The percentage error value is very much important under experimental calculations. It allows us to see how far apart our estimates and the exact value were, in terms of a percentage. Thus we need to compute percentage error in many a situation. In this topic, we will discuss the Percent Error Formula with examples.

**What is the Percentage Error?**

Percent error or percentage error expresses as a percentage the difference between the approximate value and exact values. It is also used in science to report the difference between the measured or experimental value and the exact value.

## Percent Error Formula

Percentage error is the difference between a measured and exact value, divided by the known value, and hence multiplied by 100%. For many applications, percentage error is expressed as a positive value. Normally, the absolute value of the error is divided by an accepted value and given as a percent. This is how we arrive at the Percent Error Formula

**Absolute Difference =Accepted value – Experimental value**

**\(Percentage Error = \frac{Absolute Difference} {Accepted Value}\times 100\)**

We can also use it without the Absolute Value. This will give a positive or negative result, which may be useful to know. For chemistry and with other sciences, it is necessary to keep a negative value. Whether error is positive or negative but it is important. For example, we may not expect to have a positive percent error comparing actual. If a positive value was calculated, then this will give as the potential problems with the procedure or unaccounted reactions.

While calculation the experimental or measured value minus the known or theoretical value is always taken as absolute. Therefore, this Percent Error Formula will be,

**\(Percentage Error = \frac {(experimental value – theoretical value)}{ Theoretical value} \times 100\)**

In various measurement, measuring instruments are not exact. Hence we can use the Percentage Error to estimate the possible error while measuring.

### Percent Error Calculation Steps:

- Subtract one value from other values. Here the order does not matter. This value will be the error value.
- Divide the error by the theoretical value.
- Convert the above decimal number into a percentage by multiplying it by 100. to get the percentage error value.

## Solved Examples

Q.1: I thought 70 people would turn up to the concert organized. But on the day of the performance, only 80 people came. Find out the percentage error in my calculation.

Solution: First we will find the absolute difference as, i.e. 70 – 80 = 10

Then apply the formula,

\(Percentage Error = \frac{Absolute Difference} {Accepted Value}\times 100 \)

\(Percentage Error = \frac{10 } { 80 }\times 100 \)

= 12.5 %

I was having error by 12.5%.

Q.2: A scale measures wrongly a value as 14 cm due to some marginal errors. Calculate the percentage error if the actual measurement of the value is 10 cm.

Solution: Given in the problem,

Experimental value = 14 cm

Theoretical value = 10 cm

Applying the formula for the computation,

\(Percentage \;Error = \frac {(experimental value – theoretical value)}{ Theoretical value} \times 100\)

\(= \frac {14 -10 }{ 10} \times 100\)

\(= \frac {4 }{ 10} \times 100\)

Percentage Error calculated as 40 %

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