# Percentage Error Calculator

## What is the use to calculate percentage error?

With the help of calculation of the percentage error, an individual will be able to compare an estimate value to that of an exact value. In addition to this, with this percentage error, one will get to know the difference between approximate & the exact values in the form of the percentage of exact value.

## Percentage error Calculator

 Exact value : Approximate value: Percentage error:

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This shall further help an individual to check as to how close their guess or the estimate was when the real value is concerned. However, in order to know the percentage error, you would first be required to have approximate as well as the exact value.

### Formula for percentage error is –

$$%\, error\,= \frac{|exact\, value\,-\,approximate\, value\,|}{exact \, value}\times \, 100$$

## What is mean percentage error?

When it comes to statistics then the MPE or the mean percentage error happens to be the computed average of the percentage errors with the help of which forecasts can be made of a given model which further differ from the actual values of that particular quantity which is being forecasted.

### Formula for mean percentage error is –

$$MPE\,=\, \frac{100%}{n}\, \sum_{t=1}^{n} \, \frac{a_t\, -\, f_t}{a_t}$$

In the above equation, is the actual value of quantity to be forecasted while forecast & n is the number of those different times when variable is forecast.

## What is approximation error?

Approximation error is some kind of data which turns out to be the discrepancy between that of the exact value & that of an approximation to it. The major reasons for this approximation to happen is that the measurement of the data does not happen to be precise & the reason can be instruments while on the other hand, the other reason can be that the approximations are used rather than the real data. Whereas as far as the mathematical field is concerned especially of the numerical analysis then the numerical stability of the algorithm in this numerical analysis is all about how this error turns to be propagated by algorithm.

### Absolute error formula is –

$$\epsilon\, = \,|\upsilon\,-\,\upsilon_{approx} \, |$$

In the above equation, vertical bars represent absolute value.

If , then the relative error formula would be –

$$\eta \, = \, \frac{\epsilon}{|\upsilon|}\, = \, \|\frac {\upsilon-\upsilon_{approx}}{\upsilon}\|\,=\, \|1\, -\, \frac{\upsilon_{approx}}{\upsilon}\|$$

### Percent error formula is –

$$\delta\, = \, 100% \,\times \,\eta \, = \, 100% \, \times \, \frac{\epsilon}{|\upsilon|}\, = \, 100% \, \time \,|\frac{ \upsilon\, – \, \upsilon_{approx}}{\upsilon} |$$

### What is symmetric mean absolute percentage error?

SMAPE or sMAPE are the acronyms of symmetric mean absolute percentage error which is nothing but an accuracy measure that is based on the percentage or the relative errors.

Formula for SMAPE / sMAPE or the symmetric mean absolute percentage error is –

$$SMAPE\, =\, \frac {\sum_{t=1}^{n} | F_t\, – \,A_t |}{\sum_{t=1}^{n} (A_t\, + \,F_t )}$$

## How to use a percentage error calculator?

An individual will have to keep the fact in mind that the percent error is nothing but the percentage ratio of observed value besides the true value difference over true value. And in order to make use of the percentage error calculator, you will have to first enter the observed value followed by true value & click on calculate to know the result.