Free Engineering Tool · NFPA 92
Stack Effect Calculator
In cold weather the warm air in a stair, elevator shaft or tall building pushes out near the top and pulls in near the bottom. Enter the height and the inside and outside temperatures to get the stack effect pressure difference at any height, the neutral plane and the air leakage through a gap, the condition NFPA 92 asks every pressurization design to handle.
- Based on NFPA 92
- Free, runs in your browser; your inputs stay on your device
- Screening tool, not reviewed or sealed by a licensed engineer
- Last updated October 2026
Screening tool, not engineering advice. This calculator estimates results with simplified published methods. It has not been reviewed or sealed by a licensed engineer for your project, and DGA does not warrant that its results are accurate, complete or suitable for any use. Check every result independently and have the licensed professional responsible for your project review it before you rely on it. Use is subject to the Terms of Use.
Advanced method. The correlations behind this tool come from research and test data with narrow ranges of validity. Outside those ranges results can be wrong by a wide margin, and they are no substitute for a fire model or an analysis by a qualified fire protection engineer.
Shaft and Temperatures
Neutral Plane
Mid-height is right for a shaft with evenly spread leakage. Use the openings option when most of the leakage is near the top or the bottom.
Leakage Path
A closed door with 1/8 in. (3 mm) gaps around a 3 by 7 ft leaf leaks about 0.2 ft² (0.02 m²). A flow coefficient of 0.65 is usual for cracks and gaps in buildings.
Result
Pressure Profile
About This Tool
Stack effect comes from the difference in density between the air inside a shaft and the air outside. Pressure falls with height on both sides, but faster in the colder, denser air, so the pressure difference changes linearly with height. At standard atmospheric pressure it is Δp = Ks (1/To − 1/Ti) (z − hn), where To and Ti are the absolute outside and inside temperatures, z the height and hn the height of the neutral plane, where the inside and outside pressures are equal. Ks is 3,460 with Δp in Pa, T in K and heights in m (about 7.6 with inches of water, °R and ft). A positive value means the shaft is at a higher pressure than outside and air leaks out; a negative value means air leaks in.
The neutral plane sits at mid-height when leakage is spread evenly over the height. When most of the leakage is near the top or the bottom, the neutral plane moves toward the larger opening. Balancing the mass flow through a top opening At and a bottom opening Ab gives hn/H = 1 / [1 + (Ab/At)² ρb/ρt], where ρb and ρt are the densities of the air passing through each opening (in winter, outside air at the bottom and inside air at the top). The flow through a gap of area A follows the orifice equation Q = C A √(2 Δp / ρ), with C about 0.65 for cracks and gaps in buildings. In US units with C = 0.65 and room air, this becomes the familiar Q = 2,610 A √Δp, with Q in cfm, A in ft² and Δp in inches of water.
Worked example
A 300 ft stair is at 70 °F on a 10 °F day, with the neutral plane at mid-height. At the top, 150 ft above the neutral plane, Δp = 7.62 × (1/469.7 − 1/529.7) × 150 = 0.28 in. of water, and the bottom is 0.28 in. below outside. The difference changes by about 0.18 in. of water per 100 ft. A closed door at the top with 0.25 ft² of gaps leaks about 340 cfm. If the stair leaks twice as much near the bottom as near the top, the neutral plane drops to about 54 ft and the top pressure rises to 0.45 in.
Assumptions and limits
The calculator treats one shaft or one building with uniform inside temperature, sea-level atmospheric pressure and no wind, fans or fire. The neutral plane from openings uses two concentrated openings; real buildings with many floors, shafts and leakage paths can have more than one neutral plane and need a network model. Stack effect in a pressurized stair adds to or subtracts from the fan pressure; it does not replace a pressurization analysis.
When to bring in an engineer
Tall stairs pressurized with untreated outside air, buildings with mixed floor plans, and cold-climate high-rises often need a network analysis to show the system holds the minimum pressure difference at the top and bottom without exceeding door opening forces. DGA designs and reviews smoke control systems and prepares fire and smoke modeling for performance-based designs.
References
- NFPA 92, Standard for Smoke Control Systems, National Fire Protection Association, 2024 edition: stack effect as a design condition for pressurization systems and the stack effect equation in the annex.
- Klote, J.H., A General Routine for Analysis of Stack Effect, NISTIR 4588, National Institute of Standards and Technology, Gaithersburg, MD, 1991.
- ASHRAE, ASHRAE Handbook: Fundamentals, current edition, chapter on ventilation and infiltration: stack pressure and the neutral pressure level.
- Klote, J.H., Milke, J.A., Turnbull, P.G., Kashef, A. and Ferreira, M.J., Handbook of Smoke Control Engineering, ASHRAE, Atlanta, 2012: stack effect, flow areas and the orifice equation.
Frequently Asked Questions
How do you calculate stack effect pressure?
Multiply 3,460 by the difference of the reciprocal absolute temperatures (1/T outside minus 1/T inside, in kelvin) and by the height above the neutral plane in meters to get pascals. In US units use about 7.6 with temperatures in degrees Rankine, height in feet and pressure in inches of water.
Where is the neutral plane in a building?
For a shaft with leakage spread evenly over its height, the neutral plane is near mid-height. It moves toward the larger openings: a shaft with a large opening at the bottom, such as an open ground floor door, has its neutral plane low, which raises the pressure difference at the top.
What is reverse stack effect?
In hot weather, when the shaft is cooler than outside, air flows down the shaft. It enters near the top and leaves near the bottom, and the pressure differences are usually smaller than in winter because the temperature difference is smaller.
Why does stack effect matter for stair pressurization?
A pressurized stair has to keep its minimum pressure difference at every door while staying under the door opening force limit. Stack effect makes the pressure difference vary with height, so a tall stair can be over-pressurized at one end and under-pressurized at the other.
Related Tools and Services
More smoke control and tenability calculators →
Engineering aid only, provided as is and without warranty. Results depend on the inputs and on the simplifying assumptions of the method summarized on each tool page, and DGA has not verified them for your application. They do not replace code-required design, testing or review by the licensed engineer responsible for the project. Use of the tools is subject to the Terms of Use.