This percentage error calculator lets you calculate the percentage error if you know the expected and observed values. It can also calculate for you the observed (or expected) value if you know the percentage error and the expected (observed) value.

The calculator will give you not just the answer, but also the step by step solution.

## Usage Guide

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#### i. Valid Inputs

Each input can be a real number in any format — integers, decimals, fractions, or even mixed numbers. Here are a few examples.

- Whole numbers or decimals → $\hspace{0.2em} 2 \hspace{0.2em}$, $\hspace{0.2em} -4.25 \hspace{0.2em}$, $\hspace{0.2em} 0 \hspace{0.2em}$, $\hspace{0.2em} 0.33 \hspace{0.2em}$
- Fractions → $\hspace{0.2em} 2/3 \hspace{0.2em}$, $\hspace{0.2em} -1/5 \hspace{0.2em}$
- Mixed numbers → $\hspace{0.2em} 5 \hspace{0.5em} 1/4 \hspace{0.2em}$

IMPORTANT — Percentage error cannot be negative. The input has to be zero or positive.

#### ii. Example

If you would like to see an example of the calculator's working, just click the "example" button.

#### iii. Solutions

As mentioned earlier, the calculator won't just tell you the answer but also the steps you can follow to do the calculation yourself. The "show/hide solution" button would be available to you after the calculator has processed your input.

#### iv. Share

We would love to see you share our calculators with your family, friends, or anyone else who might find it useful.

By checking the "include calculation" checkbox, you can share your calculation as well.

Here's a quick overview of what we mean by percentage error and how to calculate it.

## Percentage Error

Percentage error is a measure of the how much the observed (experimental) value deviates from the expected (theoretical) value

It is the absolute value of the error (the difference between the observed and expected values) expressed as a percentage of the expected value.

$\% \hspace{0.3em} \text{error} \hspace{0.25em} = \hspace{0.25em} \left | \hspace{0.25em} \frac{\text{observed value} - \text{expected value}}{\text{expected value}} \hspace{0.25em} \right | \times 100 \hspace{0.25em}\%$

Here's an example to demonstrate how we use this formula to calculate the percentage error.

Example

Through an experiment, a student determined the density of a substance to be $\hspace{0.2em} 2.25 \text{ g/cm}^3 \hspace{0.2em}$. If the theoretical density of the substance is $\hspace{0.2em} 2.45 \text{ g/cm}^3 \hspace{0.2em}$, calculate the percentage error in the student's measurement.

Solution

The question tells us that the observed value is $\hspace{0.2em} 2.25 \text{ g/cm}^3 \hspace{0.2em}$ and the theoretical value is $\hspace{0.2em} 2.45 \text{ g/cm}^3 \hspace{0.2em}$. Now, using the formula for percentage error, we have —

$\begin{align*} \% \hspace{0.3em} \text{error} \hspace{0.25em} &= \hspace{0.25em} \left | \hspace{0.25em} \frac{\text{observed value} - \text{expected value}}{\text{expected value}} \hspace{0.25em} \right | \times 100 \hspace{0.25em}\% \\[1.75em] &= \hspace{0.25em} \left | \hspace{0.25em} \frac{2.25 - 2.45}{2.45} \hspace{0.25em} \right | \times 100 \hspace{0.25em}\% \\[1.75em] &= \hspace{0.25em} 8.16 \hspace{0.25em}\% \end{align*}$