View source for Heat release rate per unit area

The '''heat release rate per unit area''' is the [[heat release rate]] of a fire divided by the area that is burning. It says how intensely a fire burns on each square metre of fuel surface or floor.<ref name="VR-4.6">Van Rossum (2027), §4.6.</ref><ref name="CF-417">Cadorin and Franssen (2003), p. 417.</ref> It is usually written as q̇″ and expressed in kilowatts per square metre (kW/m<sup>2</sup>). Other names in the sources are heat release rate density, rate of heat release per unit area of fire and, in fire simulation software, HRRPUA.<ref name="VR-4.6" /><ref name="Cad-435">Cadorin et al. (2003), p. 435.</ref><ref name="FDS-82">McGrattan et al. (2026), p. 82.</ref>

The quantity links the size of a fire to its power. When the heat release rate per unit area and the burning area are known, the total heat release rate follows by multiplication, and the reverse also holds.<ref name="VR-4.6" /> ''Introduction to Fire Safety Engineering'' gives about 250 kW/m<sup>2</sup> for a developed fire in an average building other than storage.<ref name="VR-4.5">Van Rossum (2027), §4.5.</ref> Measured values range from about 100 kW/m<sup>2</sup> for some cable insulation to several thousand kW/m<sup>2</sup> for liquid pools and high stacks of wood pallets.<ref name="NUREG-2-20">Iqbal and Salley (2004), p. 2-20.</ref><ref name="NUREG-2-22">Iqbal and Salley (2004), p. 2-22.</ref> Engineers use it to set the area of a [[design fire]] in fire models, to estimate the diameter of a fire for plume and flame calculations, and to estimate how long fuel can burn.<ref name="CVM2-20">Ministry of Business, Innovation and Employment (2025b), p. 20.</ref><ref name="Hesk-2-3">Heskestad (2002), p. 2-3.</ref><ref name="NUREG-8-2">Iqbal and Salley (2004), p. 8-2.</ref>

== Definition ==
''Introduction to Fire Safety Engineering'' defines the heat release rate density as the amount of power released per unit area. In a fire it means how much heat release rate is produced per square metre of burning surface, so it says something about how intensely a fire burns on a given area.<ref name="VR-4.6" /> The documentation of the OZone software defines it in the same way, as the energy released by one square metre of fire per second.<ref name="CF-417" /> A small fire with a high value can be locally very intense, while a larger fire with a lower value spreads the same power over a wider area.<ref name="VR-4.6" />

The area in the definition is not always the same. For pools, spills and cone calorimeter specimens it is the area of the fuel surface itself.<ref name="Bab-3-24">Babrauskas (2002b), p. 3-24.</ref> For fuel arrays such as storage or wood pallets, the tables usually give the heat release rate per unit floor area covered by the fuel.<ref name="Hesk-2-15">Heskestad (2002), p. 2-15.</ref><ref name="NUREG-8-2" /> In compartment fire models such as OZone, the area is the floor area on which fuel is burning, and the maximum fire area is the floor area on which combustible material is present.<ref name="Cad-435" /> A value per unit floor area of a high storage rack can therefore be much larger than a value per unit exposed surface.

The heat release rate of a fire equals the mass burning rate of the fuel times its effective heat of combustion.<ref name="WT-173">Walton and Thomas (2002), p. 3-173.</ref> Per unit area, the heat release rate per unit area is therefore the [[burning rate]] per square metre multiplied by the effective heat of combustion.<ref name="Gottuk-2-312">Gottuk and White (2002), p. 2-312.</ref> The effective heat of combustion is lower than the value from a bomb calorimeter, because combustion in a real fire is incomplete.<ref name="WT-173" /> In the OZone design fire, the effective heat release rate per unit area is defined as the maximum that can be released per unit area of fire in a steady state. It assumes that the available ventilation does not limit the fire, and it already accounts for incomplete combustion.<ref name="Cad-435" />

== Relation between heat release rate and fire area ==
The basic relation is a simple product. The heat release rate of a fire equals its heat release rate per unit area times its burning area.<ref name="VR-4.6" /><ref name="CF-418">Cadorin and Franssen (2003), p. 418.</ref> It can be rearranged to give the fire area from a known heat release rate, or the heat release rate per unit area from a measured fire.<ref name="VR-4.6" />

