How this calculation works
Positive correlation raises the variance of the sum. Perfect negative correlation cancels it completely when the spreads are equal.
THE FORMULA
Var(X+Y)=σₓ²+σᵧ²+2ρσₓσᵧA worked example
Standard deviations 3 and 4 with correlation 0.5 give 9+16+12 = 37.
Good to know
Correlation is meaningful when both standard deviations are positive.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Combine two variances with their covariance contribution.
The primary result is labeled “Variance of sum”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Correlation is meaningful when both standard deviations are positive.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
Standard deviations 3 and 4 with correlation 0.5 give 9+16+12 = 37.
Which rule does this calculator apply?
Var(X+Y)=σₓ²+σᵧ²+2ρσₓσᵧ