# Absolute Uncertainty Calculator

Created by Artur Kosior
Reviewed by Dominik Czernia, PhD and Adena Benn
Last updated: Feb 19, 2023

The absolute uncertainty calculator helps you to find the uncertainty of a measured quantity from its relative uncertainty. This estimation is extremely useful when preparing statistical analyses, where some measurement imprecision must be taken into account.

In the following article, you will learn what absolute uncertainty is, the absolute uncertainty formula and how to find absolute uncertainty from relative uncertainty. If you don't know the latter value, don't worry! Visit our standard deviation of sample mean calculator, which estimates how the sample size influences the error of our estimates.

🙋 A good example would be the measurement error when a coach uses a stopwatch to measure the time a cadre of runners finishes a 400 m run. The accuracy of the device he is using may be as low as 0.01 seconds. Still, the absolute uncertainty, in this case, would be as high as 0.5 seconds due to the coach's minimum reaction time, which, due to the limitations of human perception, cannot be shorter.

Be sure also to check the relative error calculator to find out more about a similar concept to uncertainty but, in fact, is fundamentally different - the error of the measurement.

## What is absolute uncertainty?

You will always get a quantity with some error for measurements such as length, mass, or time whenever you measure it. It may be tiny and irrelevant in most situations, e.g., 0.2 inches or 0.5 centimeters, when you measure the length of the table. Sometimes, however, the error may be significant and needs to be taken into account.

The main problem with estimating errors is that we don't know the true value of a measured quantity. So, you may not be able to use our percent error calculator. Instead, you can use absolute uncertainty, which is the statistical dispersion of your measurements, e.g., a standard deviation. It will tell you where a true value lies with a satisfactory probability.

To find the standard deviation, you can use our standard deviation calculator.

## Absolute uncertainty formula

Let's see how to calculate absolute uncertainty using relative uncertainty:

$\mathrm{AU} = \mathrm{MV} \times \frac{R}{100}$

where:

• $\mathrm{AU}$ - The absolute uncertainty.
• $\mathrm{MV}$ - The measured value.
• $R$ - The relative uncertainty in percentages, namely: the ratio of the absolute uncertainty to the measured value. If you don't know $R$, you need to calculate the absolute uncertainty from the standard deviation of the mean, which we mentioned at the beginning of this text.

## How to use the absolute uncertainty calculator

To apply the absolute uncertainty formula in our tool, follow the below steps:

1. Input the measured value $\mathrm{MV}$ in the first field.
2. Enter the relative uncertainty $R$.
3. Read the final result in the last box of the absolute uncertainty calculator.
4. Let's say you know how to find absolute uncertainty from a measurement. Then, you can use our tool to check the $R$ value instead!

Do you need to know what absolute uncertainty is for a variable that depends on other variables with known uncertainty? In such a situation, use our error propagation calculator!

## Absolute uncertainty example

The absolute uncertainty formula is also commonly used to calculate air temperature fluctuations. How to calculate absolute uncertainty here? When the value read from a measuring device fluctuates, the absolute uncertainty is used here to determine the range of these hesitations.

Here, too, we can use a concrete example. A meteorologist observed the changing values of outdoor temperature from 12:00 pm to 4:00 pm and recorded ten temperatures with a mean of 60 °F (15.6 °C). The standard deviation of the mean was 1.8 °F (1 °C) which was taken as the absolute uncertainty. It means that most values were between 58.2 - 61.8 °F (14.6 - 16.6 °C).

Artur Kosior
Measured value
Relative uncertainty
%
Absolute uncertainty
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