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Contents
  1. 1Definition and the black body
  2. 2Grey-body radiation
  3. 3Typical values for surfaces
  4. 4Gases, smoke and flames
  5. 5Use in design and regulation
  6. 6Limits and common misconceptions
  7. 7See also
  8. 8Notes
  9. 9References

Emissivity is a dimensionless number between 0 and 1 that describes how well a surface, a gas or a flame emits thermal radiation. It is the ratio of the radiant energy emitted by a body to the energy emitted by a perfect radiator, a black body, at the same temperature.[1] A black body has an emissivity of 1 and a reflectivity of zero.[2] Polished silver has an emissivity of 0.02, while rough concrete reaches 0.91 and human skin 0.97 or more.[3]

In fire safety engineering, emissivity sets how much heat a hot smoke layer, a flame or a heated wall radiates towards people, fuel and structure. Together with the temperature and the geometry, it determines the radiant heat flux on a target.[3] Hot gases and flames become better emitters as they contain more soot and as they grow thicker, so large sooty fires radiate almost like black bodies.[4][5] For this reason, design guidance often sets the emissivity of flames and fire gases to 1.0 as a conservative choice.[6] In New Zealand, the second edition of Verification Method C/VM2 (2025) prescribes that value for its radiation calculations.[7] Emissivity is also an input for fire models that calculate the heating of walls and other solid surfaces.[8]

Definition and the black body

All materials with a temperature above absolute zero (0 K) emit radiation. Introduction to Fire Safety Engineering defines emissivity as the ratio between the radiation of the real material and that of a black body.[3] A black body is an idealised object that absorbs all electromagnetic radiation falling on it and reflects nothing. At a given temperature it emits the largest possible amount of energy per unit area at every wavelength.[3] Tien, Lee and Stretton describe the same ideal surface as a perfect emitter and absorber. They note that it is best approximated by a small opening into an enclosed cavity.[9]

Emissivity has no unit. A value of 1 describes a perfect radiator, and real materials lie between 0 and 1.[1] The black body serves as the reference because its emission depends on temperature alone. The Stefan-Boltzmann law gives that emission, and emissivity scales it down to the value for a real surface.[9][3] As a hot surface gets hotter, the peak of its emission shifts towards shorter wavelengths. At about 550 °C enough radiation falls in the visible range to be seen as a red glow.[9][3]

Emission and absorption are closely linked. Kirchhoff's law states that, at each wavelength, a body in thermal equilibrium absorbs the same fraction of incoming radiation as it emits compared with a black body.[10] For total values over all wavelengths, absorptivity equals emissivity only for a so-called grey body. The incident radiation then has the same spectral distribution as black-body radiation.[10] A good emitter is therefore also a good absorber. For an opaque surface, the absorbed and the reflected fractions add up to one, so a shiny, poorly emitting surface reflects much of the radiation that reaches it.[9]

Black body, painted surface and polished metal at one temperature: emission arrows shrink with emissivity; the metal reflects most radiation.
Three surfaces at the same temperature. A black body (ε = 1) absorbs all incoming radiation and emits the most; a grey surface emits a fraction ε; a polished metal reflects most incoming radiation and emits little. Based on Van Rossum (2027), §5.4, and Tien et al. (2002), pp. 1-74–1-75.

Grey-body radiation

Strictly, the emissivity of a material depends on the wavelength. The total radiant flux would then follow from adding up the emission over all wavelengths.[3] This approach is not practical, because the wavelength-dependent emissivity is difficult to determine. In practice one emissivity per material is used, which treats the surface as a grey radiator.[3]

The SFPE Handbook explains why this works. Real surfaces have such complex radiation properties that measured data are missing for many common materials, and the uncertainties in the data and the calculation usually reduce the result to one overall flux.[11] The grey diffuse surface model gives reasonably accurate results in many practical situations.[11] It also assumes that the radiation leaving a surface does not depend on the direction of the incoming radiation, which greatly reduces the computing effort.[11]

For a grey radiator, the emitted heat flux per unit area is the black-body emission multiplied by the emissivity. If the emissivity is set to 1, the relation describes a black body.[3] Introduction to Fire Safety Engineering uses this relation to find the source radiation of a hot material or a hot gas:[3]

E=εσT4

Symbol Description Unit
E emissive power of the radiating surface (radiant heat flux leaving it) W/m²
ε emissivity of the material or gas –
σ Stefan-Boltzmann constant, 5.67 × 10−8 W/(m²·K4)
T absolute temperature of the radiating surface K