<math display="block">\dot{Q} = \dot{q}''\,A</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\dot{Q}</math> || heat release rate of the fire || kW
|-
| <math>\dot{q}''</math> || heat release rate per unit area || kW/m<sup>2</sup>
|-
| <math>A</math> || burning area of the fire || m<sup>2</sup>
|}

The relation holds at every moment of a fire if both the area and the heat release rate per unit area are known at that moment. Design methods usually keep the heat release rate per unit area constant, so that any change in heat release rate is caused by a change in burning area.<ref name="Cad-436">Cadorin et al. (2003), p. 436.</ref> The relation describes a fire that is not limited by ventilation. Once the fire becomes ventilation controlled, the heat release rate inside the room is set by the air supply instead.<ref name="Cad-435" /><ref name="WT-173" />

''Introduction to Fire Safety Engineering'' gives a simple example. A fire of 1,000,000 W with a heat release rate per unit area of 250,000 W/m<sup>2</sup> has a burning area of 4 m<sup>2</sup>.<ref name="VR-4.6" /> A circle with this area has a diameter of about 2.3 m. Heskestad used this approach for storage fires. He took the fire diameter as that of a circle whose area equals the heat release rate divided by the heat release rate per unit area.<ref name="Hesk-2-3" />

[[File:fse-heat-release-rate-per-unit-area-v1.svg|thumb|upright=1.5|alt=Plan view of two circular fires of 1 MW each: a wide one of 4 m² at 250 kW/m² and a small one of 1 m² at 1,000 kW/m².|Two fires of 1 MW: at 250 kW/m² the burning area is 4 m², at 1,000 kW/m² it is 1 m². Based on Van Rossum (2027), §4.6.]]

A second worked example comes from New Zealand. C/VM2 (second edition, 2025) sets a peak heat release rate of 20 MW for most buildings. It gives 250 kW/m<sup>2</sup> for use in a zone model and a range of 500 to 1,000 kW/m<sup>2</sup> for a computational fluid dynamics (CFD) model.<ref name="CVM2-20" /> With 250 kW/m<sup>2</sup>, the fully grown design fire covers 20,000 / 250 = 80 m<sup>2</sup>. With 500 and 1,000 kW/m<sup>2</sup>, the same fire covers 40 m<sup>2</sup> and 20 m<sup>2</sup>, a square of about 6.3 m and 4.5 m wide.

Liquid spills give a third example. In the SFPE Handbook, Gottuk and White consider 208 litres of gasoline spilled across a warehouse floor, with an estimated burning area of 116 m<sup>2</sup>. For an unconfined spill they take one-fifth of the maximum pool burning rate, 0.011 kg/(m<sup>2</sup>·s), with a heat of combustion of 43.7 MJ/kg.<ref name="Gottuk-2-314">Gottuk and White (2002), p. 2-314.</ref> The heat release rate per unit area is then about 480 kW/m<sup>2</sup>, and the fire reaches 0.011 × 116 × 43.7 = 56 MW.<ref name="Gottuk-2-314" />

== Typical values ==
Values depend strongly on the type of fuel and its arrangement. The Fire Dynamics Tools of the US Nuclear Regulatory Commission collect measured values for fuels found in nuclear power plants. The table gives a selection, together with the general design values of ''Introduction to Fire Safety Engineering'' and C/VM2.<ref name="NUREG-2-19">Iqbal and Salley (2004), p. 2-19.</ref>

[[File:fse-heat-release-rate-per-unit-area-v2.svg|thumb|upright=1.5|alt=Horizontal bar chart of heat release rate per unit area for eight fuels, from 81 kW/m² for treated plywood to 3,290 kW/m² for gasoline.|Measured heat release rates per unit area of fuels in nuclear power plants, with the design value of 250 kW/m² for a developed fire in an ordinary building. Based on Iqbal and Salley (2004), pp. 2-20 to 2-22 and 8-3, and Van Rossum (2027), §4.5.]]

