Error Propagation Calculator

Your details

The mathematical operation that combines X and Y (or X and exponent n).
The first measured quantity (e.g. a length, mass, voltage).
The absolute uncertainty (one standard deviation or half the instrument resolution) of X. Must be >= 0.
For add/subtract/multiply/divide: the second measured quantity. For power Z = X^n: enter n (the exponent). Not used for ln.
Quadrature assumes X and Y are independent: dZ = sqrt(dA^2 + dB^2). Linear (worst-case) adds the absolute terms: dZ = |dA| + |dB|. Use linear when errors are fully correlated.
Result ZLow uncertainty (1-5%)
8

Calculated value of the operation

Absolute uncertainty (dZ)0.1118
Relative uncertainty (dZ/Z)1.398%
Result with uncertainty8.000 +- 0.1118
1.398%
Very low (< 1%)<1%Low (1-5%)1%-5%Moderate (5-15%)5%-15%High (> 15%)15%+

Result: 8.000 +- 0.1118 (1.40% relative uncertainty)

  • After addition, the propagated absolute uncertainty is 0.1118, giving a relative uncertainty of 1.40%.
  • The quadrature (Gaussian) rule assumes X and Y are statistically independent. If they are correlated, switch to the linear (worst-case) rule for a conservative bound.

Next stepTo reduce total uncertainty, identify the dominant error source (the largest individual dZ contribution) and improve precision there first. Use the step-by-step panel below to see each contribution.

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