film

R1=0.25 K/W, R2=0.05 K/W

R = 0.25 + 0.05

R = 0.30 K/W

Thermal Resistance calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 16/16 tests · Production surface contract 5/5
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: Conduction R = L/(k A). Convection R = 1/(h A). Series R = Σ R_i. Parallel 1/R = Σ 1/R_i. Optional Q = ΔT/R.
What it calculates: Lumped thermal resistance from geometry or series/parallel networks. Optional heat rate Q=ΔT/R.
Inputs: mode?
k?
h?
A?
L?
R1… | resistances[]
dT?
Outputs: R
Q?
dT?
mode
Formula: R = L/(k A) | R = 1/(h A) | R = Σ R_i | 1/R = Σ 1/R_i
Assumptions: Lumped thermal resistances; SI K/W
Series R=ΣR_i; parallel 1/R=Σ1/R_i; Q=ΔT/R
Not Fourier/Newton Q pages
Not heatsink θ, not steam, not radiation
Units: SI; R in K/W; Q in W; k in W/(m·K); h in W/(m²·K)
Boundary conditions: missing k, A, L, h, or a second R when required → MISSING_REQUIRED_INPUT
k, A, L, h, or R ≤ 0 → VALUE_MUST_BE_POSITIVE
conduction with h, or convection with k/L, or resistances[] with R1… → MIXED_INPUT_ENCODING
heat-transfer, heatsink, radiation, or steam as mode → INVALID_MODE
Example: k=1 A=2 L=0.5 → R=0.25 K/W
Validation cases: 3 published on this page · 16/16 tests · Production surface contract 5/5 · View evidence
k=1 A=2 L=0.5 → R=0.25
mode=series R1=0.25 R2=0.05 → R=0.30
mode=heat-transfer k=1 A=2 L=0.5 → INVALID_MODE
Sources: Incropera, F.P. and DeWitt, D.P. Fundamentals of Heat and Mass Transfer — Thermal resistance networks
Supports: R_cond = L/(k A); R_conv = 1/(h A); series and parallel 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 lumped thermal resistance and optional heat rate.

Supported and not supported

Supported — conduction R, convection R, series, parallel · optional Q=ΔT/R · API physics.thermo.thermal_resistance

Not supported — Fourier/Newton Q as the primary product, heatsink θJC/θSA, steam, radiation, transient Zth, CFD

Agent / API notes

Capability id: physics.thermo.thermal_resistance · tool id: thermal-resistance · pin 1.0.0.

{ "mode": "conduction", "k": 1, "A": 2, "L": 0.5 }

Series: { "mode": "series", "R1": 0.25, "R2": 0.05 }. Optional "dT": 10 adds Q. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

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

Other calculators in this family: Boyle's Law Calculator, Charles's Law Calculator, Composite Wall Calculator, Heat Transfer Calculator, Ideal Gas Law Calculator, Specific Heat Capacity Calculator, Stefan–Boltzmann 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 reports R and composes series/parallel networks. Optional Q uses Q = ΔT/R.

Is this heatsink θJA / θSA?

No. Package junction-to-ambient and heatsink stack are /calc/electric/heatsink-rth. Do not mix θJC with a wall network on this page.

How do I model a composite wall?

Use /calc/physics/composite-wall with a layer list (k, L) that share A. This page is for one conduction/convection R or for composing already-known R in series/parallel.

Where does this run?

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