Thermal Radiation Calculator
Fast, accurate and free online promieniowania cieplnego calculator tool running directly in your browser.
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Enter radiation data
Enter the parameters of emissivity, surface area and body and ambient temperatures, and then click the "Calculate" button.
Physical legend:
- ε (emissivity): The ability to emit energy (from 0 to 1). A blackbody has an emissivity of 1.
- A (area): Total radiating surface area in $m^2$.
- T (temperature): Temperature of the emitting body (automatically converted to Kelvin).
- Ts (temperatura otoczenia): Temperature of the surrounding area absorbing radiation.
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Related tools
Other tools you may find usefulThermal Radiation Calculator - Stefan Boltzmann in Practice
This tool calculates the power of radiated heat between two surfaces based on the Stefan Boltzmann equation. You select the calculation mode and indicate the unknown. Typical input fields are supported: emissivityepsilon, areaA, temperaturesT1 i T2in Kelvin and optionally aspect ratioF12. The result is the radiation powerQdotor another desired quantity. The calculator also provides a variant with a linear approximation of the temperature difference for small ΔT, which makes it easier to combine with convection.
Formulas and physical model
Stefan Boltzmann equation - net flux between two surfaces
Qdot = epsilon_eff · sigma · A · (T1^4 - T2^4)
wheresigma = 5.670374419 × 10⁻⁸ W m⁻² · K⁻⁴is the Stefan Boltzmann constant,epsilon_effis the effective emissivity of the system taking into account the properties and mutual visibility of surfaces,Ais the surface area,T1 i T2are absolute temperatures.
Effective emissivity taking into account the aspect ratio
epsilon_eff = 1 / ( (1/epsilon1) + (1/epsilon2 - 1) · (1/F12) )
In the large environment - small object system, the typical assumption isepsilon_eff ≈ epsilon1 i F12 ≈ 1. In the case of two parallel plates separated by more than a few thicknesses of surface layers, one can assumeF12 ≈ 1.
Linear approximation for small temperature differences
Qdot ≈ h_rad · A · (T1 - T2)
h_rad = 4 · epsilon_eff · sigma · T_m^3, T_m = (T1 + T2)/2
Useful for summing radiation with convection:Qdot_total = (h_conv + h_rad) · A · (T1 - T2).
Calculator modes - transformations
Qdot mode- unknown power:
Qdot = epsilon_eff · sigma · A · (T1^4 - T2^4)
T1 mode- searched body temperature 1:
T1 = ( Qdot/(epsilon_eff · sigma ·A) + T2^4 )^(1/4)
A mode- required area:
A = Qdot / (epsilon_eff · sigma · (T1^4 - T2^4))
Epsilon mode- required emissivity:
epsilon_eff = Qdot / ( sigma · A · (T1^4 - T2^4) )
Assumptions and limitations
- Radiation in the far infrared band - no flames and sources of high-energy photons.
- Gray surfaces - emissivity independent of the wavelength in the analyzed range.
- No translucency - most metals, ceramics and technical coatings meet this in IR.
- Uniform surface temperatures and constant properties in steady-state analysis.
Form fields and units
- mode- unknown selection: Qdot, T1, A, epsilon.
- epsilonorepsilon1, epsilon2- surface emissivity [without dimension].
- F12- field of view aspect ratio [0..1].
- A- exchange area [m², cm²].
- T1, T2- absolute temperatures [K]. For data in °C, use the conversion T[K] = t[°C] + 273.15.
- precision- number of decimal places in the results presentation.
| Size | Symbol | Units | Default |
|---|---|---|---|
| Radiation power | Qdot | W, kW | W |
| Emissivity | epsilon, epsilon_eff | - | - |
| Area | A | m², cm² | m² |
| Body temperature 1 | T1 | K | K |
| Body temperature 2 | T2 | K | K |
| Stefan Boltzmann constant | sigma | W m⁻² K⁻⁴ | 5.670374419e-8 |
| Shape factor | F12 | - | 1 |
Emissivity tables - guide values
| Material or surface | epsilon [-] | Notes |
|---|---|---|
| Black body | 1.00 | Limit value |
| Matt black paint | 0.90 - 0.98 | Increases IR emission and absorption |
| Oxidized steel | 0.70 - 0.85 | Strong dependence on surface condition |
| Polished aluminum | 0.03 - 0.10 | Low emissivity, good radiation barrier |
| Polished copper | 0.02 - 0.05 | Very low emission |
| Glass | 0.80 - 0.95 | In the far IR behaves like a gray body |
| Concrete | 0.85 - 0.95 | Rough surface, similar to diffusion |
| Technical ceramics | 0.80 - 0.95 | Stable at high temperatures |
| Aluminum coating with oxidation | 0.10 - 0.30 | Increase in emissivity after oxidation |
Calculation examples
Example 1 - radiation power of a small object to the surroundings
- epsilon = 0.90
- A = 0.25 m²
- T1 = 373.15 K (100°C)
- T2 = 293.15 K (20°C)
Qdot = 0.90 · sigma · 0.25 · (373.15^4 - 293.15^4) ≈ 0.90 · 5.67e-8 · 0.25 · 1.63e10 ≈ 208 W. An object with an area of 0.25 m² at 100°C emits approximately 200 W solely through radiation.