The temperature must be in kelvin, and it enters to the fourth power. Radiation therefore becomes the dominant mode of heat transfer at higher temperatures, roughly from 400 °C, while convection dominates below that.[3] The relation describes the radiation leaving the source. The flux that reaches a target also depends on the view factor, the fraction of the source radiation that falls on the target.[3] When the target is not much colder than the source, the book replaces the fourth power of the source temperature by the difference between the fourth powers of the hot and the cold temperature.[3]

A worked example shows the effect of emissivity. The method of Babrauskas for predicting flashover, as described by Walton and Thomas, uses a gas temperature of 873 K (about 600 °C) and an emissivity of the hot gas of 0.5.[12] With these values the gas emits 0.5 × 5.67 × 10−8 × 8734 W/m², which is about 16.5 kW/m². If the same gas were a black body, the emission would double to about 33 kW/m². A thin layer of smoke from a wood fire, with an emissivity of about 0.33, would emit about 10.9 kW/m² at the same temperature.[13] Emissivity thus scales the emitted flux in direct proportion, while a change in temperature acts to the fourth power.

Emitted heat flux against temperature for emissivities 0.33, 0.5 and 1; at 600 °C about 11, 16.5 and 33 kW/m².
Emitted heat flux E = εσT⁴ against gas temperature for three emissivities. Based on Van Rossum (2027), §5.4, Walton and Thomas (2002), p. 3-184, and Tien et al. (2002), p. 1-85.

The relation applies to surfaces and to gas volumes that can be treated as uniform in temperature. It assumes one emissivity for all wavelengths and directions.[11] For a smoke layer or a flame the emissivity is not a material constant but depends on the thickness and the soot content of the gas, as described below.[14]

Typical values for surfaces

Most building materials have a high emissivity. Introduction to Fire Safety Engineering lists 0.88 for asphalt, 0.9 for stone and for paint (including white paint), 0.91 for rough concrete, 0.92 for limestone and 0.89 for rough gypsum.[3] Concrete exposed to fire has a lower value of 0.7 in the same table. Metals behave very differently depending on their surface. Anodised aluminium has an emissivity of 0.9, polished aluminium 0.04 and polished silver only 0.02.[3] Human skin is close to a black body, with values from 0.97 to 0.999.[3]

Bar chart of emissivity: polished metals 0.02 to 0.04, concrete in fire 0.7, building materials 0.88 to 0.92, human skin 0.97 to 0.999.
Emissivity of common materials. Most building materials lie close to 0.9; polished metals lie close to zero. Based on Van Rossum (2027), §5.4.

Other sources give similar values. The SFPE Handbook uses 0.9 for wood and 0.94 for concrete walls painted with zinc white oil paint in a worked example.[13] Water has an emissivity of 0.95 to 0.963 between 298 K and 373 K.[15] In tests for the World Trade Center investigation, the true emissivities of clean steel and of Alumel thermocouple wire were taken as 0.8 and 0.2. Once the surfaces were covered with soot, their emission came closer to that of a black body.[16] For electrical cables, typically cited surface emissivities range from 0.85 to 0.95.[17]

Because most surfaces in buildings have high emissivities, the technical guide of the zone model CFAST notes that typical surface emissivities vary only over a small range.[18] The MAGIC zone model fixes the wall emissivity at 0.9.[19] In deriving burning properties of office workstation materials for the World Trade Center investigation, all surface emissivities were set at 0.95.[20] Heat flux gauges are made to behave almost like black bodies. They are usually painted black, which gives a surface emissivity of about 0.95 in the infrared.[21]

Gases, smoke and flames

Not every gas takes part in radiation. Gases with symmetric molecules, such as nitrogen, oxygen and hydrogen, hardly emit or absorb thermal radiation.[10] Water vapour and carbon dioxide, which are formed in combustion, absorb and emit strongly between 1 and 100 µm.[22] The emissivity of these gases depends on their temperature, their partial pressure and the length of the radiating path. Engineers traditionally read the total emissivity from charts based on the work of Hottel.[23] The emissivities of a gas mixture cannot simply be added, because the absorption bands of the gases overlap.[24]

