Home / All Calculators / Math / Percentage Error Calculator

Percentage Error Calculator

Percentage Error Calculator Header Showcase

Observed Value:

True Value:

Round (decimal places):


Calculate the relative percentage error between a true value and the observed value found in a measurement.

What Is Percentage Error

Percentage error is a metric used to see what the relative (percentage) error is between a theoretical number and a measured or observed number.

For instance percentage error is often used in physics such as when estimating how fast an object will fall due to earths gravity versus how fast it actually falls. By knowing the strength of earths gravity one can calculate how long it will take to fall. This number is likely to deviate from the time one is able to measure as timing it may not be entirely precise or drag may slow the object down if the object is say a piece of paper versus a bowling ball.

Essentially just because you can reliably predict the numerical outcome of some experiment does not mean that you can also reliably measure the results of that outcome in the real world.


The formula used for calculating percentage error is: percentage error = (true value - observed value) / true value × 100%.

The formula simplified is: percentage error = (tv - ov) / tv × 100%. Where tv represents the true value and ov represents the observed value.


You calculate that a bowling ball will take 15 seconds to fall to the ground from a rather high height. For the purposes of this example the height it dropped from is irrelevant.

After dropping the bowling ball from this same height you measure the fall with a stop watch to have taken 15.35 seconds.

In this example, the true value is 15 seconds and the observed value is the 15.35 seconds you captured with a stop watch.

Using the formula above: percentage error = (tv - ov) / tv × 100%. In this case tv = 15 seconds and ov = 15.35 seconds.

Substitute these values into the formula: percentage error = (15 - 15.35) / 15 × 100%.

Simplified: percentage error = 0.35 / 15 × 100%

Yields: percentage error = -2.333333333333333%

Therefore, the percentage error in this case is about -2.33%. This means that the person timing the event was off by about 2.33% in total in their ability to both start and stop their stop watch.


Though every effort has been made to test this calculator, we are not to be held liable for any special, incidental, indirect or consequential damages or monetary losses of any kind arising out of or in connection with the use of any of the calculator tools and information sourced from this website. This calculator is provided as a service to you, please use at your own risk. Do not use calculations for anything where loss of life, money, property, etc could result from inaccurate calculations.

For more information: please see our full disclaimer.



Check out our free app for iOS & Android.

For more information about our app visit here!

Add to Home Screen

Add Math Converse as app to your home screen.


Check out our free desktop application for macOS, Windows & Linux.

For more information about our desktop application visit here!

Browser Extension

Check out our free browser extension for Chrome, Firefox, Edge, Safari, & Opera.

For more information about our browser extension visit here!

Welcome to Math Converse



Cite This Page

QR Code

Take a photo of the qr code to share this page or to open it quickly on your phone:


Cite Page
Google Classroom
Google Bookmarks
Facebook Messenger
QR Code