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Combined standard uncertainty calculator

Combine three independent standard uncertainties by the root-sum-of-squares method.

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Your result

Combined standard uncertainty5
First variance contribution9
Second variance contribution16
Third variance contribution0

Calculator controls

How to calculate

Combined standard uncertaintyUse zero for an unused component. A quoted expanded uncertainty must first be converted to a standard uncertainty using its stated coverage factor. Concept diagram; not to scale.Combined standard uncertainty1Standard uncertainty 132Standard uncertainty 243Combined standard uncertainty5MyCalCute.com
Use zero for an unused component. A quoted expanded uncertainty must first be converted to a standard uncertainty using its stated coverage factor. Concept diagram; not to scale.

Combine three independent standard uncertainties by the root-sum-of-squares method.

Combined standard uncertainty = sqrt(u1^2+u2^2+u3^2)
First variance contribution = u1^2
Second variance contribution = u2^2
Third variance contribution = u3^2

Worked example

  • Standard uncertainty 1: 3
  • Standard uncertainty 2: 4
  • Standard uncertainty 3: 0
  • Combined standard uncertainty: 5
  • First variance contribution: 9
  • Second variance contribution: 16
  • Third variance contribution: 0

Assumptions and limits

Components must already be standard uncertainties in the output unit, with sensitivity factors applied. Correlated inputs require covariance terms; this is not an expanded uncertainty or guaranteed error bound.

Results are rounded for display; calculations use unrounded values. Read our calculation methodology.

Understanding the result

Combine three independent standard uncertainties by the root-sum-of-squares method. Use zero for an unused component. A quoted expanded uncertainty must first be converted to a standard uncertainty using its stated coverage factor.

When this tool is useful

Use zero for an unused component. A quoted expanded uncertainty must first be converted to a standard uncertainty using its stated coverage factor.

Understanding your inputs

InputExample
Standard uncertainty 1 u13
Standard uncertainty 2 u24
Standard uncertainty 3 u30

Frequently asked questions

What does this model leave out?

Components must already be standard uncertainties in the output unit, with sensitivity factors applied. Correlated inputs require covariance terms; this is not an expanded uncertainty or guaranteed error bound.

How do I reproduce the example?

Enter the displayed example values in their labelled units. Apply the formula before rounding; change one input at a time to compare scenarios.

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