Soot usually contributes more to the radiation of a fire than the gases do.[22] Soot particles are very small, between 50 and 1000 Å, and their volume fraction in a flame is generally about one part per million.[25][14] Unlike the gases, soot radiates over a continuous spectrum. The emissivity of a smoke-filled gas therefore depends on the soot volume fraction, the absorption coefficient of the soot, the temperature, the path length and the partial pressures of the gases.[14] The SFPE Handbook tabulates effective absorption coefficients for soot. These range from 0.8 m−1 for wood and 0.5 m−1 for Plexiglas to 13.32 m−1 for propane.[14]

For a uniform layer of gas, the emissivity rises with the product of the absorption coefficient and the thickness of the layer. It equals one minus the exponential of minus that product.[24] A thin layer is optically thin and emits weakly, while a thick layer is optically thick and approaches a black body.[24]

The International Fire Engineering Guidelines use this relation for radiation from a hot smoke layer. They recommend an absorption coefficient of 0.8 m−1 for solid wood fuels unless a better estimate is available.[26] A 0.5 m smoke layer from a wood fire then has an emissivity of about 0.33.[13] Calculated with the same coefficient, the emissivity reaches about 0.80 for a 2 m layer and about 0.96 for a 4 m layer.

Three rising curves of smoke layer emissivity against layer thickness from 0 to 6 m, all approaching 1; the wood curve gives 0.33 at 0.5 m.
Emissivity of a uniform smoke layer against its thickness, ε = 1 − exp(−κS), for the soot absorption coefficients of Plexiglas, wood and polystyrene flames. Based on Tien et al. (2002), pp. 1-78 and 1-82, and National Research Council of Canada et al. (2005), p. 2.4-10.

Flame radiation follows the same pattern. Radiation is the dominant mode of heat transfer in flames larger than about 0.2 m, while convection matters more in smaller flames.[22] At high soot concentrations, the emissivity of a flame approaches unity and its luminosity no longer depends on the amount of soot.[4]

Sooty fires are better emitters than clean-burning fires. Fires of flammable liquids also produce taller flames, so an observer near such a fire feels more heat than near an ordinary combustibles fire of comparable size.[1] Small flames in bench-scale tests are optically thin and have a low emissivity.[27] In large-scale compartment experiments for the World Trade Center investigation, the measured heat fluxes showed that the emissivity of the upper layer was nearly 1.[28]

Use in design and regulation

Introduction to Fire Safety Engineering uses emissivity in two common calculations. The first estimates the radiation from a smoke layer to a person below it. In the worked example, a layer at 400 °C with an emissivity of 0.9 delivers 8.33 kW/m² to the head of a person.[3] The second derives a temperature limit for escape under a smoke layer. With a view factor of 1 and an emissivity of 1, a layer of 200 °C gives about 2.5 kW/m² at a person of 37 °C. Within these conservative assumptions, the layer should therefore not be hotter than about 200 °C.[29]

For radiation from flames to a target, the International Fire Engineering Guidelines (2005) represent the flame as a radiating panel. The emissivity of the flames may conservatively be taken as 1.0, which represents thick luminous flames.[30][6] The pool fire method of Shokri and Beyler goes one step further. It treats the flame as a black, uniform cylinder with an average emissive power fitted to experiments.[31]

In New Zealand, the second edition of C/VM2 (2025) requires the emissivity of fire gases to be taken as 1.0. This applies to radiation from a window to occupants on an escape route and to the design fire for fire spread to neighbouring property.[7][32] The commentary on the first edition (2013) explains that the emissivity had been raised from 0.95 to 1.0. The emitted heat fluxes were lowered slightly, so that the overall radiation received at a given distance stayed the same.[33]

For structural steel, emissivity enters the calculation of how fast an unprotected member heats up. NUREG-1805, written for US nuclear power plants, lists resultant emissivities that depend on how the member is exposed.[34] A column exposed to fire on all sides has a value of 0.7, and a column outside the facade 0.3. A floor girder with a concrete slab, exposed only on the underside of its bottom flange, has 0.5.[34] Lie calculated temperature-time curves for ventilation-controlled compartment fires from a heat balance, using an emissivity of 0.7 between the hot gases and the bounding surfaces.[35] The zone model CFAST and the Fire Dynamics Simulator both require the emissivity of each solid surface as an input, together with density, thermal conductivity and specific heat.[36][8]

Limits and common misconceptions

The assumption of one emissivity per material is a simplification. Real emissivity varies with wavelength, and the absorptivity of a gas also depends on the temperature of the source that sends radiation into it.[10] For cables, a higher assumed emissivity speeds up the predicted heating and is therefore the conservative choice.[17] For a radiating fire, a value of 1.0 is the conservative choice, because it maximises the emitted flux.[6]

A common misconception is that a larger, smokier fire always radiates more per unit area. The average emissive power of large pool fires actually falls as the pool diameter increases. Black smoke outside the flame increasingly hides the radiation from the luminous flame.[37] Soot thus raises the emissivity of the flame itself, but black smoke outside the flame can shield its surroundings.

