Portfolio Variance Calculator: Standard Deviation and Correlation

Portfolio Variance Calculator

Calculate two- or three-asset portfolio variance and standard deviation from weights, individual volatilities and correlations. Review every variance and covariance contribution.



Use percentages from the same return interval.

Asset inputs




Return correlations


Enter a coefficient from −1 through 1.


Portfolio variance formula

For a portfolio with weights w, standard deviations σ and correlations ρ:

Portfolio variance = Σ(wᵢ²σᵢ²) + 2Σ(wᵢwⱼσᵢσⱼρᵢⱼ), for i < j

Portfolio standard deviation, also called portfolio volatility, is the square root of portfolio variance. Enter all asset standard deviations for the same return interval—for example, all monthly or all annual. Variance is reported both as a decimal squared and in percentage-points squared (%²).

Verified examples

InputsVariancePortfolio standard deviation
60% at 15%, 40% at 10%, correlation 0.300.011860 or 118.6000%²10.8904%
50% at 12%, 30% at 18%, 20% at 8%; correlations 0.20, 0.10 and 0.400.0089512 or 89.5120%²9.4611%
50% at 10%, 50% at 10%, correlation −1.0000%

How to use this calculator

  1. Select two or three assets.
  2. Enter portfolio weights that total 100%.
  3. Enter each asset’s standard deviation and the pairwise correlations, all measured from compatible returns.
  4. Calculate and review total variance, volatility, the diversification reduction and each component.

Limits and assumptions

  • Weights must range from 0% through 100% and total 100% within 0.01 percentage point. Short positions and leverage are not modeled.
  • Standard deviations must range from 0% through 1,000%. Correlations must range from −1 through 1. Numeric inputs accept up to six decimal places.
  • For three assets, the three correlations must form a mathematically valid correlation matrix. Pairwise values can each look valid but still be impossible together.
  • The weighted-average volatility card is the perfect-positive-correlation benchmark, not another estimate of actual portfolio risk.
  • Historical volatility and correlation can change. This calculator does not estimate inputs from prices, forecast losses, model non-normal returns or provide investment advice.

Frequently asked questions

Is portfolio variance the same as portfolio standard deviation?

No. Standard deviation is the square root of variance and is expressed in the same percentage unit as returns. Variance is expressed in squared units.

Why does correlation affect portfolio risk?

Assets that do not move together perfectly can offset part of each other’s variability. Lower correlation generally reduces portfolio standard deviation for nonnegative weights.

Can three correlations be invalid even when each is between −1 and 1?

Yes. They must also be jointly consistent. The calculator checks the determinant condition for a three-asset correlation matrix.

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