Uncertainty in addition and subtraction

The Uncertainty in Addition and Subtraction calculator computes the uncertainty in addition and subtraction based on the experimental absolute uncertainty in three measurements.

INSTRUCTIONS:   Enter the following:

• (e₁)  This is the experimental absolute uncertainty of one measurement (unit-less).
• (e₂)  This is the experimental absolute uncertainty of another measurement (unit-less).
• (e₃)  This is the experimental absolute uncertainty of a third measurement (unit-less).

Uncertainty in Addition and Subtraction (e₄): The uncertainty is returned as a real number.  However, this can be automatically converted to a percentage or decibels via the pull-down menu.

Related Calculators

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

The Math / Science

The uncertainty in addition and subtraction^[1] equation calculates the absolute uncertainty for measurements with absolute uncertainties that are being added or subtracted.

The equation for uncertainty in addition and subtraction is 

  `e_4 = sqrt(e_1^2 + e_2^2 + e_3^2)`

where 

• e₁ is experimental  absolute uncertainty of one measurement in the (unit-less)
• e₂ is experimental absolute uncertainty of another measurement (unit-less)
• e₃ is experimental absolute uncertainty of a third measurement (unit-less)
• e₄ is the absolute uncertainty of the combined absolute uncertainty measurement. 

Related Topics

• Relative Uncertainty (for the Spanish site click here)
• Percent Relative Uncertainty (for the Spanish site click here)

References

Harris, D., Quantitative Chemical Analysis, 9th Ed., W. H. Freeman,  Pp.52 (2015).

[1] For the Spanish site click here.