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Conduction Calculator

Solve plane-wall, cylindrical-wall, spherical-shell, or direct-resistance conduction with unit normalization and heat-flow direction.

Conduction inputs

Result section

warningplane; solve for heat-rate

Heat-transfer rate

500 W

Secondary results

Thermal resistance: 0.02 K/W
Heat flux: 50 W/m^2
Heat-flow interpretation: Positive heat transfer follows the stated hot-to-cold or heat-added sign convention.

Unit conversion summary

Unit-normalization summary: SI base units; plane

Warnings

Thermal properties can vary with temperature, pressure, composition, grade, direction, phase, surface condition, manufacturing process, and data source. Verify all values for the actual operating condition.

Assumptions

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.

Calculation steps

Apply conduction resistance500 W

Steady one-dimensional conduction

Qdot = k A deltaT / L

Technical visual

Calculate steady 1D conduction heat rate, resistance, and heat flux for common geometries.

Engineering interpretation

Positive heat transfer follows the stated hot-to-cold or heat-added sign convention.

What is steady heat conduction and how does this Conduction Calculator work?

Conduction transfers thermal energy through matter in response to a temperature gradient. Fourier's law links heat rate to conductivity, area, geometry, thickness or radii, and temperature difference, with separate resistance forms for plane walls, cylinders, and spheres.

Conduction Calculator applies this concept to its defined inputs and workflow. This conduction calculator applies Fourier-law resistance forms for steady one-dimensional plane, cylindrical, and spherical conduction using user-entered conductivity and geometry. Its governing relationship or workflow is stated as follows: Plane-wall, cylindrical, spherical, or direct-resistance steady conduction.

The calculator evaluates Calculation mode, Temperature difference, and Display precision and returns Conduction, base-unit normalization, formula substitution, and calculation steps using the stated method. The selected units and sign or reference conventions must describe one consistent physical case. Users should interpret the output within the assumptions shown on the page and repeat the check with trusted reference values when the result affects engineering or research decisions. Thermal properties are treated as constant user-entered values.

How to use the conduction calculator

Select plane wall, cylinder, sphere, or direct thermal resistance.
Enter the signed temperature difference and geometry values in the selected unit system.
Review heat rate, resistance, and heat-flow direction before applying the result.

Input explanations

Plane-wall area is the normal area to heat flow.
Radial cylinder and sphere formulas use inner and outer radii directly, not a mean area shortcut.
Thermal conductivity must be verified for the operating temperature.

Notation

Formula notation
Symbol	Meaning	Unit
k	Thermal conductivity	W/(m K)
A	Area normal to heat flow	m2
L	Plane-wall thickness	m
r1, r2	Inner and outer radii	m
Rcond	Conduction resistance	K/W

Worked examples

For k = 0.5 W/(m K), A = 10 m2, delta T = 20 K, and L = 0.1 m, Qdot = 1000 W and R = 0.02 K/W.

For a cylindrical wall with k = 15 W/(m K), L = 1 m, r1 = 0.05 m, r2 = 0.10 m, and delta T = 50 K, R = 0.00735452 K/W.

Cross-tool workflow

The conduction calculator applies Fourier-law resistance forms for steady one-dimensional plane, cylindrical, and spherical conduction using user-entered conductivity and geometry.

Add to resistance network Use in overall U

Common mistakes

Using diameter where radius is required.
Using plane-wall area approximations for radial conduction.
Forgetting that a negative delta T reverses the heat-flow direction.

Limitations

Thermal properties are treated as constant user-entered values.
The tool does not select material, fluid, steam, refrigerant, phase-change, or fouling data automatically.
Results are preliminary engineering estimates and do not certify code compliance or safety.
Multidimensional effects, transient storage, contact details, and property variation must be evaluated separately when important.
No convection, radiation, internal heat generation, or contact resistance is included unless represented separately.
No transient storage or multidimensional edge effects are modeled.

References

Fundamentals of Heat and Mass Transfer: Incropera, DeWitt, Bergman, and Lavine, Fundamentals of Heat and Mass Transfer.
Heat and Mass Transfer: Cengel and Ghajar, Heat and Mass Transfer: Fundamentals and Applications.
Heat Transfer: Holman, Heat Transfer.
Compact Heat Exchangers: Kays and London, Compact Heat Exchangers.
SI units: BIPM, The International System of Units (SI Brochure).
NIST unit guidance: NIST Special Publication 811, Guide for the Use of the International System of Units.

