`%e_4 = sqrt(%e_1^2+%e_2^2+%e_3^2)`

Enter a value for all fields

The Uncertainty in Multiplication and Division calculator computes the relative uncertainty of measurements that are combined through multiplication or division. 

INSTRUCTIONS: Enter the following:

• (%e₁)  This is the percent relative uncertainty of the first measurement.
• (%e₂)  This is the percent relative uncertainty of the second measurement.
• (%e₃)  This is the percent relative uncertainty of the third measurement.

Uncertainty in Multiplication and Division (%e₄): The final relative uncertainty is returned as a percentage.

Related Calculators

• Uncertainty in Multiplication and Division
• Uncertainty in Addition and Subtraction
• Relative Uncertainty

The Math / Science

The uncertainty in multiplication and division equation calculates the relative uncertainty of measurements that are combined through multiplication or division. However, for the relative uncertainties must be all converted in to percentages to be used in the equation above.  The equation for the uncertainty in multiplication and division is:

  ` %e_4 = sqrt(%e_1^2 + %e_2^2 + %e_3^2)`

where 

• %e₁ is the percent relative uncertainty associated with the first measurement. 
• %e₂ is the percent relative uncertainty associated with the the second measurement. 
• %e₃ is the percent relative uncertainty associated with the third measurement.
• %e₄ is the final relative uncertainty. 

Related Topics

• Uncertainty in addition and subtraction (for the Spanish site click here)
• Percent relative uncertainty (for the Spanish site click here)
• Relative uncertainty (for the Spanish site click here)

References

Harris, 9th Edition.  Pp.53

[1] For the Spanish site click here