Relative Risk Calculator

What the relative risk calculator does

Relative risk, also called the risk ratio, compares how often an outcome happens in one group against another. This calculator works it out from a two-by-two table of counts: the events and non-events in an exposed group and in a control group. The result says how many times more, or less, likely the outcome is in the exposed group.

It is one of the core measures of epidemiology, the standard way to express whether an exposure raises or lowers risk. Below is how it works and an important limit on what it tells you.

How to use it

1. Enter the exposed group counts: the number of events and the number of non-events.
2. Enter the control group counts in the same way.
3. Press Calculate for the relative risk, or Reset to clear it.

How relative risk is worked out

First the calculator finds the risk in each group on its own, the events divided by the group total, which is the plain probability of the outcome for someone in that group. Then it divides one by the other:

Relative risk = risk in the exposed group ÷ risk in the control group

So relative risk is a ratio of two ordinary risks. Each risk is a simple proportion, and dividing the exposed group's risk by the control group's turns them into a single number that captures how the two compare. A ratio above 1 means the outcome is more common in the exposed group, and below 1 means it is less common.

Reading the relative risk

The value has a direct reading. A relative risk of exactly 1 means the outcome is equally likely in both groups, so the exposure makes no difference. Above 1 means higher risk in the exposed group, and the number is how many times higher: a relative risk of 3 means three times as likely.

Below 1 means the exposure is linked to lower risk, which is often called protective. A relative risk of 0.5 means the exposed group has half the risk. This makes relative risk easy to talk about, since it maps onto everyday phrases like "twice as likely" or "half as likely", which is part of why it is so widely used.

Relative risk hides the baseline

Here is the catch that matters most, and where relative risk is most often misread. A ratio tells you how the two risks compare, but not how large either one is to begin with. Tripling a risk sounds alarming, but tripling a risk of 1 in a million still leaves it at 3 in a million, which is tiny.

This is why a relative risk should always be read alongside the actual, absolute risks, which this calculator's inputs also give you. A large relative risk on a rare outcome can be far less important than a small relative risk on a common one. Headlines that shout a doubled risk without saying doubled from what are leaving out the very thing you need to judge whether it matters.

A worked example

Suppose that among 100 exposed people, 30 develop a condition and 70 do not, while among 100 control people, 10 develop it and 90 do not. The risk in the exposed group is 30 out of 100, or 0.30, and in the control group it is 10 out of 100, or 0.10.

The relative risk is 0.30 divided by 0.10 = 3, so the exposed group is three times as likely to develop the condition. Note that this is meaningful here because the risks are sizeable, 30 percent versus 10 percent. Had they been 3 in 10,000 versus 1 in 10,000, the relative risk would still be 3, but both risks would be small enough that the difference might barely matter in practice.

Entering your values

Enter the event and non-event counts for the exposed group and the control group as whole numbers. The calculator returns the relative risk. Keep the underlying risks in mind too, the events over each group's total, since those absolute figures are what tell you whether a given relative risk is a big deal or not.

Questions people ask

What is relative risk?

The ratio of the risk of an outcome in an exposed group to the risk in a control group. It says how many times more or less likely the outcome is with the exposure.

What does a relative risk of 1 mean?

That the outcome is equally likely in both groups, so the exposure makes no difference. Above 1 is higher risk, below 1 is lower, or protective.

Why does the baseline risk matter?

Because relative risk only compares the two risks, not their size. Tripling a tiny risk still leaves it tiny, so the actual risks are needed to judge whether a relative risk is important.

What does a relative risk below 1 mean?

That the exposed group has lower risk than the control group. A relative risk of 0.5, for instance, means half the risk, which is often described as a protective effect.

References

A quick note on where the methods here come from. Relative risk and the comparison of proportions between groups are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook covering risk, proportions, and their comparison.

1. NIST/SEMATECH e-Handbook of Statistical Methods (comparing proportions and risk). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (proportions and their comparison). https://openstax.org/details/books/introductory-statistics-2e