A second misconception is that an emissivity of 1 gives a realistic upper bound for any fire. Babrauskas shows that a black body at an adiabatic flame temperature of about 2300 K would emit some 1500 kW/m². This is nearly ten times the actual maximum found in normal building fires.[5]

Emissivity also affects measurements. A water-cooled heat flux gauge with a black surface stays much colder than most real surfaces, so it gives a conservative estimate of the heat flux to them.[21] Clean steel and thermocouple wire have emissivities well below 1 until soot covers them, which reduces the radiation they absorb early in a test.[16] For the heater of the cone calorimeter, Janssens derived an emissivity of 0.91 over heat fluxes of 10 to 90 kW/m². This value is close enough to 1 that the heater spectrum resembles that of a room fire.[38]

See also

Notes

  1. ↑ 1.0 1.1 1.2 Iqbal and Salley (2004), p. 5-2.
  2. ↑ Iqbal and Salley (2004), p. 5-6.
  3. ↑ 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15 3.16 Van Rossum (2027), §5.4.
  4. ↑ 4.0 4.1 Tewarson (2002), p. 3-131.
  5. ↑ 5.0 5.1 Babrauskas (2002b), p. 3-6.
  6. ↑ 6.0 6.1 6.2 National Research Council of Canada et al. (2005), p. 2.4-9.
  7. ↑ 7.0 7.1 Ministry of Business, Innovation and Employment (2025b), p. 35.
  8. ↑ 8.0 8.1 McGrattan (2007), p. 2-3.
  9. ↑ 9.0 9.1 9.2 9.3 Tien et al. (2002), p. 1-74.
  10. ↑ 10.0 10.1 10.2 10.3 Tien et al. (2002), p. 1-75.
  11. ↑ 11.0 11.1 11.2 11.3 Tien et al. (2002), p. 1-76.
  12. ↑ Walton and Thomas (2002), p. 3-184.
  13. ↑ 13.0 13.1 13.2 Tien et al. (2002), p. 1-85.
  14. ↑ 14.0 14.1 14.2 14.3 Tien et al. (2002), p. 1-82.
  15. ↑ Tewarson (2002), p. 3-100.
  16. ↑ 16.0 16.1 Hamins, Maranghides, McGrattan, Johnsson, et al. (2005), p. 135.
  17. ↑ 17.0 17.1 Nowlen et al. (2005b), p. H-7.
  18. ↑ Peacock et al. (2026), p. 25.
  19. ↑ Joglar et al. (2007), p. 3-2.
  20. ↑ Ohlemiller et al. (2005), p. 74.
  21. ↑ 21.0 21.1 Lattimer (2002), p. 2-269.
  22. ↑ 22.0 22.1 22.2 Tien et al. (2002), p. 1-73.
  23. ↑ Tien et al. (2002), p. 1-79.
  24. ↑ 24.0 24.1 24.2 Tien et al. (2002), p. 1-78.
  25. ↑ Tien et al. (2002), p. 1-81.
  26. ↑ National Research Council of Canada et al. (2005), p. 2.4-10.
  27. ↑ Babrauskas (2002a), p. 3-66.
  28. ↑ McGrattan et al. (2005), p. 24.
  29. ↑ Van Rossum (2027), §7.7.
  30. ↑ National Research Council of Canada et al. (2005), p. 2.4-7.
  31. ↑ Iqbal and Salley (2004), p. 5-7.
  32. ↑ Ministry of Business, Innovation and Employment (2025b), p. 44.
  33. ↑ Ministry of Business, Innovation and Employment (2013), p. 133.
  34. ↑ 34.0 34.1 Iqbal and Salley (2004), p. 17-19.
  35. ↑ Lie (2002), p. 4-204.
  36. ↑ Peacock and Reneke (2007), p. 2-3.
  37. ↑ Beyler (2002a), p. 3-277.
  38. ↑ Babrauskas (2002a), p. 3-67.

