Dispersion Modeling Calculator
Downwind concentration from AERMOD-style Gaussian dispersion.
About this calculator
This calculator estimates ground-level pollutant concentration downwind of an elevated point source (a smokestack, vent, or similar) using the Gaussian plume equation: C = Q / (2π × u × σy × σz) × exp(−H² / (2σz²)). The plume is modeled as spreading outward in a bell-curve shape both horizontally (σy) and vertically (σz) as it travels downwind, with the horizontal and vertical spread rates set by a Pasquill-Gifford stability class you choose from 1 (A, very unstable — strong sun, light wind, maximum turbulent mixing) through 6 (F, stable — clear nighttime skies, minimal mixing, plume stays narrow and doesn't disperse well). Given emission rate, wind speed, effective stack height (physical height plus any plume rise), downwind distance, and stability class, the calculator computes the dispersion coefficients as power-law functions of distance, then solves for the ground-level centerline concentration at that specific point.
It also solves separately for the single downwind distance where ground-level concentration peaks — this occurs where the vertical spread σz grows to roughly H/√2, since closer than that the plume hasn't dispersed down to ground level yet, and farther than that it has diluted below its peak. A plume width at 10% of centerline concentration (≈ 4.3σy) is also reported to give a sense of the affected area. This is a simplified, screening-level version of what real dispersion tools like AERMOD do — it uses fixed representative coefficients rather than site-specific terrain, building downwash, or real-time meteorology, and it assumes flat terrain and steady wind conditions throughout, so treat results as an order-of-magnitude estimate for siting and permitting screening, not a regulatory-grade air quality determination.
Inputs
Results
Ground concentration (µg/m³)
265.67
How to Use This Calculator
- Enter Emission rate (g/s), Wind speed (m/s), and Effective stack height (m).
- Set Downwind distance (m) and Stability class (1=A…6=F).
- Review the Ground concentration (µg/m³) result.
- Use Max ground conc. (µg/m³) and Max conc. distance (m) to inform your decision.
How the result changes with Effective stack height (m)
| Effective stack height (m) | Ground concentration (µg/m³) |
|---|---|
| 15 | 467.39 |
| 23 | 362.4 |
| 45 | 103.62 |
| 75 | 5.09 |
What each input means
- Emission rate (g/s)
- Pollutant mass emission rate from the source in grams per second.
- Wind speed (m/s)
- Mean wind speed at stack height in meters per second.
- Effective stack height (m)
- Physical stack height plus plume rise in meters.
- Downwind distance (m)
- Distance downwind from the source along the plume centerline.
- Stability class (1=A…6=F)
- Pasquill stability class. 1=A (very unstable, sunny), 4=D (neutral, overcast), 6=F (stable, nighttime).
What each result means
- Ground concentration (µg/m³)
- Ground-level centerline concentration at the specified downwind distance.
- Max ground conc. (µg/m³)
- Maximum possible ground-level concentration from this source.
- Max conc. distance (m)
- Downwind distance where maximum ground-level concentration occurs.
- σy horizontal dispersion (m)
- Horizontal dispersion coefficient at the downwind distance.
- σz vertical dispersion (m)
- Vertical dispersion coefficient at the downwind distance.
- Plume width at 10% (m)
- Approximate plume width at 10% of centerline concentration (≈4.3σy).
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersEmission rate (g/s) = 10, Wind speed (m/s) = 3, Effective stack height (m) = 30, Downwind distance (m) = 1000 = 5 input(s) provided
- Calculate Ground concentrationGround concentration = concentrationGM3 * 1e6265.673 = 265.673
- Calculate Max ground conc.Max ground conc. = cMax * 1e6276.663 = 276.663
- Calculate Max conc. distanceMax conc. distance = pow(targetSigmaZ / coeff.az, 1 / coeff.bz)850 = 850
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does the ground-level concentration first rise then fall as I increase downwind distance?
Right at the stack, the plume hasn't spread down to ground level yet, so ground concentration starts near zero even though emissions are high overhead. As distance increases, the vertical dispersion coefficient σz grows and the plume mixes downward, raising ground concentration — until σz grows large enough that the plume has diluted horizontally and vertically faster than it's reaching the ground, at which point concentration falls off. The calculator's "max conc. distance" output finds the peak of that curve, where σz ≈ H/√2.
How much does changing the stability class actually change my result?
Stability class controls both dispersion coefficients (σy and σz) via different power-law exponents and multipliers — unstable Class A (turbulent, sunny) spreads the plume faster both horizontally and vertically than stable Class F (calm, nighttime), which keeps the plume narrow and can produce higher concentrations at certain distances because the pollutant hasn't diluted as much. Since the exponent on σz ranges from 1.00 (Class A) down to 0.83 (Class F) in this model, the same downwind distance can give meaningfully different ground concentrations across the six classes.
Why does raising the effective stack height change the result even though emission rate stays the same?
Effective stack height (H) appears in the exponential term exp(−H²/(2σz²)), which suppresses ground-level concentration when the plume centerline is still high above the ground relative to how much it has vertically dispersed. A taller effective stack height (physical height plus plume rise) pushes the concentration peak farther downwind and lowers the near-field concentration, since the plume needs to travel farther before σz grows enough to bring much of it down to ground level.
How accurate is this compared to a regulatory tool like AERMOD?
This is a simplified screening-level Gaussian plume calculation using fixed representative Pasquill-Gifford coefficients, flat terrain, and steady wind assumptions — it doesn't account for site-specific terrain, building downwash, or real meteorological data the way AERMOD does. Treat the output as an order-of-magnitude estimate for early siting or permitting screening, not as a substitute for a regulatory-grade air dispersion modeling study.
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