Fourier’s Law Thermal Conduction, Heat Flux & U-Value Calculator

Compute conductive heat loss Q = k·A·ΔT / L and metric R-value.

Conductive Heat Transfer Rate (Q)
140.8 W
Heat Flux Density (q = Q/A) 5.87 W/m²
Thermal Resistance (R_SI) 3.75 m²·K/W
US Imperial Equivalent R-Value 21.29 ft²·°F·h/BTU
Inputs
W/(m·K)
Material thermal conductivity k in W/(m·K) (0.04 mineral wool, 1.7 concrete).
m²
Wall or slab cross-sectional area in square meters.
m
Material thickness in meters.
°C
Inside-to-outside temperature difference (ΔT) in °C or K.
Results & Graph
Conductive Heat Transfer Rate (Q)
140.8 W
Heat Flux Density (q = Q/A)
5.87 W/m²
Thermal Resistance (R_SI)
3.75 m²·K/W
US Imperial Equivalent R-Value
21.29 ft²·°F·h/BTU

Conductive Heat Transfer Rate (Q)

Graph 1 • Thermal Conductivity Wmk Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 W 114.0 W 228.1 W 50%: 70.4 W 70.4 50% 75%: 105.6 W 105.6 75% 100%: 140.8 W 140.8 100% 125%: 176 W 176 125% 150%: 211.2 W 211.2 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Conductive Heat Transfer Rate (Q) 140.8 W Heat Flux Density (q = Q/A) 5.87 W/m² Thermal Resistance (R_SI) 3.75 m²·K/W US Imperial Equivalent R-Value 21.29 ft²·°F·h/BTU
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Conductive Heat Transfer Rate (Q)140.8 WHeat Flux Density (q = Q/A)5.87 W/m²Thermal Resistance (R_SI)3.75 m²·K/WUS Imperial Equivalent R-Value21.29 ft²·°F·h/BTU
Summary: Across 24 m² (L=0.15 m, k=0.04 W/m·K) with ΔT=22°C, thermal resistance is R-3.75 m²·K/W and steady heat transfer is 140.8 W.
Summary: Across 24 m² (L=0.15 m, k=0.04 W/m·K) with ΔT=22°C, thermal resistance is R-3.75 m²·K/W and steady heat transfer is 140.8 W.
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Formula & Mathematical Methodology: Fourier Heat Conduction Physics & Engineering Equation

Qwatts = (k × Area × ΔT) / Thicknessm
RSI = Thicknessm / k
Q_watts = (k × Area × ΔT) / Thickness_m; R_SI = Thickness_m / k
  • thermalConductivityWmk: Thermal Conductivity Wmk (W/(m·K))
  • surfaceAreaM2: Surface Area M2 (m²)
  • thicknessMeters: Thickness Meters (m)
  • temperatureDeltaC: Temperature Delta C (°C)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Fourier Heat Conduction

Compute conductive heat loss Q = k·A·ΔT / L and metric R-value.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: Q_watts = (k × Area × ΔT) / Thickness_m; R_SI = Thickness_m / k.
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Fourier Heat Conduction via Q_watts = (k × Area × ΔT) / Thickness_m; R_SI = Thickness_m / k.

Frequently Asked Questions

What equation powers the Fourier’s Law Thermal Conduction, Heat Flux & U-Value Calculator?

It evaluates Q_watts = (k × Area × ΔT) / Thickness_m; R_SI = Thickness_m / k using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Thermodynamics & Heat Transfer

Fourier’s Law Thermal Conduction, Heat Flux & U-Value Calculator: inputs, method, and how to read the result

Compute conductive heat loss Q = k·A·ΔT / L and metric R-value.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Thermal Conductivity Wmk: Material thermal conductivity k in W/(m·K) (0.04 mineral wool, 1.7 concrete).
  • Surface Area M2: Wall or slab cross-sectional area in square meters.
  • Thickness Meters: Material thickness in meters.
  • Temperature Delta C: Inside-to-outside temperature difference (ΔT) in °C or K.

What the calculation includes

With the default values shown, Conductive Heat Transfer Rate (Q) is 140.8 W. The calculation follows Fourier Heat Conduction Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Thermal Conductivity Wmk from 0.04 W/(m·K) to 0.05 W/(m·K) changes Conductive Heat Transfer Rate (Q) from 140.8 W to 176 W. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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