Understanding Percent Error Formula Calculator

Percent error tells us the size of the error relative to the actual value, showing how precise or close the estimation is. It is usually expressed as a positive percentage regardless of whether the estimation is higher or lower than the true number.

The Percent Error Formula

The formula to calculate percent error is:

$$\text{Percent Error}=\genfrac{}{}{0ex}{}{\text{Estimated Value}-\text{Actual Value}}{\text{Actual Value}}\times 100$$

• The absolute value (denoted by | |) ensures the result is always positive.

• Multiply by 100 to convert the decimal into a percentage.

How to Calculate Percent Error Step-by-Step

To use the formula, follow these simple steps:

1. Subtract the actual value from the estimated value. Ignore any negatives by taking the absolute value.

2. Divide the result by the actual value.

3. Multiply by 100 to turn it into a percentage.

4. Add the % symbol to show it is a percentage.

Example Using Percent Error Calculator

Suppose the actual length of a rope is 50 cm, but it is measured as 48 cm. The percent error calculator would work as:

• Step 1: |48 - 50| = 2

• Step 2: 2 / 50 = 0.04

• Step 3: 0.04 × 100 = 4%

So, the percent error is 4%, meaning the measured length is 4% less than the actual length.

Why Use a Percent Error Calculator?

A calculator makes this process much faster and reduces the chances of mistakes, especially with complex numbers. Also, some errors might be very small decimals, so using a calculator ensures an accurate percentage.

Important Notes

• Percent error gives an idea of accuracy but always assumes the actual value is correct.

• A smaller percent error means measurements are very close to the true value.

• If the percent error is zero, the estimated value is the same as the actual value.