COVID area - infection probability calculator

Covid infection probability in group of people

The probability that someone is infected in the group of people can be calculated. It is not so hard. Only 3 numbers is needed. You have to know the population in your area (it can be village, city, state or whole country). You have to know or determine the number of infected people in that area. The last thing is to count the size of your group (party, colleagues in office, sport club, concert, meeting, ...) Put these numbers into our calculator and see what happens.

Fill the numbers or use example.

Total population in area:
Total active cases in area:
Group of people:

probability that at least one person is infected in group of people


1) Party for 30 people in California

November 1, 2020

Total population39,512,223
Active cases436,869
show results

2) 200 people attend demonstration in France

November 1, 2020

Total population65,322,146
Active cases1,213,179
show results

3) 100 people at concert in Prague

November 1, 2020

Total population1,309,000
Active cases23,184
show results

Calculation background

Covid area calculator uses modified math rule known as birthday paradox or birthday problem (wiki). The formula is adapted like this:

function doAreaCalc(totalPopulation, activeCovidCases, peopleCount) {
    let p = 1

    for (let i = 0; i < peopleCount; i++) {
        p = p * ((totalPopulation - i - activeCovidCases)/(totalPopulation - i))

    return ((1 - p) * 100);

Why it is called paradox? The more people together, the greater risk of infection. Everyone probably understands that. But how fast is the risk of infection growing with the growing number of people? Intuition cannot be trusted here. We have to do the math. If you take only 23 random people, you have a 50% chance that at least 2 of them will have the same date of birth. In the case of 57 people, it is already a 99% probability. The paradox points out that this is a much higher probability than one would intuitively think.

What is it useful for? There is always group of people when you arrange meeting, event or simple when you go shopping. Imagine that you are living in the city with a population of about 1.2 million. Imagine that there are 60,000 infected people in this city. Lets make a party in this city. What is the probability of having infected person at your party event?
For 10 participants is 33.5 % probability one of them is infected.
For 20 participants is 55.8 % probability one of them is infected.
For 30 participants is 70.6 % probability one of them is infected.
For 40 participants is 80.5 % probability one of them is infected.

This is one of the reasons why they limit gathering people in pandemic crisis. The chances of spreading the disease from a single meeting are high. One infected person whose probability of participation is unexpectedly relatively high can easily spread the disease. Even with a low number of officially infected people. Due to the significant number of those infected with only mild symptoms or asymptomatic, this is a real possible problem.

Try to use numbers from your area and you will see the risk of covid infection. Be sure that you are using correct numbers. Total active cases is amount of people who are currently infected.

Signs and symptoms of COVID-19

Symptomatic patients

In laboratory-confirmed cases of COVID-19, the most common clinical symptoms include fever (88%), dry cough (68%), fatigue (38%), dyspnoea (19%), muscle and joint pain (15%), and less common diarrhea (4%) and loss of appetite, nausea and vomiting (5%) are common, in severe cases pneumonia. Loss of smell and taste and conjunctivitis have also been reported in some patients. Thrombotic complications (31% of patients), especially venous thromboembolism (27%) or arterial thrombosis (2.7%), occurred in patients hospitalized in intensive care units even after standard thromboprophylaxis. In addition to thrombosis, cardiomyopathy, acute renal impairment and encephalitis have been reported in patients with severe COVID-19.

For the purposes of surveillance of COVID-19 disease in the countries of the European Union, a case definition was established (ECDC 29 May 2020). A person with at least one of the following symptoms meets the clinical criteria for COVID-19 (source):

  • Cough
  • Fever
  • Stuffiness
  • Sudden loss of smell, taste, change in taste perception
  • Other non-specific symptoms may include headache, chills, muscle aches, fatigue, vomiting and / or diarrhea

Asymptomatic patients

According to the data available so far, courses of asymptomatic patients are reported in 10-50% of individuals, ie no clinical signs are present in these individuals, and only testing shows the presence of the virus. They are usually detected / diagnosed, for example, when searching for contacts of obviously ill people. In some people, the symptoms develop later. Some individuals are asymptomatic throughout. It is people without symptoms that can play an important role in the spread of COVID-19.

Covid transmission

Contact and droplet transfer

Transmission through direct, indirect or close contact with an infected person via infectious secretions such as saliva and respiratory secretions or their respiratory droplets, which are excreted by coughing, sneezing, speaking or singing.

Airborne transmission

The spread of an infection caused by the dissemination (spread) of infectious aerosols, which float in the air over long distances for a long time. Discussions are underway as to whether aerosol spread may occur in indoor facilities with poor ventilation.

Transmission through contaminated surfaces

Respiratory secretions or droplets excreted by an infected individual may contaminate surfaces and objects. Viable SARS-Cov-2 virus and / or RNA detected by RT-PCR can be found on contaminated surfaces for hours to days depending on the environment (including temperature and humidity) and the type of surfaces.

Other ways

Many questions have not yet been answered.

How to reduce risk of getting Covid

  • Follow advice, recommendations and regulations announced by your local authorities.
  • Keep your social distance.
  • Wear a mask.
  • Open windows more often.
  • Clean your hands and avoid touching surfaces.
  • For more visit: Coronavirus disease (COVID-19) advice for the public

Data sources

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