How this calculation works
An air change is a volume-flow ratio, not a promise that every original molecule has left the room. In a perfectly mixed room, clean incoming air mixes with air already present, so the remaining excess concentration decays exponentially.
ACH = flow/volume; C(t) = background + (initial − background)exp(−effective ACH × t)A worked example
A 100 m³ room with 300 m³/h effective clean-air flow has three air changes per hour. Starting at one hundred concentration units with zero background, one hour leaves about 4.979 units. Reaching ten units requires ln(10)/3 hours, about 46.052 minutes. Halving the effective clean-air share doubles that time under the same ideal assumptions.
Good to know
Fixed-volume source-free well-mixed decay only; no ongoing emissions, deposition, multi-zone exchange or health clearance. Do not treat the effective-flow input as a universal correction for every pollutant. A filter’s removal, outdoor-air fraction and actual mixing can have different constituent-specific effects.
Reference: ASHRAE — ventilation and infiltration (opens in a new tab) ↗
What the model answers
An air change is a volume-flow ratio, not a promise that every original molecule has left the room. In a perfectly mixed room, clean incoming air mixes with air already present, so the remaining excess concentration decays exponentially.
This page follows a constituent after its source stops. The background concentration is the limiting value approached by dilution. A continuing source, variable outdoor conditions or poorly mixed zones would require a different balance.
The Duct leakage pressure conversion calculator examines leakage measurements at specified test pressures. Duct leakage is not automatically equivalent to clean air delivered to the occupied room.
Measure and enter consistently
Room volume and flow must use matching cubic-metre and hour units. The effective share represents the portion of flow that actually supplies clean-air-equivalent removal for the modeled constituent. It is not an automatically determined room mixing factor.
All concentration inputs use one consistent unit. Their relative values determine the decay. Initial concentration must be at least background, because this page models removal of excess concentration rather than buildup from a cleaner initial state.
Interpret the result
A target already met at the initial state has zero elapsed time. A lower target at or below background is not reached in finite time by this asymptotic model. Zero effective removal also cannot lower the starting concentration.
The plotted curve and the time metric describe the same rate constant. They do not establish safe occupancy, infection risk, a regulatory exposure limit or that the room actually mixes uniformly. Those questions require appropriate measurements and guidance.
Work through the numbers
A 100 m³ room with 300 m³/h effective clean-air flow has three air changes per hour. Starting at one hundred concentration units with zero background, one hour leaves about 4.979 units.
Reaching ten units requires ln(10)/3 hours, about 46.052 minutes. Halving the effective clean-air share doubles that time under the same ideal assumptions.
Where this model stops
Fixed-volume source-free well-mixed decay only; no ongoing emissions, deposition, multi-zone exchange or health clearance.
Do not treat the effective-flow input as a universal correction for every pollutant. A filter’s removal, outdoor-air fraction and actual mixing can have different constituent-specific effects.
A few questions, answered
Does one air change remove everything?
No. Perfect mixing leaves exp(−1), about 36.8 percent of the initial excess after one effective air change.
Why can the target be unreachable?
A target at or below the fixed background cannot be crossed by source-free dilution toward that background.