Air Purifier Smoke Clearance Time Calculator

How this smoke clearance time calculator works

This calculator estimates how long a room air purifier needs to reduce fine particle pollution (PM2.5) from wildfire smoke or similar sources down to a cleaner target level. You enter your room size, the clean air delivery rate (CADR) of your purifier, and the starting and target PM2.5 concentrations. The calculator then estimates the time required, assuming the room air is well mixed and no new smoke is added.

The tool is designed for practical planning during wildfire smoke events, controlled burns, nearby structure fires, or other times when outdoor air is unusually smoky and you are trying to create a cleaner indoor space. It does not replace medical advice or official public health guidance.

Key concepts: room volume, CADR, and air changes per hour

The clearance time depends mainly on three pieces of information:

• Room volume – The total air volume in the room, based on its length, width, and ceiling height.
• Clean Air Delivery Rate (CADR) – How much clean, filtered air the purifier delivers, usually given in cubic feet per minute (CFM) for U.S. models.
• Air Changes per Hour (ACH) – How many times per hour the entire room volume is effectively cleaned by the purifier.

First, the calculator converts your room dimensions to a volume. In imperial units, the volume in cubic feet is:

Room volume (ft³) = length (ft) × width (ft) × height (ft)

Next, it converts CADR into an equivalent rate of air changes per hour. If CADR is in cubic feet per minute (CFM), then:

ACH = (CADR × 60) ÷ room volume

The higher the ACH, the faster smoke particles are removed from the air. Doubling CADR or using two purifiers of the same size roughly doubles ACH, and usually cuts the clearance time about in half, all else being equal.

The clearance formula

Once ACH is known, the calculator uses a standard exponential decay model for a well-mixed room. The PM2.5 concentration over time, C(t), is modeled as:

C(t) = C₀ · e^(−ACH · t)

where:

• C₀ is the initial PM2.5 concentration (µg/m³).
• C(t) is the concentration at time t (in hours).
• ACH is air changes per hour.

To find how long it takes for the concentration to drop from C₀ to a target level C_t, we rearrange the equation to solve for time t:

Setting C(t) equal to your target concentration C_t and solving for t gives:

t = − (1 ÷ ACH) · ln(Ct ÷ C₀)

Important details:

• The natural logarithm ln(Ct ÷ C₀) is only valid when the target concentration is lower than the starting concentration. The calculator enforces this requirement.
• t is calculated in hours and usually presented in minutes for convenience.
• The same formula applies whether you use imperial or metric dimensions for the room, as long as CADR and volume are converted to consistent units internally.

How to interpret the results

The output shows how long you should expect to run the purifier at its specified CADR to reach your target PM2.5 level. Use it as a planning guide, not an exact prediction.

• Short times (for example, under 20–30 minutes) usually indicate a strong purifier relative to room size and a modest drop in pollution levels.
• Moderate times (30–90 minutes) are common when cleaning a bedroom or living room that has become smoky but is not extremely polluted.
• Very long times (over 1–2 hours) can signal that CADR is too low for the room volume, that the starting concentration is extremely high, or that the target level is very strict.

If the calculator shows a long clearance time and outdoor smoke levels remain severe, consider moving to a smaller room, improving sealing around doors and windows, or adding an additional purifier. If you start to feel unwell, follow advice from your healthcare provider or local public health authorities rather than relying on the calculator alone.

Worked example: bedroom during wildfire smoke

Imagine a bedroom that is 12 ft long, 11 ft wide, with an 8 ft ceiling. A portable purifier with a CADR of 250 CFM is placed in the room. A low-cost PM2.5 sensor shows 180 µg/m³ after smoke has seeped indoors. You want to reach 12 µg/m³.

1. Calculate room volume.
   Volume = 12 ft × 11 ft × 8 ft = 1,056 ft³
2. Calculate ACH.
   ACH = (CADR × 60) ÷ volume = (250 × 60) ÷ 1,056 ≈ 14.2 air changes per hour
3. Apply the clearance formula.
   Starting concentration C₀ = 180 µg/m³
   Target concentration Ct = 12 µg/m³
   Ratio Ct ÷ C₀ = 12 ÷ 180 = 0.0667
   Natural log ln(0.0667) ≈ −2.708
   Time in hours:
   t = −(1 ÷ 14.2) × (−2.708) ≈ 0.191 hours
4. Convert to minutes.
   0.191 hours × 60 ≈ 11.5 minutes

Under these assumptions, it takes roughly 12 minutes for the purifier to bring PM2.5 down from 180 to 12 µg/m³. In practice, you might run the purifier on high for at least 20–30 minutes, then recheck your sensor and switch to a quieter setting for maintenance once levels are stable.

Example clearance scenarios

The table below illustrates how different combinations of room size and CADR influence clearance time to a target of 12 µg/m³, starting from 150 µg/m³. Values are rounded and assume closed windows, no new smoke, and well-mixed air.

Use these examples as rough benchmarks. Your actual room may clear faster or slower depending on how well it is sealed, how air circulates, and whether new smoke continues to enter.