What assumptions does the conduction calculator use?

It uses the stated steady or lumped formula with user-entered properties and does not infer hidden losses, standards factors, or temperature-dependent property data.

Are Celsius and Fahrenheit temperature differences handled as offsets?

No. Absolute temperature and temperature difference are separate quantities. Temperature differences use delta units without absolute-temperature offsets.

Can I use the result for final design approval?

No. Use the result for education, estimation, and preliminary review only. Critical work must be checked with standards, validated software, measured properties, and qualified engineering judgment.

Does the calculation run on a remote thermal-property API?

No. Calculations are performed locally in your browser and are not submitted to a third-party calculation API.

Engineering disclaimer

This tool is intended for educational, estimation, and preliminary engineering use. Always verify critical heat-transfer calculations with applicable standards, validated software, measured properties, and qualified professional judgment before using results in real design, manufacturing, construction, safety, or compliance decisions.

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Conduction inputs

Result section

warningplane; solve for heat-rate

Heat-transfer rate

500 W

Secondary results

Thermal resistance: 0.02 K/W
Heat flux: 50 W/m^2
Heat-flow interpretation: Positive heat transfer follows the stated hot-to-cold or heat-added sign convention.

Unit conversion summary

Unit-normalization summary: SI base units; plane

Warnings

Thermal properties can vary with temperature, pressure, composition, grade, direction, phase, surface condition, manufacturing process, and data source. Verify all values for the actual operating condition.

Assumptions

Calculations are performed locally in your browser and are not submitted to a third-party calculation API.

Calculation steps

Apply conduction resistance500 W

Steady one-dimensional conduction

Qdot = k A deltaT / L

What is steady heat conduction and how does this Conduction Calculator work?

Symbol

Meaning

Unit

Thermal conductivity

W/(m K)

Area normal to heat flow

Plane-wall thickness

r1, r2

Inner and outer radii

Rcond

Conduction resistance

K/W

Limitations

Thermal properties are treated as constant user-entered values.

The tool does not select material, fluid, steam, refrigerant, phase-change, or fouling data automatically.

Results are preliminary engineering estimates and do not certify code compliance or safety.

Multidimensional effects, transient storage, contact details, and property variation must be evaluated separately when important.

No convection, radiation, internal heat generation, or contact resistance is included unless represented separately.

No transient storage or multidimensional edge effects are modeled.

References

Fundamentals of Heat and Mass Transfer: Incropera, DeWitt, Bergman, and Lavine, Fundamentals of Heat and Mass Transfer.

Heat and Mass Transfer: Cengel and Ghajar, Heat and Mass Transfer: Fundamentals and Applications.

Heat Transfer: Holman, Heat Transfer.

Compact Heat Exchangers: Kays and London, Compact Heat Exchangers.

SI units: BIPM, The International System of Units (SI Brochure).

NIST unit guidance: NIST Special Publication 811, Guide for the Use of the International System of Units.

Engineering disclaimer

Conduction inputs

Calculation mode

Conduction inputs

Result section

Secondary results

Unit conversion summary

Warnings

Assumptions

Calculation steps

Steady one-dimensional conduction

Technical visual

Engineering interpretation

What is steady heat conduction and how does this Conduction Calculator work?

How to use the conduction calculator

Input explanations

Notation

Worked examples

Cross-tool workflow

Common mistakes

Limitations

References

Related tools

Print summary

Engineering disclaimer

Need Professional Support?

Conduction inputs

Calculation mode

Conduction inputs

Result section

Secondary results

Unit conversion summary

Warnings

Assumptions

Calculation steps

Steady one-dimensional conduction

Technical visual

Engineering interpretation

What is steady heat conduction and how does this Conduction Calculator work?

How to use the conduction calculator

Input explanations

Notation

Worked examples

Cross-tool workflow

Common mistakes

Limitations

References

Related tools

Print summary

Engineering disclaimer

Need Professional Support?