What relative risk is and why you calculate it

Relative risk is a number that tells you how much more (or less) likely something is to happen in one group compared to another group. It answers the question: "Is this outcome twice as common in group A as in group B, or half as common?" You calculate it by dividing the risk in one group by the risk in the other group.

Relative risk appears in medical studies, workplace safety reports, and public health data. A relative risk of 2 means the outcome is twice as likely. A relative risk of 0.5 means it is half as likely. A relative risk of 1 means both groups have the same risk — no difference at all.

The calculation itself is straightforward arithmetic, but the setup matters. You need to know how many people in each group experienced the outcome, and how many people were in each group to begin with. Without those numbers, you cannot compute relative risk.

Key Takeaways

  • Relative risk is calculated by dividing the risk in group A by the risk in group B, where risk means the number of people with the outcome divided by the total number of people in that group.
  • You need four pieces of information: how many in group A had the outcome, the total size of group A, how many in group B had the outcome, and the total size of group B.
  • A relative risk above 1 means group A has higher risk; below 1 means group A has lower risk; exactly 1 means no difference.
  • Relative risk is different from absolute risk, which is just the percentage of people in one group who experienced the outcome.

The formula and what each part means

The formula for relative risk is:

Relative Risk = (Risk in Group A) ÷ (Risk in Group B)

Each "risk" is itself a fraction. Risk in Group A means: the number of people in group A who had the outcome, divided by the total number of people in group A. The same applies to group B.

Here is a concrete example. Suppose you are comparing smokers and non-smokers for lung cancer diagnosis over ten years. In a study of 1,000 smokers, 40 developed lung cancer. In a study of 1,000 non-smokers, 4 developed lung cancer.

Risk in smokers = 40 ÷ 1,000 = 0.04 (or 4 percent). Risk in non-smokers = 4 ÷ 1,000 = 0.004 (or 0.4 percent). Relative risk = 0.04 ÷ 0.004 = 10. This means smokers in this study were 10 times as likely to develop lung cancer as non-smokers.

Step-by-step calculation with a real example

Start by organizing your data into a straightforward table. You need four numbers: outcomes in group A, total in group A, outcomes in group B, total in group B.

Suppose a company tests two safety training programs. Program X is given to 500 workers; 10 had workplace injuries in the next year. Program Y is given to 500 workers; 20 had workplace injuries in the next year. You want to know if Program X reduces injury risk relative to Program Y.

Step 1: Calculate risk in Program X. Divide 10 by 500. Risk = 0.02 (or 2 percent).

Step 2: Calculate risk in Program Y. Divide 20 by 500. Risk = 0.04 (or 4 percent).

Step 3: Divide the first risk by the second. 0.02 ÷ 0.04 = 0.5.

The relative risk is 0.5. This means workers in Program X were half as likely to be injured as workers in Program Y. Equivalently, Program Y workers were twice as likely to be injured.

When the groups are different sizes

The groups do not have to be the same size. The calculation works the same way: divide the number of outcomes by the total in each group, then divide one risk by the other.

Suppose a hospital tracks readmission rates for two wards. Ward A treats 300 patients and 15 are readmitted within 30 days. Ward B treats 450 patients and 18 are readmitted within 30 days. Risk in Ward A = 15 ÷ 300 = 0.05. Risk in Ward B = 18 ÷ 450 = 0.04. Relative risk = 0.05 ÷ 0.04 = 1.25. Ward A patients are 1.25 times as likely to be readmitted.

The unequal group sizes do not change the method. What matters is that you calculate the risk (outcome divided by total) separately for each group, then divide one by the other.

Relative risk versus absolute risk

Absolute risk is straightforward the percentage of people in one group who experienced the outcome. Relative risk compares that percentage across two groups. They answer different questions.

In the smoking example above, the absolute risk of lung cancer in smokers was 4 percent. The absolute risk in non-smokers was 0.4 percent. The relative risk was 10. All three numbers are correct; they just tell you different things. Absolute risk tells you the actual chance. Relative risk tells you how much the chance differs between groups.

Relative risk can make a small absolute difference sound large, or vice versa. If a disease is very rare, a relative risk of 10 might still mean only a 1 percent absolute risk in the exposed group. If a disease is common, a relative risk of 1.2 might mean a 20 percent absolute risk in one group and a 17 percent risk in the other — a real difference in absolute terms.

Common mistakes and how to avoid them

The most common mistake is mixing up the numerator and denominator. Relative risk is not symmetric: the risk of A relative to B is not the same as the risk of B relative to A. If you reverse the groups, you get the reciprocal (the flipped fraction). In the safety training example, the relative risk of Program X versus Program Y was 0.5, but the relative risk of Program Y versus Program X is 2. Always be clear which group is in the numerator.

Another mistake is forgetting to divide by the group total. You cannot just compare the raw number of outcomes. If group A has 10 outcomes out of 100 people and group B has 10 outcomes out of 1,000 people, group A has higher risk even though the outcome count is the same. The risk in A is 0.1; in B it is 0.01; relative risk is 10.

A third mistake is using relative risk when the data does not support it. Relative risk requires that you know the total number of people at risk in each group. If you only know that 40 smokers got cancer and 4 non-smokers got cancer, but you do not know how many smokers and non-smokers were studied, you cannot calculate relative risk.

When to use relative risk in your own work

Use relative risk when you are comparing the likelihood of an outcome across two distinct groups and you have the full count data for both groups. It works well for comparing treatment outcomes, disease rates between populations, safety records between departments, or success rates between methods.

Relative risk is less useful when you are looking at rare events in very large populations, because the numbers can become hard to interpret. It is also not the right tool if your data comes from a case-control study (where you start with people who have the outcome and look backward), because the group sizes are artificially determined by the study design. In that case, you would use odds ratio instead, which is a different calculation.

For most straightforward comparisons where you have outcome counts and group totals, relative risk is the clearest way to communicate how much more or less likely something is in one group than another.

Frequently Asked Questions

What does a relative risk of 1 mean?

A relative risk of 1 means both groups have the same risk. The outcome is equally likely in group A and group B. There is no difference between the groups.

Can relative risk be negative?

No. Relative risk is always a positive number because it is one positive number divided by another positive number. Risk itself cannot be negative — it is always between 0 and 1 (or 0 and 100 percent).

Is relative risk the same as odds ratio?

No. Relative risk divides one risk by another. Odds ratio divides one odds by another. They are similar but not identical, and they are calculated differently. Odds ratio is used in case-control studies; relative risk is used when you know the group totals.

What if one group has zero outcomes?

If group A has zero outcomes, the risk in group A is zero, and relative risk becomes zero (assuming group B has at least one outcome). This is mathematically valid but can be hard to interpret. It means the outcome never occurred in group A but did occur in group B.

Do I need statistical software to calculate relative risk?

No. The calculation is straightforward division and can be done with a calculator or spreadsheet. Statistical software is useful if you want to calculate confidence intervals around the relative risk or test whether the difference is statistically significant, but the basic calculation requires only arithmetic.