Calculator Inputs
Example Data Table
| Scenario | Mode | Temperatures | Spacing | k (W/m·K) | Expected |∇T| |
|---|---|---|---|---|---|
| Wall conduction | Linear 1D | T₁=80°C, T₂=20°C | L=0.05 m | 1.0 | 1200 °C/m |
| Plate with x‑gradient | Finite difference | T(x+Δx)=75°C, T(x−Δx)=65°C | Δx=0.05 m | 205 | 100 °C/m |
| 3D test point | Finite difference | x: 75/65, y: 70/60, z: 72/62 | Δ=0.05/0.02/0.02 m | 16 | ≈ 269 °C/m |
Values are illustrative; your material and geometry may differ.
Formula Used
Temperature gradient describes how temperature changes with distance. In one dimension, the average gradient across a thickness is:
For local gradients using a central finite difference:
If enabled, Fourier’s law estimates heat flux: q = −k ∇T (W/m²).
How to Use This Calculator
- Select a calculation mode: linear 1D or finite difference.
- Choose input and output temperature units and a length unit.
- Enter temperatures and spacing steps. Use positive distances.
- Enable y and z only when you have those measurements.
- Optionally enable Fourier heat flux and provide k.
- Press Submit to view results above the form.
- Use CSV or PDF buttons to download your latest results.
FAQs
1) What is a temperature gradient?
It is the rate of temperature change with distance. In heat transfer, it helps estimate direction and intensity of conduction through a material or region.
2) When should I use linear 1D mode?
Use it when temperature changes mostly across one thickness, like a wall, slab, or insulation layer. It computes an average gradient between two surfaces.
3) What does finite difference mode represent?
It estimates local gradients using measurements on both sides of a point. Central differences reduce bias compared with one‑sided differences when spacing is symmetric.
4) Why do °F gradients differ from °C gradients?
A temperature difference of 1°F equals 5/9 K. Therefore, a gradient in °F per length is larger by 9/5 compared with K or °C per the same length.
5) What is the meaning of the gradient sign?
The sign indicates direction along the axis. Positive dT/dx means temperature increases with x. With positive conductivity, heat flux points opposite the gradient.
6) What is Fourier heat flux and its units?
Fourier’s law estimates conductive heat flux: q = −k∇T. With k in W/m·K and gradient in K/m, the result is W/m².
7) Can I use centimeters or inches for spacing?
Yes. Enter the distance in your chosen unit. The calculator converts internally to meters, then returns gradients per your selected length unit.
8) How accurate are these results?
Accuracy depends on your temperature measurements and spacing. Linear mode gives an average. Finite differences approximate local derivatives and improve with smaller, well‑measured steps.