{| class="wikitable"
! Fuel or situation !! Heat release rate per unit area (kW/m<sup>2</sup>) !! Source
|-
| Fire-retardant treated plywood || 81 || Iqbal and Salley (2004), p. 2-22
|-
| Douglas fir plywood || 124 || Iqbal and Salley (2004), p. 2-22
|-
| Cable jacketing PE/PVC || 590 || Iqbal and Salley (2004), p. 2-20
|-
| Polyurethane || 710 || Iqbal and Salley (2004), p. 8-3
|-
| Polyethylene || 1,408 || Iqbal and Salley (2004), p. 8-3
|-
| Wood pallets stacked 1.5 ft (0.46 m) high || 1,420 || Iqbal and Salley (2004), p. 2-22
|-
| Wood pallets stacked 10 ft (3.05 m) high || 6,800 || Iqbal and Salley (2004), p. 2-22
|-
| Diesel oil || 1,985 || Iqbal and Salley (2004), p. 2-21
|-
| Gasoline || 3,290 || Iqbal and Salley (2004), p. 2-21
|-
| Developed fire in an average building other than storage || 250 || Van Rossum (2027), §4.5
|-
| Design fire in a zone model, New Zealand || 250 || Ministry of Business, Innovation and Employment (2025b), p. 20
|-
| Design fire in a CFD model, New Zealand (storage) || 500 to 1,000 (1,000 to 2,500) || Ministry of Business, Innovation and Employment (2025b), p. 20
|}

Several patterns stand out. Liquid fuels give much higher values than plywood or cable insulation.<ref name="NUREG-2-21">Iqbal and Salley (2004), p. 2-21.</ref><ref name="NUREG-2-22" /> For stacked fuels the value per unit floor area rises with stack height, from 1,420 kW/m<sup>2</sup> for pallets 1.5 ft high to 10,200 kW/m<sup>2</sup> for pallets 16 ft high.<ref name="NUREG-2-22" /> Heskestad likewise uses 4,000 kW/m<sup>2</sup> for a fully involved storage 3 m deep, and notes that methyl alcohol gave 500 kW/m<sup>2</sup> against 2,500 kW/m<sup>2</sup> for heptane in the same example.<ref name="Hesk-2-11">Heskestad (2002), p. 2-11.</ref>

[[File:fse-heat-release-rate-per-unit-area-v4.svg|thumb|upright=1.5|alt=Line chart: heat release rate per unit floor area of wood pallet stacks rises from 1,420 kW/m² at 0.46 m to 10,200 kW/m² at 4.88 m.|Heat release rate per unit floor area of stacked wood pallets against stack height. Based on Iqbal and Salley (2004), p. 2-22.]]

''Introduction to Fire Safety Engineering'' also lists values per type of use, taken from the Dutch national annex to EN 1991-1-2. Most uses, including dwellings, offices, hotels, classrooms and health care, receive 250 kW/m<sup>2</sup>. Theatres and cinemas, libraries and retail such as supermarkets and DIY stores receive 500 kW/m<sup>2</sup>, and storage receives 500 kW/m<sup>2</sup> per metre of storage height.<ref name="VR-8.5">Van Rossum (2027), §8.5.</ref> The book stresses that these are normative values for the assessment of structures. For a conservative model of the first phase of a fire, such as in an escape analysis, variant calculations with higher values may be needed.<ref name="VR-8.5" />

Thin liquid spills burn much less intensely than deep pools. Putorti and co-workers found that gasoline spills on smooth floors gave only about one-fifth of the value expected for deep pools, which in the same size range would reach about 1,900 to 2,400 kW/m<sup>2</sup>. On carpets the value was about 70% to 80% of the deep-pool value.<ref name="Bab-3-25">Babrauskas (2002b), p. 3-25.</ref> Gottuk and White therefore suggest estimating unconfined spills at one-fifth of the maximum pool burning rate. For large continuous releases, above about 10 litres per minute, they recommend the full pool rates as a conservative choice.<ref name="Gottuk-2-312" />