Example 2 - required radiant heat sink area
- Qdot = 500 W
- epsilon = 0.95
- T1 = 333.15 K (60°C)
- T2 = 293.15 K (20°C)
A = Qdot / [epsilon · sigma · (T1^4 - T2^4)]. The difference of fourth powers ≈ 1.20e10. A ≈ 500 / (0.95 · 5.67e-8 · 1.20e10) ≈ 0.77 m². The matte black coating significantly reduces the required area compared to polished aluminum.
Example 3 - selection of emissivity to limit losses
- Qdot max = 150 W
- A = 0.4 m²
- T1 = 353.15 K (80°C)
- T2 = 293.15 K (20°C)
epsilon_eff = Qdot / [sigma · A · (T1^4 - T2^4)] ≈ 150 / (5.67e-8 · 0.4 · 5.85e9) ≈ 0.11. A low-emissivity surface is sufficient, e.g. polished aluminum with a clean protective coating.
Example 4 - h_rad and sum with convection
- epsilon = 0.80
- T1 = 350 K
- T2 = 300 K
- h_conv = 8 W·m⁻²·K⁻¹
- A = 0.6 m²
T_m = 325 K. h_rad = 4 · 0.80 · 5.67e-8 · 325^3 ≈ 4.9 W·m⁻²·K⁻¹. h_total ≈ 12.9 W·m⁻²·K⁻¹. Qdot_total ≈ 12.9 · 0.6 · 50 ≈ 387 W. At moderate temperatures, the radiative contribution is comparable to the convective contribution.
Engineering scenarios
| Task | Data | Assumptions | Result |
|---|---|---|---|
| Estimation of losses at night from the roof | epsilon, A, T1, T2 of the effective sky | F12 ≈ 1, no fog | Qdot radiative in W |
| Dryer design | T1 shelves, T2 air, shell epsilon | Summing with convection | h_rad, Qdot_total |
| Satellite radiator | Qdot, T1 permissible, T2 space | F12 ≈ 1, no convection | A required |
| Thermal shield | Qdot max, A, T1, T2 | Low emissivity | epsilon_eff required |
How to use the
- calculator effectively Determine the unknown in themodefield: Qdot, T1, A, or epsilon.
- Enter the surface properties:epsilonorepsilon1 i epsilon2, as well asF12if it is not equal to 1.
- Enter the temperaturesT1 i T2in Kelvin. When you have data in °C, convert by T = t + 273.15.
- Enter the area of A. Take care of the appropriate effective exchange surface.
- Setprecisionaccording to the desired presentation accuracy.
- Read the result and, if necessary, additional auxiliary quantities such ash_rad.
Common pitfalls and tips
- Use temperatures in kelvins. This is the condition for correct raising to the fourth power.
- Emissivity depends on the surface condition. Polishing and pure metallic coatings strongly reduce epsilon.
- High temperatures enhance radiation. A 10 percent increase in T increases T^4 by over 46 percent.
- For small ΔT, useh_radand sum withh_convin an additive manner.
- If objects cannot fully see each other, setF12less than 1, which will reduce the result.
- Matte black coatings facilitate heat emission. Low-emissivity screens reduce losses.
FAQ
Can I calculate in °C
Not directly. The equation requires kelvins. First convert T = t + 273.15, and only then substitute to the fourth power.
How to estimate F12
For a small object inside a large environment, F12 ≈ 1 is taken. For two large parallel plates, consider F12 close to 1. For cylinders, cavities, and screens, geometric formulas or a shape table are needed.
Is glass transparent to IR
To far IR, glass is usually not transparent. In thermal radiation calculations, it is usually treated as a gray body with high emissivity.
How to reduce radiation losses
Use low-emissivity surfaces, multi-layer screens, polished metals, and lower T1 or limit A-field.
Can I sum convection and radiation
Yes. Use linear approximation and sum h_conv with h_rad. For accurate calculations, count the Qdot separately and add the components.
Summary
Thermal radiation calculator provides fast and reliable results for energy exchange between surfaces. By supporting effective emissivity, aspect ratio and linear variant with h_rad it allows you to design heat sinks, thermal screens and radiation insulation. Combined with the convection and conductivity calculator, it creates a coherent set for heat balances in engineering, energy, electronics and architecture. While maintaining correct units and realistic assumptions, the results provide a solid basis for design and teaching decisions.