Radiation Heat Transfer Calculator
Calculate radiative heat transfer Q = εσA(T₁⁴ - T₂⁴) with common emissivity reference values
This free online radiation heat transfer calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Supports both metric (SI) and imperial units with built-in unit selection dropdowns on every input field, so you can work in whatever units your problem provides. Designed for engineering students and professionals working through coursework, design projects, or quick reference calculations.
Radiation Heat Transfer Calculator
Calculate radiative heat exchange between a surface and surroundings.
Formula
Q = ε · σ · A · (T₁⁴ − T₂⁴)
σ = 5.67 × 10⁻⁸ W/(m²·K⁴) — temperatures must be in Kelvin
0 (perfect reflector) – 1 (black body)
Emissivity Presets
Results
Heat Transfer Rate Q
17857.08 W
Surface emits heat to surroundings
Heat Flux q
17857.08 W/m²
Linearised h_rad
37.2022 W/m²K
Calculation Steps
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Radiation Heat Transfer Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Radiation Heat Transfer Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Stefan-Boltzmann Law
Q = ε·σ·A·(T₁⁴ − T₂⁴)
Variables: ε = emissivity, σ = Stefan-Boltzmann constant (5.67×10⁻⁸ W/m²·K⁴), T in Kelvin
When to Use This Calculator
- •Use the Radiation Heat Transfer Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
- •Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
- •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
- •Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
- •Use it in the field when a quick estimate is needed and a full engineering software package is not available.
About This Calculator
The Radiation Heat Transfer Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Calculate radiative heat transfer Q = εσA(T₁⁴ - T₂⁴) with common emissivity reference values All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.
The Theory Behind It
Thermal radiation is energy transfer by electromagnetic waves from any body at absolute temperature above 0 K. The Stefan-Boltzmann law gives the total radiation emitted from a black body: Q/A = σ·T⁴, where σ = 5.67 × 10⁻⁸ W/(m²·K⁴) is the Stefan-Boltzmann constant and T is absolute temperature. For a real (gray) body with emissivity ε (0 < ε < 1), the emission is Q/A = ε·σ·T⁴. Net radiation exchange between two surfaces is Q = ε·σ·A·(T₁⁴ − T₂⁴), where T₁ is the hot surface and T₂ is the cold surroundings (assuming the geometry is such that one surface sees only the other). For more complex geometries with view factors F, the formula becomes Q = σ·A₁·F_{12}·(T₁⁴ − T₂⁴) for two black surfaces. The T⁴ temperature dependence means radiation heat transfer is very sensitive to temperature — a body at 600 K radiates 16× more energy than at 300 K. This is why radiation dominates heat transfer at high temperatures (flames, furnaces, incandescent surfaces) but is often negligible at room temperature compared to conduction and convection. Typical emissivities: polished metal 0.02-0.1, oxidized metal 0.5-0.8, painted surfaces 0.85-0.95, glass 0.85, water 0.95, snow 0.85, brick 0.93, carbon black 0.95-0.98. High emissivity means good radiator (and absorber, by Kirchhoff's law); low emissivity means good reflector. Radiation shields work by placing a low-emissivity surface between two hot bodies, reducing net radiation exchange. The calculator computes net radiative heat transfer between two surfaces with specified emissivities and temperatures.
Real-World Applications
- •Furnace and boiler heat transfer: at temperatures above 500°C, radiation is the dominant mode of heat transfer. Combustion gas radiation to furnace walls accounts for most of the heat transfer in fired heaters and boilers.
- •Solar collector performance: solar radiation heats the collector surface; re-radiation from the collector back to the sky is a major loss mechanism. Low-emissivity coatings (selective surfaces) absorb solar radiation but radiate less heat.
- •Building windows and radiant heating: radiation from warm floors, walls, and ceilings to occupants is a major contributor to thermal comfort. Radiant heating systems exploit this to provide comfort at lower air temperatures.
- •Spacecraft thermal design: in space, only radiation transfers heat (no convection or conduction to surroundings). Spacecraft surfaces with specific emissivity/absorptivity ratios maintain thermal balance against solar and Earth-emitted radiation.
- •Thermal imaging and infrared thermometers: these devices detect infrared radiation emitted by objects and compute their temperature using the Stefan-Boltzmann law or more complex multi-band models. Emissivity must be known or assumed for accurate temperature measurement.
Frequently Asked Questions
What is the Stefan-Boltzmann law?
Q/A = ε·σ·T⁴, where Q/A is the radiant flux emitted per unit area, ε is emissivity (0 for perfect reflector, 1 for black body), σ = 5.67 × 10⁻⁸ W/(m²·K⁴) is the Stefan-Boltzmann constant, and T is absolute temperature in Kelvin. Temperature must be absolute (K or °R) because radiation is proportional to T⁴ and using Celsius or Fahrenheit would give wrong results.
What is emissivity?
Emissivity ε is the ratio of actual radiant emission to that of a perfect black body at the same temperature. Values range from 0 (perfect reflector, no emission) to 1 (perfect black body). Typical values: polished metals 0.02-0.10 (low emissivity, high reflectance); oxidized metals 0.5-0.8; painted surfaces 0.85-0.95; human skin 0.95-0.97; water and glass 0.95. High emissivity = good radiator = good absorber (by Kirchhoff's law).
Why is radiation proportional to T⁴?
The T⁴ dependence comes from quantum mechanics of blackbody radiation: Planck's law describes the intensity at each wavelength, and integrating over all wavelengths gives Stefan-Boltzmann's T⁴ form. Physically, the higher the temperature, the more photons are emitted AND the higher their average energy — both effects contribute to the T⁴ scaling. This makes radiation very temperature-sensitive: doubling T from 300 K to 600 K increases radiation by 16×.
When does radiation dominate over convection?
At high temperatures. For small temperature differences, radiation and convection are comparable, with radiation often slightly less. But radiation scales as T⁴ − T_∞⁴, which grows explosively at high T. Above about 400°C, radiation typically exceeds convection; above 800°C, it dominates completely. Furnaces, boilers, flames, and incandescent surfaces all have radiation as the primary heat transfer mode.
What's a radiation shield?
A low-emissivity surface placed between two hot bodies to reduce radiative heat exchange. A single shield at temperature T_s between bodies at T₁ and T₂ roughly halves the heat transfer because radiation must pass through TWO exchange surfaces instead of one. Multiple shields further reduce transfer: n shields reduce it by a factor of n+1. Silver-coated mirrors and aluminized Mylar are common shield materials. Used in spacecraft insulation, cryogenic storage, vacuum flasks (thermos bottles), and high-temperature furnace viewports.
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