Stack Emission Rate Calculator
Solve the stack-testing emission equation for emission rate, concentration, or flow rate — with reference tables and a live emission-rate-vs-flow chart.
Curve holds concentration (C) at your current input value and varies flow rate (Q) — showing why emission rate rises with stack flow even when concentration itself stays constant.
| Source type | Typical concentration |
|---|---|
| Natural gas boiler (NOx) | ~100–300 mg/m³ |
| Coal-fired boiler (PM) | ~50–200 mg/m³ |
| Cement kiln (PM) | ~20–50 mg/m³ |
| MSW incinerator (SO₂) | ~50–150 mg/m³ |
| Steel EAF (PM) | ~10–30 mg/m³ |
| Source type | Typical flow rate |
|---|---|
| Small process vent | ~0.05–1 m³/s |
| Small industrial boiler | ~1–5 m³/s |
| MSW incinerator | ~20–60 m³/s |
| Cement kiln | ~50–150 m³/s |
| Large utility boiler | ~200–800 m³/s |
Concentration ↑, Flow fixed
More pollutant mass per unit gas volume increases emission rate proportionally — this is what add-on controls (scrubbers, baghouses) are designed to reduce.
Flow Rate ↑, Concentration fixed
More gas volume exiting the stack carries proportionally more pollutant mass, even with concentration unchanged — e.g. when production throughput increases.
Concentration ↓ via control
Cutting C directly (better capture, control equipment) reduces E without needing to slow the process itself.
Flow reduction / better capture
Tighter capture hoods or reduced exhaust volume lower Q, cutting E for the same source concentration.
What Is Stack Emission Rate?
Stack emission rate (E) is the mass of a pollutant released from a stack or vent per unit of time. It comes directly from how concentrated the pollutant is in the exhaust gas (C) and how much gas volume is moving through the stack (Q). This is the core relationship behind most stack testing and permitting calculations.
Stack Emission Rate Formula
Here, C is the pollutant concentration in the stack gas and Q is the volumetric flow rate of that gas. Multiplying a mass-per-volume concentration by a volume-per-time flow rate gives a mass-per-time emission rate.
How to Calculate Emission Rate
Choose the unknown variable above, enter the other two in whichever units suit your data, and the calculator rearranges the formula automatically:
| Solve for | Rearranged formula |
|---|---|
| E | E = C × Q |
| C | C = E / Q |
| Q | Q = E / C |
Stack Emission Rate Formula Variables
| Symbol | Meaning | Typical unit |
|---|---|---|
| E | Emission rate | g/s, kg/hr, lb/hr, t/yr |
| C | Pollutant concentration | mg/m³, g/m³, gr/dscf |
| Q | Stack gas flow rate | m³/s, m³/hr, cfm |
How Concentration Affects Emission Rate
Emission rate scales directly with concentration — double the pollutant loading per unit gas volume and, for the same flow, emission rate doubles too. This is why control technologies (scrubbers, filters, baghouses) target concentration directly.
How Flow Rate Affects Emission Rate
Emission rate also scales directly with flow rate — even a clean-burning, low-concentration source can have a high emission rate if enough gas volume is exiting the stack, which is why large sources are tested carefully even when their concentration limits are modest.
Stack Emission Rate Calculation Example
E = 0.5 × 10
E = 5.0 g/s (≈ 18 kg/hr, ≈ 39.7 lb/hr)
Frequently Asked Questions
Concentration (C) describes how much pollutant is in a given volume of gas; emission rate (E) describes the total mass leaving the stack per unit time. A low concentration can still mean a high emission rate if the flow rate is large enough.
Only if concentration stays the same. In practice, increasing flow (e.g. through dilution) while holding total pollutant mass constant lowers concentration and can leave emission rate unchanged — E depends on both terms together.
These are common US stack-testing units: grains per dry standard cubic foot (concentration) and dry standard cubic feet per minute (flow, at standard temperature, pressure and moisture conditions). This calculator's gr/dscf and cfm options use the standard volume conversions.
Yes — the E = C × Q relationship is generic to any pollutant measured as a mass concentration in a gas stream (particulate matter, NOx, SO₂, etc.), as long as C and E use consistent mass units.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| E | Emission rate | g/s |
| C | Pollutant concentration in stack gas | g/m3 |
| Q | Stack gas volumetric flow rate | m3/s |
What it means
The stack emission rate is the mass of pollutant emitted per unit time (e.g., kg/h). It is calculated by multiplying the pollutant concentration (C) in the exhaust gas by the volumetric flow rate (Q) of the gas stream. This is a fundamental calculation for air pollution control. It is used to determine compliance with emission limits, to design control equipment, and to estimate the contribution of a source to ambient air concentrations. The concentration can be measured continuously or via periodic sampling. Example: A stack has a flow rate of 100,000 m³/h and a measured concentration of SO₂ of 0.5 g/m³. The emission rate is E = 0.5 × 100,000 = 50,000 g/h = 50 kg/h. This would be compared to the permitted limit and may require additional control measures.
Worked example
Stack Emission Rate – Two Examples
Real‑World| Parameter | Value |
|---|---|
| C | 0.05 g/m³ |
| Q | 20 m³/s |
| Parameter | Value |
|---|---|
| C | 0.1 g/m³ |
| Q | 15 m³/s |
Common mistakes
- Concentration C: The pollutant concentration in the stack gas – e.g., µg/m³.
- Flow rate Q: The volumetric flow rate of the stack gas – in m³/s or m³/h.
- Units: E = C × Q – ensure units are consistent (e.g., µg/s, kg/day).
- Reference conditions: Flow and concentration are often corrected to standard conditions (e.g., dry, 0°C, 1 atm).
- Sampling: Concentration may vary over time – use average values for emission calculations.
Applications
Stack emission rate is the product of pollutant concentration (C) and volumetric flow rate (Q) of the flue gas, providing the mass of pollutant emitted per unit time (e.g., kg/hr). This is a fundamental calculation for industrial emission inventories, permit compliance, and design of pollution control equipment. Environmental engineers use it to estimate annual emissions, to determine the efficiency of control devices (e.g., scrubbers, baghouses), and to report to regulatory agencies. Accurate stack emission rates are required for dispersion modelling, health risk assessments, and greenhouse gas reporting. By quantifying emissions, facilities can identify major sources, implement reduction strategies, and demonstrate environmental stewardship.
- Compliance with air permits and emission standards
- Inventory of pollutants for reporting (e.g., EPA TRI, E‑Permitting)
- Design and performance testing of air pollution control devices
- Fugitive emission estimation and leak detection programmes
- Modelling of atmospheric dispersion and human health risk
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