== Measurement ==
The heat release rate per unit area of a material is measured at bench scale with the [[cone calorimeter]]. The instrument uses oxygen consumption calorimetry to determine the heat release rate of a specimen of 100 mm by 100 mm. The specimen is normally horizontal and face up, and a conical heater exposes it to a heat flux between 0 and 110 kW/m<sup>2</sup>.<ref name="Bab-3-63">Babrauskas (2002a), p. 3-63.</ref> Its measuring functions also include the mass loss rate and the effective heat of combustion, which together explain the measured heat release.<ref name="Bab-3-63" />

Bench-scale values do not transfer directly to large fires. The size of the specimen affects the result, because flames over larger specimens are thicker and radiate more strongly. For horizontal PMMA, each doubling of the specimen area raised the heat release rate per unit area by about 10%.<ref name="Bab-3-70">Babrauskas (2002a), p. 3-70.</ref> For liquid pools, the diameter must exceed about 1 m before the size effect becomes negligible. Vertical PMMA walls showed a rate that kept rising roughly linearly with height up to the largest height tested, 3.56 m.<ref name="Bab-3-70" />

Full-scale values come from burning whole items or arrays under a large hood. NFPA 204M, cited by Heskestad, gives tables of heat release rate per unit floor area and growth times for a number of fuel arrays.<ref name="Hesk-2-15" /> The values in the Fire Dynamics Tools for pallets, cartons and plastics are of this kind.<ref name="NUREG-8-3">Iqbal and Salley (2004), p. 8-3.</ref> Such data describe free burning in the open. A pool in a room that receives significant radiation from a hot layer can burn faster, and no simple formula exists for that increase.<ref name="Bab-3-26">Babrauskas (2002b), p. 3-26.</ref>

== Use in design fires and fire models ==
In a design fire, the heat release rate per unit area converts a heat release rate curve into a fire area. The OZone method first builds the heat release rate curve and then derives the fire area by dividing it by the effective heat release rate per unit area. The maximum heat release rate is reached when the whole floor area carrying fuel is burning.<ref name="Cad-435" /><ref name="Cad-436" /> At flashover the OZone model jumps directly to this maximum, the full fire area times the heat release rate per unit area.<ref name="Cad-438">Cadorin et al. (2003), p. 438.</ref>

The area matters for several calculations. Plume entrainment and flame height correlations need the diameter of the fire, which follows from the area.<ref name="CF-418" /><ref name="Hesk-2-3" /> In CFD models, the fire is modelled as a burning surface. C/VM2 (second edition, 2025) states that its plan area follows from the peak heat release rate per unit area, and gives a range to suit different heat release rates and mesh sizes.<ref name="CVM2-20" /> The Fire Dynamics Simulator converts a specified heat release rate per unit area, a time ramp and a heat of combustion into a mass flux of fuel from the burning surface.<ref name="FDS-82" />

A [[t-squared fire]] can be interpreted with the same quantity. The Fire Dynamics Tools describe it as a fire in which the heat release rate per unit area is constant and the burning area spreads as a circle with a steadily growing radius.<ref name="NUREG-B-4">Iqbal and Salley (2004), p. B-4.</ref> The 2013 commentary on C/VM2 uses the same picture of a constant flame speed.<ref name="MBIE13-55">Ministry of Business, Innovation and Employment (2013), p. 55.</ref> Heskestad applied it to a storage fire with a growth time of 140 s and 2,270 kW/m<sup>2</sup>, which gave a fire diameter growing in proportion to time.<ref name="Hesk-2-13">Heskestad (2002), p. 2-13.</ref>

[[File:fse-heat-release-rate-per-unit-area-v3.svg|thumb|upright=1.5|alt=Plan view of three concentric circles of burning fuel at 140, 280 and 420 s, with diameters 0.75, 1.5 and 2.25 m and fires of 1, 4 and 9 MW.|A t-squared fire at a constant 2,270 kW/m²: the diameter grows in proportion to time and the heat release rate with its square. Based on Heskestad (2002), p. 2-13 and Iqbal and Salley (2004), p. B-4.]]

