What this Indoor Smoke Particle Decay Calculator does
The Indoor Smoke Particle Decay Calculator estimates how much of a starting smoke particle concentration remains after a chosen number of hours. It uses three values: an initial concentration in units, a decay fraction per hour, and elapsed time in hours. Its result, Remaining concentration (units), is a mathematical estimate based on those entries.
The model treats the entered concentration as a quantity that falls by the same fraction during every hour. For example, a decay fraction of 0.25 means the model removes 25 percent of the amount present in each hour. It does not subtract 25 percent of the original amount repeatedly. Since the fraction applies to what remains, the modeled decline is exponential.
This is a simplified worksheet-style calculation. It does not measure air, identify particle types, or predict a room’s measured air quality. Real indoor conditions can change over time as smoke sources, ventilation, filtration, doors, windows, and air movement change. Use a consistent concentration unit for the initial value and the result. The tool carries that unit through the arithmetic.
How to use the Indoor Smoke Particle Decay Calculator
Enter an initial concentration between 0 and 1,000,000 units. This represents the starting value for the calculation. The number may come from a hypothetical example or a measurement, but the calculator does not verify where it came from or what it represents.
Next, enter a decay fraction from 0 to 0.99. Use a decimal fraction rather than a percentage number. For example, enter 0.25 for 25 percent per hour, or 0.1 for 10 percent per hour. The value describes the assumed fraction removed from the amount present during each hour. It is not a universal rate for indoor smoke.
Finally, enter elapsed time from 0 to 1,000 hours. The calculator allows decimal hours, so 1.5 represents one and a half hours. Review the result in the same concentration units used for the starting value.
- Initial concentration: the amount at the start of the modeled period.
- Decay fraction per hour: the assumed share removed from the amount present each hour.
- Elapsed time: the duration over which the repeated reduction is applied.
At zero elapsed hours, the result equals the initial concentration. At a zero decay fraction, the model keeps the concentration unchanged regardless of elapsed time. A higher decay fraction generally produces a lower modeled remainder after the same positive duration.
How the Indoor Smoke Particle Decay Calculator formula works
The formula is initial_concentration × (1 − decay_fraction_per_hour)hours. In calculator notation, the exponent is evaluated with Math.pow. First, the formula subtracts the hourly decay fraction from 1. That gives the share remaining after one hour. It then raises that share to the number of elapsed hours and multiplies by the initial concentration.
Consider a worked example with an initial concentration of 1,000 units, a decay fraction of 0.25 per hour, and 2 hours. The hourly remaining share is 1 − 0.25, or 0.75. The two-hour factor is 0.75 raised to the power of 2, which is 0.5625. Multiplying 1,000 units by 0.5625 gives 562.5 units. The calculation leaves the concentration unit unchanged.
The repeated-fraction assumption matters. After the first hour in this example, 750 units remain. The second hour removes 25 percent of 750, leaving 562.5. This differs from subtracting a fixed 250 units in each hour. If a real process follows a different pattern, this formula may not describe it well.
The formula accepts a fraction up to 0.99, so the hourly remaining share stays at or above 0.01. This avoids a negative base and keeps the result defined for the supported nonnegative time range. At the maximum fraction, the model retains one percent of the current amount per hour.
Use cases for the Indoor Smoke Particle Decay Calculator
The calculator can help explain how a repeated proportional decrease behaves. It can support a classroom exercise, a personal air-quality discussion, or a rough comparison of hypothetical scenarios. For instance, a reader can keep the initial concentration and time fixed while trying different assumed hourly fractions to see how sensitive the result is to that assumption.
It can also make time easier to reason about. A fraction that sounds modest may compound over several hours, while the same fraction over a short interval has a smaller effect. The output gives one numerical result for the specified inputs, which can help readers follow the arithmetic or document a simple scenario.
For wellness and activity planning, treat this estimate as a conceptual aid only. It does not establish that a room is safe for exercise, sleep, or other activity, and it cannot replace appropriate measurement or health guidance. If the starting concentration is not measured using a known method, the numeric result may have little practical meaning beyond demonstrating the formula.
Other factors to consider when calculating indoor particle decay
Indoor air does not necessarily behave as a single well-mixed space. Concentrations may differ across rooms or locations, and air movement may carry particles between areas. A decay fraction entered for one scenario may not apply at another time or place.
Smoke can also continue to enter the air while the model assumes no new source. Opening a window, changing ventilation, running filtration, or moving between indoor and outdoor spaces can alter the conditions. The formula has no separate inputs for these events, particle size, room dimensions, or source strength. It cannot distinguish particles from different sources.
For a meaningful comparison, keep the units consistent and document where the initial value and assumed fraction came from. Avoid presenting an estimated output as a direct measurement. If a decision depends on actual exposure or health effects, use suitable measurement and advice from qualified sources for the specific situation.
Frequently asked questions
What does the decay fraction per hour mean?
It is the assumed share removed from the concentration that is present during each hour. A value of 0.2 means 20 percent per hour in the model. It is an input assumption, not a rate supplied or validated by the calculator.
Can I enter a percentage such as 25?
No. Enter a decimal fraction between 0 and 0.99. For 25 percent, enter 0.25. Entering 25 exceeds the supported range and does not represent 25 percent in this formula.
Why does the result use the same units as the initial concentration?
The formula multiplies the initial concentration by a dimensionless fraction. The hourly decay fraction and elapsed-time exponent do not change the concentration unit, so the output remains in the unit you entered.
Does the result predict a measured room concentration?
No. It is the result of a simplified exponential model. It does not account for ongoing smoke, changing ventilation, uneven mixing, or other room-specific conditions, and it is not an air-quality measurement.
What happens if I enter zero hours?
The exponent becomes zero, so the time factor is 1. The result equals the initial concentration, reflecting that no modeled decay time has passed.