Transmission Probability Calculator

Calculator Form

Enter Your Inputs

Choose a calculation mode, provide values, and submit. The page returns the result above this form.

Calculation mode

Observed mode uses transmissions and exposures. Repeated mode stacks per-contact risk. Rate mode converts a rate over time into a probability.

Observed transmissions

Count successful transmissions.

Total exposures

Count total transmission opportunities.

Future exposures

Used for forward projection.

Confidence level

Applied to the Wilson interval.

Per-contact probability (%)

Enter the risk for one contact.

Current contacts

Contacts in the current scenario.

Future contacts

Optional comparison horizon.

Rate per chosen time unit

Example units: day, week, or month.

Current duration

Duration for the main estimate.

Future duration

Optional comparison period.

Graph horizon / points

Controls chart depth and smoothness.

Decimal places

Applies to displayed results.

Example Data Table

Sample Scenarios

Scenario	Inputs	Main Formula	Result
Observed count	18 transmissions, 120 exposures	p = x / n	15.0000%
Repeated contacts	4% per contact, 10 contacts	1 − (1 − p)^k	33.5167%
Rate conversion	0.12 per day, 14 days	1 − e^−λt	81.3626%
Observed zero events	0 transmissions, 40 exposures	p = x / n	0.0000%

Formula Used

Transmission Probability Formulas

1) Observed count mode

Point estimate: p = x / n

Standard error: SE = √(p(1−p)/n)

Future cumulative probability: P(at least one) = 1 − (1 − p)^m

2) Repeated contact mode

Per-contact risk: p_c

Zero transmissions after k contacts: (1 − p_c)^k

At least one transmission: 1 − (1 − p_c)^k

3) Rate to probability mode

Rate: λ

Duration: t

Probability over time: P = 1 − e^−λt

The observed mode also reports a Wilson confidence interval. This interval behaves better than a simple normal approximation, especially with small samples or probabilities near zero and one.

How to Use This Calculator

Steps

Select the mode that matches your data structure.
Enter either observed counts, per-contact risk, or a transmission rate.
Add future exposures, contacts, or duration for projection.
Choose your preferred decimal precision.
Submit the form to view the result above the calculator.
Review the graph, export the values, and compare sample scenarios.

FAQs

Frequently Asked Questions

1) What does transmission probability mean?

It is the chance that a transmission event occurs in a defined setting. The setting may be one exposure, several contacts, or a continuous period represented by a rate.

2) Which mode should I choose?

Use observed mode when you have actual transmission counts and total exposures. Use repeated mode for per-contact risk. Use rate mode when risk accumulates continuously over time.

3) Why is a confidence interval helpful?

A confidence interval shows the uncertainty around an estimate. Two samples can have the same point estimate but very different reliability, especially when sample sizes are different.

4) What if I observed zero transmissions?

The point estimate becomes zero, but uncertainty still matters. A confidence interval can remain above zero because limited data never proves impossibility.

5) Can the cumulative probability exceed 100%?

No. The calculator caps probability at the valid range from 0% to 100%. Repeated contacts can raise the risk sharply, but the result never exceeds certainty.

6) Is expected transmissions the same as cumulative probability?

No. Expected transmissions is an average count. Cumulative probability is the chance of at least one transmission. They answer different planning questions.

7) What does the graph show?

The chart shows how probability changes as exposures, contacts, or time increase. It helps you see how quickly risk accumulates under the chosen model.

8) Can I export my results?

Yes. The result section includes CSV and PDF download options. CSV is useful for spreadsheets, while PDF is convenient for reports and sharing.