Practical steps to clear smoke faster

To get the most accurate and useful results from the calculator, combine it with good practical steps:

• Close doors and windows to reduce ongoing smoke infiltration.
• Seal obvious gaps around windows, sliding doors, and vents using weatherstripping, towels, or temporary tape where safe.
• Run the purifier on its highest setting during the initial cleanup phase. Higher fan speed means higher effective CADR.
• Promote mixing with a ceiling fan or a box fan pointing upward so that more room air passes through the filter over time.
• Replace clogged filters on schedule. A loaded filter can significantly reduce CADR and extend the clearance time beyond what the calculation suggests.
• Consider supplemental filtration for large spaces, such as a second purifier or a DIY Corsi–Rosenthal box using a box fan and high-MERV filters.

If a calculation suggests a long clearance time and you cannot add more filtration, using a smaller, better sealed room as a “cleaner air room” can make the time more manageable.

Health guidelines and decision-making

Public health agencies often reference two key PM2.5 benchmarks for long-term exposure:

• Annual average guideline around 12 µg/m³ (for relatively clean indoor air over long periods).
• 24-hour average guideline around 35 µg/m³ (for daily exposure).

During wildfire smoke events, indoor PM2.5 can easily exceed 100–300 µg/m³ if outdoor air is very polluted. In these conditions, even reducing indoor levels to somewhere below 35 µg/m³ can be a meaningful improvement while you work toward cleaner air.

Ways to use the calculator in context:

• If it shows a short time to reach your chosen target, you can be more confident that staying in that space with the purifier running is helping substantially.
• If it estimates more than an hour to reach an intermediate target (for example, 35 µg/m³), it may be worth moving to a smaller room, adding another purifier, or using a community cleaner air shelter if available.
• If you or someone in the space is in a sensitive group (children, older adults, pregnant people, or those with heart or lung disease), treat the calculation as a rough guide and follow medical advice first.

This tool cannot tell you whether it is medically safe to remain in a particular room. Always defer to your clinician or local health authority during severe smoke events.

Assumptions and limitations

The calculator uses a simplified model. Keep these assumptions and limitations in mind:

• No new smoke added: It assumes doors and windows stay closed and no new significant smoke enters while the purifier runs.
• Well-mixed air: It assumes the entire room has about the same PM2.5 level at any given time, which is more accurate when a fan or the purifier’s airflow circulates air effectively.
• Stable CADR: It assumes the purifier maintains its rated CADR. Real-world CADR can be lower if filters are clogged, fan speed is reduced, or the device is poorly positioned.
• Correct units: It expects CADR in cubic feet per minute when using imperial room dimensions. If your purifier lists CADR in m³/h, you will need to convert it or calculate ACH separately.
• PM2.5 only: It focuses on fine particles and does not directly address gases or odors. For noticeable smells, a purifier with activated carbon media can help, but that is not captured in the formula.
• Informational use only: Results are estimates for planning. They are not guarantees of air quality or health outcomes.

Units, inputs, and common questions

To reduce confusion about units and typical ranges:

• CADR units: Most portable purifiers in North America list CADR in CFM. If you see CADR in m³/h, divide by about 1.7 to approximate CFM, or calculate ACH directly and enter that value using a separate ACH-focused tool.
• Room size: Bedroom volumes are often between 800 and 1,500 ft³, while large open-plan areas can exceed 3,000 ft³.
• PM2.5 levels: Indoor air away from smoke events may be below 12 µg/m³. In smoky conditions, indoor readings over 100 µg/m³ are not unusual, especially if windows or ventilation bring in outdoor air.

Examples of common questions:

• Can I use this for cigarette or cooking smoke? The math is the same for particles, so you can use it as a rough guide, but real-world sources may be more intermittent.
• What if I use multiple purifiers? You can add up their CADR values if they are in the same room and unobstructed, then enter the total CADR in the calculator.
• What if my purifier has a lower speed setting? Use the CADR that corresponds to the fan speed you actually plan to use. Manufacturer documentation sometimes lists CADR at different speeds.

Related planning tools

For deeper planning around indoor air quality during smoke events, you may find these related tools helpful:

• Air Changes per Hour Calculator: Convert room size and CADR to ACH, or compare different purifiers and speeds.
• Portable Air Cleaner Smoke Runtime Planner: Estimate how long to run a purifier over the course of a day while balancing noise and energy use.
• Air Quality Index (AQI) Calculator: Translate PM2.5 measurements into AQI categories used by public health agencies.
• Wildfire Smoke Infiltration Risk Calculator: Explore how building tightness and ventilation affect how much outdoor smoke enters indoors.

References and data sources

The model used here is based on standard first-order removal kinetics for well-mixed indoor spaces, which is widely used in ventilation and filtration calculations. PM2.5 guideline values and health context are informed by public health agencies such as the U.S. Environmental Protection Agency (EPA) and the World Health Organization (WHO). For official recommendations, always consult those primary sources and your local air quality advisories.