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Stack Plume Rise Calculator

Enter your stack and atmospheric conditions to estimate the plume rise.

How it is calculated

The tool uses Holland's plume rise equation: ΔH = (Vs × d ÷ u) × (1.5 + 2.68×10⁻³ × P × d × (Ts − Ta) ÷ Ts). Vs is the stack exit velocity in m/s, d the inner stack diameter in m, u the wind speed in m/s, P the atmospheric pressure in millibars (about 1013 at sea level), and Ts and Ta the stack gas and ambient air temperatures in kelvin. The first factor is the momentum term and the bracket adds buoyancy, which grows with the temperature excess. The result is the rise in metres above the stack top, to two decimals. Wind speed and Ts must be above zero. The tool has no stability correction, and if Ts is below Ta the buoyancy term turns negative and the rise can go below zero, which is not physical.

Worked example

Take a stack with an exit velocity of 15 m/s, a diameter of 2 m, a wind of 5 m/s, a pressure of 1013 mbar, a gas temperature of 420 K and ambient air at 288 K. The momentum factor is 15 × 2 ÷ 5 = 6. The temperature ratio is (420 − 288) ÷ 420 = 0.3143. The buoyancy term is 2.68×10⁻³ × 1013 × 2 × 0.3143 = 1.7065. Adding 1.5 gives 3.2065, and 6 × 3.2065 = 19.24 m of plume rise above the stack top.

Try this example →

Common mistakes

  • Entering Ts and Ta in °C; the temperature ratio needs kelvin, so 147 °C must be entered as 420 K.
  • Giving the pressure in kPa, for example 101.3 (1 kPa = 10 mbar); the equation expects millibars, and 101.3 drops the same stack's rise from 19.24 m to 10.02 m.
  • Treating the result as the total plume height; it is only the rise above the stack top, so the stack height must be added for the effective height.
  • Using ambient temperature above the gas temperature, which gives a smaller rise or even a negative one.
  • Entering the wind speed measured at ground level or in km/h rather than m/s at stack height; the rise is inversely proportional to the wind speed.

About this calculator

Holland's equation, developed in 1953 for meteorological dispersion modeling, estimates how far an exhaust plume rises above a stack's physical top before it levels off and begins drifting downwind — a critical input because the plume's effective height, not the stack's height alone, determines ground-level pollutant concentrations. It calculates rise from the stack's exit velocity and diameter, the ambient wind speed, and a buoyancy term built from the difference between the gas exit temperature and the ambient air temperature (this calculator applies no correction for atmospheric stability).

This calculator takes your stack's exit velocity, diameter, and gas temperature along with wind speed and pressure to estimate the plume rise in meters above the stack top. Environmental engineers preparing air-quality permit applications, industrial hygienists modeling emissions dispersion, and regulatory compliance staff at power plants and factories use it as a quick screening estimate before running full Gaussian dispersion models like AERMOD, since plume rise directly feeds into how far downwind pollutants travel before reaching breathable air.

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  • Editorial team

    The figure is the rise above the stack top, so add the physical stack height yourself to get an effective release height before using it in dispersion work. The default values give 17.84 m. Holland's formula is usually regarded as on the conservative side and has no stability correction, so treat it as a screening estimate and compare it with whatever method your regulator specifies. What kind of source are you screening?

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