The heat release rate per unit area also links power to the duration of burning. The Fire Dynamics Tools estimate the burning duration of a solid fuel as its mass times its heat of combustion, divided by the heat release rate per unit area times the exposed area.<ref name="NUREG-8-2" /> Energy per unit area is the [[fire load density]], so dividing it by the heat release rate per unit area gives a first estimate of how long each square metre can burn. For an office FLED of 800 MJ/m<sup>2</sup> and 250 kW/m<sup>2</sup>, the result is 3,200 s, or about 53 minutes.<ref name="CVM2-22">Ministry of Business, Innovation and Employment (2025b), p. 22.</ref><ref name="CVM2-20" /> In the gasoline spill example, the whole spill would burn away in about 2 minutes, which Gottuk and White consider most likely too short, because flames take time to spread across the spill.<ref name="Gottuk-2-314" />

== Limits and common misconceptions ==
The assumption of a constant heat release rate per unit area is a simplification. The OZone authors call it quite crude, particularly in the early stages of a fire, although they expect a small influence on the overall design.<ref name="Cad-436" /> In real fires, the rate per unit area changes as items ignite, burn at their peak and burn out, so a single value describes an average.<ref name="Cad-436" /><ref name="Bab-3-70" />

A common misconception is to confuse the heat release rate per unit area with heat flux. Heat flux is the heat arriving at a surface, such as the radiation from the cone heater onto a test specimen. The heat release rate per unit area is the heat produced by the burning fuel itself. The technical guide of the Fire Dynamics Simulator keeps them apart. It treats a cone heat flux of 50 kW/m<sup>2</sup> and the flame heat flux separately from prescribed values of 100 to 2,000 kW/m<sup>2</sup> for the heat release rate per unit area.<ref name="FDS-228">McGrattan et al. (2026), p. 228.</ref> Both quantities use the same unit, kW/m<sup>2</sup>, which adds to the confusion.<ref name="Bab-3-63" />

Another misconception is that a value per unit area is a fixed material property. It depends on the scale of the test, the arrangement of the fuel, the incident heat flux and, for liquids, the depth of the pool.<ref name="Bab-3-70" /><ref name="Bab-3-25" /> Values per unit floor area of stacked fuels also depend on stack height.<ref name="NUREG-2-22" /> Data must therefore be taken from tests that resemble the situation being modelled.

The choice of value also changes model results without changing the heat release rate. A higher value gives a smaller, more concentrated fire, while a lower value spreads the same power over a larger area.<ref name="VR-4.6" /> This is why C/VM2 gives a range for CFD models rather than a single value, and why ''Introduction to Fire Safety Engineering'' recommends variant calculations with higher values for early-phase modelling.<ref name="CVM2-20" /><ref name="VR-8.5" />

== See also ==
* [[Fire load]]
* [[Fire plume]]
* [[Flame height]]

== Notes ==
<references />

== 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.
* Cadorin, J.-F., & Franssen, J.-M. (2003). A tool to design steel elements submitted to compartment fires – OZone V2. Part 1: Pre- and post-flashover compartment fire model. ''Fire Safety Journal'', ''38'', 395–427. https://doi.org/10.1016/S0379-7112(03)00014-6
* Cadorin, J.-F., Pintea, D., Dotreppe, J.-C., & Franssen, J.-M. (2003). A tool to design steel elements submitted to compartment fires – OZone V2. Part 2: Methodology and application. ''Fire Safety Journal'', ''38'', 429–451. https://doi.org/10.1016/S0379-7112(03)00015-8
* Gottuk, D. T., & White, D. A. (2002). Liquid fuel 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. 2-297–2-316). National Fire Protection Association; Society of Fire Protection Engineers.
* Heskestad, G. (2002). Fire plumes, flame height, and air entrainment. 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. 2-1–2-17). National Fire Protection Association; Society of Fire Protection Engineers.
* 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.
* McGrattan, K., Hostikka, S., Floyd, J., McDermott, R., Vanella, M., Mueller, E., & Paul, C. (2026). ''Fire Dynamics Simulator technical reference guide: Vol. 1. Mathematical model'' (6th ed., NIST Special Publication 1018-1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.SP.1018
* 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.).
* 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.

[[Category:Fire Dynamics]]