References

  • Babrauskas, V. (2002a). The cone calorimeter. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-63–3-81). National Fire Protection Association; Society of Fire Protection Engineers.
  • Babrauskas, V. (2002b). Heat release rates. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-1–3-37). National Fire Protection Association; Society of Fire Protection Engineers.
  • Beyler, C. L. (2002a). Fire hazard calculations for large, open hydrocarbon fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-268–3-314). National Fire Protection Association; Society of Fire Protection Engineers.
  • Hamins, A., Maranghides, A., McGrattan, K. B., Johnsson, E. L., Ohlemiller, T. J., Donnelly, M. K., Yang, J. C., Mulholland, G. W., Prasad, K. R., Kukuck, S. R., Anleitner, R. L., & McAllister, T. P. (2005). Experiments and modeling of structural steel elements exposed to fire (NIST NCSTAR 1-5B). National Institute of Standards and Technology.
  • Iqbal, N., & Salley, M. H. (2004). Fire Dynamics Tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program (NUREG-1805). U.S. Nuclear Regulatory Commission, Office of Nuclear Reactor Regulation.
  • Joglar, F., Gautier, B., Gay, L., & Texeraud, J. (2007). Verification and validation of selected fire models for nuclear power plant applications: Vol. 6. MAGIC (NUREG-1824; EPRI 1011999). U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research; Electric Power Research Institute.
  • Lattimer, B. Y. (2002). Heat fluxes from fires to surfaces. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 2-269–2-296). National Fire Protection Association; Society of Fire Protection Engineers.
  • Lie, T. T. (2002). Fire temperature-time relations. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 4-201–4-208). National Fire Protection Association; Society of Fire Protection Engineers.
  • McGrattan, K. (2007). Verification and validation of selected fire models for nuclear power plant applications: Vol. 7. Fire Dynamics Simulator (NUREG-1824; EPRI 1011999). U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research; Electric Power Research Institute.
  • McGrattan, K. B., Bouldin, C., & Forney, G. P. (2005). Computer simulation of the fires in the World Trade Center towers (NIST NCSTAR 1-5F). National Institute of Standards and Technology.
  • Ministry of Business, Innovation and Employment. (2013). Commentary for Building Code clauses C1–C6 and Verification Method C/VM2.
  • Ministry of Business, Innovation and Employment. (2025b). Verification Method C/VM2: Framework for fire safety design (2nd ed.).
  • National Research Council of Canada, International Code Council, Department of Building and Housing, & Australian Building Codes Board. (2005). International fire engineering guidelines (2005 ed.). Australian Building Codes Board.
  • Nowlen, S. P., Najafi, B., Wyant, F. J., Forester, J., Kazarians, M., Kolaczkowski, A., Joglar, F., Funk, D., Hannaman, G., & Anoba, R. (2005b). EPRI/NRC-RES fire PRA methodology for nuclear power facilities: Vol. 2. Detailed methodology (NUREG/CR-6850; EPRI 1011989). Electric Power Research Institute; U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research.
  • Ohlemiller, T. J., Mulholland, G. W., Maranghides, A., Filliben, J. J., & Gann, R. G. (2005). Fire tests of single office workstations (NIST NCSTAR 1-5C). National Institute of Standards and Technology.
  • Peacock, R., & Reneke, P. (2007). Verification and validation of selected fire models for nuclear power plant applications: Vol. 5. Consolidated Fire Growth and Smoke Transport Model (CFAST) (NUREG-1824; EPRI 1011999). U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research; Electric Power Research Institute.
  • Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). CFAST – Consolidated Fire and Smoke Transport: Vol. 1. Technical reference guide (Version 7, NIST Technical Note 1889v1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.TN.1889v1
  • Tewarson, A. (2002). Generation of heat and chemical compounds in fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-82–3-161). National Fire Protection Association; Society of Fire Protection Engineers.
  • Tien, C. L., Lee, K. Y., & Stretton, A. J. (2002). Radiation heat transfer. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-73–1-89). National Fire Protection Association; Society of Fire Protection Engineers.
  • Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.
  • Walton, W. D., & Thomas, P. H. (2002). Estimating temperatures in compartment fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-171–3-188). National Fire Protection Association; Society of Fire Protection Engineers.
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