The Paulos Safety Index

Statistics of Risk are reported many ways: how many people in a million, how many people in a city, how many people in a state. The inconsistency confuses people and is further complicated by reporting different ways of figuring risk: annual risk, lifetime risk, theoretical risk for a person that lives to 75, or years of life lost. All of these ways of reporting risk are valid, however, by reporting the news using all of them, people have no standard by which to judge. How does an annual risk compare to a lifetime risk? Furthermore, many people become confused by the large numbers, Did he say, "a billion" or "a million?"

Paulos suggests creating a standard for the media and health organizations to use when reporting risk. When people become familiar with a standard they have a way of making comparisons. To address the confusion created by large numbers, he suggests using logarithms, the way they are used in pH and the Richter scale. For example we all have learned that a 6.0 on the Richter scale is a bad earthquake, where a 3.0 is not that bad, even though few people understand the logarithms or energy calculations that make up the Richter scale. Similarly, consistent use of the safety index would lead people to have a good standard for judging risk even though they will not need to use the math on which it is based.

Written 2001

Reformatted: January 2010


Here, we create a chart of collected risk data to show how the Paulos Safety Index would organize available data to help people understand risk.

Explaining the Chart:

The columns compare two of the traditional ways of reporting fatality risk with the Annual Safety Index.

  • The first column, 1 person in X, tells us what crowd size would typically have one affected member. For example, about 1 American in 10,000 will commit suicide each year. For this method, the larger the number, the safer.
  • The second column, Y people in 1 million, tells us how many people out of a crowd of one million will be affected. For example about 100 people in a million will commit suicide each year. In this case the lower the number, the safer we are.
  • The third column, the Safety Index Number, is the logarithm of the number in the first column. In this column numbers have been converted into a scale that is easy to discuss. The higher this number is the safer we are.
  • The fourth column, Annual Safety from Fatality Index, lists things that have killed Americans over the last few years.
  • The fifth column shows the safety index number for each item in the forth column. "(all)" denotes that these items were reported as a group risk; "(each)" denotes that each of these items have approximately the same safety (or risk) value.
  • Method: Safety Index = Log( number killed / total number )


Related Pages at this site:

One Person In X

Y people in 1 million
Safety Index Number Annual Safety from Fatality Index

1,000,000,000 0.001
316,227,766 0.003
100,000,000 0.01
31,622,777 0.03
10,000,000 0.1
3,162,278 0.3
1,000,000 1
316,228 3
100,000 10
31,623 31
10,000 100
3162 316
1000 1000
316 3162
100 10,000
32 31,623
10 100,000
Terrorist (in USA), Freeze (each)
Lightning, Tornado, Animal (each)
Electrocution 5.54
Airplane crash
Choking 5.20
Bicycle 5.11
Radon & Poison (each) 4.93
AIDS & Cars (each)
Breast Cancer (Female)
Stroke 3.23
Cancer (all types)
Alcohol, Tobacco, & Drugs (all) 2.66
Heart Disease
Death (all causes) 2.06
risk scale

risk scale

Safety Index as a Lesson:

Purposes: To promote thematic learning between math, science, and social studies. To motivate the use of logarithms.

Resources: The books shown in the side bar, Science News, and other science journals, the newspaper, the Internet

Method: Have students collect articles on risk from various sources. Discuss how various methods are used to report risk. Convert each into logarithm. Make a wall chart. Discuss how the chart helps compare risks. What numbers correspond to our perception of "safe?" What numbers correspond to our perception of "dangerous?"


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