Statistics & Probability

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Absolute Uncertainty Calculator.

Report a measured value with its absolute uncertainty.

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Set your values

Results update as you type.

lowerBound: 9.8

lowerBound

9.800000
upperBound: 10.2

upperBound

10.200000
absoluteUncertainty: 0.2

absoluteUncertainty

0.200000
relativeUncertaintyPercent: 2

relativeUncertaintyPercent

2.000000

Results update automatically as you type.

Use Cases

Laboratory Measurements

Use this calculator to quickly determine the uncertainty range and relative uncertainty of experimental results, such as mass, volume, or time measurements.

Example: If you measure a mass as 25.0 g with an absolute uncertainty of 0.5 g, the bounds are 24.5 g to 25.5 g, and the relative uncertainty is 2%.

Quality Control in Manufacturing

Assess the precision of manufacturing processes by calculating the uncertainty of product dimensions or specifications.

Example: A part length is measured as 10.00 cm with an absolute uncertainty of 0.02 cm, giving bounds of 9.98 cm to 10.02 cm and a relative uncertainty of 0.2%.

Frequently Asked Questions

What does the Absolute Uncertainty Calculator do?
It calculates the upper and lower bounds of a measurement and its relative uncertainty. You input the measured value and the absolute uncertainty, and it provides the range and the relative uncertainty as a percentage.
How is relative uncertainty calculated?
Relative uncertainty is calculated by dividing the absolute uncertainty by the measured value and then multiplying by 100 to get a percentage. For example, if the measured value is 10.0 and the absolute uncertainty is 0.1, the relative uncertainty is (0.1/10.0)*100 = 1%.
What are the bounds of a measurement?
The bounds are the range within which the true value is expected to lie. The lower bound is the measured value minus the absolute uncertainty, and the upper bound is the measured value plus the absolute uncertainty. For instance, with a measured value of 5.0 and absolute uncertainty 0.2, the bounds are 4.8 to 5.2.

Tips & Common Mistakes

Tips

  • Ensure the absolute uncertainty is in the same unit as the measured value to get correct bounds.
  • Use the relative uncertainty to compare the precision of different measurements, even if they have different units or magnitudes.
  • For a more accurate representation, consider multiple measurements and use the standard deviation as the absolute uncertainty.
  • Remember that the bounds represent the range of possible true values, not a guarantee that the true value lies within them.

Common Mistakes to Avoid

  • Forgetting to include the absolute uncertainty when reporting measurements, which leads to incomplete information.
  • Confusing absolute uncertainty with relative uncertainty; they are different concepts and should not be used interchangeably.
  • Using the calculator with negative values for absolute uncertainty, which is not physically meaningful; uncertainty should always be positive.

Last updated: August 12, 2026