Relative Risk Calculator Formula

Understand the math behind the relative risk calculator. Each variable explained with a worked example.

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Formulas Used

Relative Risk (RR)

relative_risk = risk1 / risk2

Risk Group 1

risk_group1 = risk1

Risk Group 2

risk_group2 = risk2

Risk Difference

risk_diff = risk1 - risk2

NNT (Number Needed to Treat)

nnt = 1 / abs(risk1 - risk2)

Variables

VariableDescriptionDefault
aGroup 1 - Event (a)30
bGroup 1 - No Event (b)70
cGroup 2 - Event (c)15
dGroup 2 - No Event (d)85
risk1Derived value= a / (a + b)calculated
risk2Derived value= c / (c + d)calculated

How It Works

How to Calculate Relative Risk

Formula

RR = [a / (a+b)] / [c / (c+d)]

Relative risk compares the probability of an event in the exposed group to the probability in the unexposed group. RR = 1 means no difference. RR > 1 means higher risk in the exposed group. RR < 1 means the exposure is protective. The Number Needed to Treat (NNT) = 1 / |Risk Difference|.

Worked Example

Group 1: 30 events out of 100. Group 2: 15 events out of 100.

a = 30b = 70c = 15d = 85
  1. 01Risk Group 1 = 30 / (30+70) = 30/100 = 0.30
  2. 02Risk Group 2 = 15 / (15+85) = 15/100 = 0.15
  3. 03RR = 0.30 / 0.15 = 2.0
  4. 04Risk Difference = 0.30 - 0.15 = 0.15
  5. 05NNT = 1 / 0.15 ≈ 6.67
  6. 06Group 1 has twice the risk; for every ~7 people treated, one event is attributable to exposure.

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