Fart Clearance Time Calculator

What this calculator estimates

This tool estimates how long it takes for an odor event to become hard to detect after it’s released into a room, assuming the smell behaves like a well-mixed airborne contaminant and the main removal mechanism is ventilation (fresh air replacing indoor air). In other words: it’s an odor dissipation estimate driven by room size, air-change rate, the amount released, and your chosen “detection threshold.”

Because real odors are complicated (different compounds, different noses, different airflow patterns), the output should be treated as a reasonable ballpark for comparing scenarios (fan on vs. off, small bathroom vs. large living room, window cracked vs. sealed), not as an exact promise.

How the estimate works (simple model)

The calculator uses a first‑order ventilation decay model (the same basic idea used for CO₂ or other indoor pollutants when removal is dominated by air exchange). The steps are:

1. Convert fart volume to an initial concentration in the room by dividing by room volume.
2. Convert ventilation (ACH) to a removal rate constant per hour.
3. Let concentration decay exponentially until it falls below your detection threshold.

Key definitions

• Room volume (m³): the total air volume. Larger rooms dilute the same release more.
• Ventilation rate (ACH): “air changes per hour.” 1 ACH means a volume of fresh air equal to the room’s air volume is exchanged in about an hour (in a well-mixed sense).
• Fart volume (L): the volume of gas released. More volume increases the initial concentration.
• Detection threshold (ppm): the concentration you consider “no longer noticeable.” Lower thresholds mean longer clearance times.

Formulas used

1) Initial concentration (ppm)

Convert the released volume to cubic meters and divide by the room volume. If V_f is fart volume in liters and V_room is room volume in m³:

• 1 L = 0.001 m³
• Volume fraction (unitless) = (V_f × 0.001) / V_room
• ppm = volume fraction × 1,000,000

2) Ventilation decay

For a well‑mixed room with ventilation rate ACH, concentration decays as:

3) Clearance time to a threshold

Set C(t) equal to the threshold C_th and solve for time:

t = (1 / ACH) × ln(C₀ / C_th)

If the initial concentration C₀ is already below the threshold, the calculator should return ~0 minutes (already “cleared”).

Interpreting your results

• Short times (minutes): typically higher ACH (fan/window), larger rooms, or higher threshold (less sensitive nose / less strict “clear”).
• Long times (tens of minutes+): low ACH (closed, still air), small rooms (bathroom, car cabin), larger release volume, or very low threshold.
• Log behavior: doubling the ventilation rate roughly halves the time, while changing the threshold affects time logarithmically (going from 5 ppm to 1 ppm adds time, but not 5× as much).

Worked example

Scenario: A small bathroom with mechanical exhaust.

• Room volume: 8 m³
• Ventilation: 4 ACH (fan running)
• Fart volume: 0.10 L
• Threshold: 5 ppm

Step 1: Initial concentration

• 0.10 L = 0.0001 m³
• Volume fraction = 0.0001 / 8 = 0.0000125
• C₀ = 0.0000125 × 1,000,000 = 12.5 ppm

Step 2: Time to 5 ppm

• t = (1 / 4) × ln(12.5 / 5)
• t = 0.25 × ln(2.5) ≈ 0.25 × 0.916 = 0.229 hours
• 0.229 hours × 60 ≈ 13.7 minutes

So in this simplified model, it takes about 14 minutes for the concentration to fall below 5 ppm in that bathroom with the fan on.

Comparison table: typical scenarios (ballpark)

The table below illustrates how room size and ventilation can change clearance time for the same release and threshold. Assumptions for the rows: fart volume 0.10 L, threshold 5 ppm, well-mixed air.

Assumptions & limitations (why real life may differ)

• Well-mixed air: The model assumes the odor instantly mixes evenly throughout the room. In reality, it forms a plume and mixes over time; near-field smells can be stronger initially.
• Ventilation dominates removal: We treat “clearance” as being driven mainly by air exchange. Real odor can also be reduced by adsorption to fabrics, chemical reactions, filtration (HEPA/charcoal), and surface deposition—sometimes faster, sometimes slower.
• Single-shot release: The math assumes one release at t = 0 with no continuing source. Ongoing sources (multiple events, lingering emissions) will extend the effective time.
• Threshold is subjective: Sensitivity varies widely between people and compounds. “5 ppm” is a modeling knob, not a universal biological constant.
• ACH is an effective average: Real ACH varies with door position, fan performance, wind, HVAC cycling, and pressure differences. Short-circuiting airflow (fresh air entering and exiting without mixing) can also reduce effective removal.
• Temperature/humidity and chemistry: Perceived odor intensity can change with humidity and temperature; the calculator does not model those effects.
• Not all smell compounds behave the same: Different gases have different detection limits and interactions. Modeling everything as a single “equivalent ppm” is a simplification.

Practical tips to reduce clearance time

• Increase ACH: turn on the exhaust fan, open a window, or crack a door to encourage cross‑flow.
• Improve mixing (carefully): a small fan can distribute air so ventilation removes it more uniformly—though it may spread odor to adjacent areas.
• Use filtration/adsorption: activated carbon can reduce certain odor compounds; this is outside the calculator but can help in practice.

FAQ

What is a “good” ACH?

It depends on the space. Bathrooms with a working exhaust may reach a few ACH when the fan is on, while a closed, still room can be well under 1 ACH. The calculator is most useful for comparing “fan off” vs “fan on” and “window closed” vs “window open.”

How do I estimate room volume?

Multiply length × width × height (in meters). If you measure in feet, convert to meters first (1 ft ≈ 0.3048 m).

Why does lowering the threshold increase time a lot?

Because clearance time depends on the natural log of the ratio C₀/C_th. Tightening the threshold from 5 ppm to 1 ppm increases time, but not in a simple linear way.