Percent error calculator

Approximated/measured value:
Exact/actual value:
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Percent error:
Percent error non absolute:
Absolute error:

Here we discuss list of online math calculators that help us for doing calculation easily.

Percent Error Calculator

The Percent Error Calculator (% error calculator) will calculate the percentage error between an experimental measured value and a theoretical actual value.

Percentage Error Formula

Percentage Error=(|E−T|)/|T|×100

Where E is the experimental value and T is the theoretical value. This formula is similar to percentage change.

The absolute error is equal to the absolute value of the difference between the exact value and the approximated value:

ε = | Vexact - Vapprox |

The percent error is equal to the 100% times the absolute error divided by the exact value:

δ = 100% × | Vexact - Vapprox | / | Vexact |

What is the percent error?

Sometimes, we try to estimate the value of a particular quantity by making repeated measurements. For example, we can try to find out what is the gravitational acceleration by measuring the time of free fall from a specific height.

The measured acceleration will probably deviate a bit from the actual acceleration of 9.80665 m/s². To check what is the relative - or percent - error, you need to know two values: the real value and observed (measured) one.

How to calculate percent error: an example

To make it easier for you to understand what percent error is, we'll analyze a simple example. Let's assume that we want to find out what is the relative error between the measured and true values of the speed of sound.

1. Check what the real value of the speed of sound is. In the air at 20°C, it is 343 m/s

2. Take your measurement. You found it was equal to 329 m/s.

3. Subtract the observed value from the true value:

343 - 329 = 14 m/s

4. 14 m/s is the absolute error. To calculate the percent error, you need to divide it by the true value:

percent error = 14 / 343 *100% = 4.082%

5. The percent error, otherwise known as the relative error, is equal to 4.082%.

Percent error, margin of error, and standard error

There are a lot of terms similar to percent error. To ensure you don't get confused and mix them up, we provide a short explanation of each of them here.

Percent error, or relative error, is precisely what we described above - the relative difference between the observed and true value. You can apply the aforementioned percent error formula to calculate it.

Standard error is a value that can be calculated for a set of data. It is a statistical term that describes the accuracy with which a sample represents the whole population.

Margin of error, on the other hand, is closely related to the confidence interval. It can be calculated by multiplying the standard error with the z-score corresponding to a certain confidence level.