# Percentage Error Calculator

Observed Value:

True Value:

Round (decimal places):

## Overview

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.

## Formula

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.

## Example

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.

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