# Heat Conduction Calculator (Fourier's Law, q=kΔT/d)

Compute 1-D steady-state heat conduction through a flat slab (Fourier's law): heat flux q = k·ΔT/d (W/m²), heat flow rate Q = k·A·ΔT/d (W), and thermal resistance R = d/(k·A) (K/W). k is the thermal conductivity (W/(m·K)); ΔT is the temperature difference (K; a °C difference equals a K difference, a °F difference is converted by ×5/9); d the slab thickness; A the cross-section area. ΔT may be negative (indicating reverse heat flow), but k, d and A must be positive. Thickness in m/cm/mm, area in m²/cm².

> Canonical page: https://elysiatools.com/en/tools/heat-conduction-calculator

- **Category:** Math & Numbers

- **Keywords:** heat conduction, Fourier's law, thermal conductivity, heat flux, heat flow rate, thermal resistance, steady state, 1D conduction, heat transfer, flat slab, wall, insulation, kΔT/d, thermal

## Overview

Calculate steady-state one-dimensional heat conduction through a flat slab using Fourier’s law. Enter thermal conductivity, temperature difference, thickness, and cross-sectional area to get heat flux, heat flow rate, and thermal resistance.

## Inputs

- **Thermal Conductivity k (W/(m·K))** (number): Thermal conductivity k of the slab material in W/(m·K).
- **Temperature Difference ΔT** (number): Temperature difference ΔT across the slab, in the selected Temperature Unit. May be negative to indicate the reverse heat-flow direction.
- **Temperature Unit** (select): Unit of the temperature difference. This is a difference, not an absolute temperature: Δ°C = ΔK and Δ°F ×5/9 = ΔK.
- **Thickness d** (number): Slab thickness d, in the selected Thickness Unit.
- **Thickness Unit** (select)
- **Cross-Section Area A** (number): Cross-section area A of the slab, in the selected Area Unit.
- **Area Unit** (select)
- **Decimal Places** (number)

## When to use

- Estimate heat transfer through an insulation layer, wall, or flat plate.
- Compare thermal resistance for different slab thicknesses or materials.
- Calculate heat flux and total heat flow when the temperature difference and area are known.

## How it works

- Enter thermal conductivity k in W/(m·K), temperature difference ΔT, slab thickness d, and cross-sectional area A.
- Select the temperature, thickness, and area units; temperature differences in °C equal the same difference in K, while °F differences are converted by multiplying by 5/9.
- The calculator applies q = k·ΔT/d, Q = k·A·ΔT/d, and R = d/(k·A).
- The JSON result reports heat flux in W/m², heat flow rate in W, and thermal resistance in K/W.

## Use cases

- Evaluate glass wool or other insulation layers for wall heat-loss estimates.
- Calculate heat transfer through metal plates and structural wall sections.
- Use thermal resistance to compare slab designs with different materials, areas, or thicknesses.

## Frequently asked questions

### What does this heat conduction calculator calculate?

It calculates heat flux q, heat flow rate Q, and thermal resistance R for one-dimensional steady conduction through a flat slab.

### Which inputs are required?

Thermal conductivity, temperature difference, and slab thickness are required. Cross-sectional area defaults to 1 m² if left unchanged.

### Can the temperature difference be negative?

Yes. A negative ΔT indicates heat flow in the reverse direction.

### What units are supported?

Temperature differences can be entered in K, °C, or °F; thickness in m, cm, or mm; and area in m² or cm².

### What values must be positive?

Thermal conductivity, thickness, and cross-sectional area must be positive. The temperature difference may be negative.

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