• Skip to secondary menu
  • Skip to main content
  • Skip to primary sidebar
  • My Store
  • Glossary
  • Home
  • About Me
  • Contact Me

Statistics By Jim

Making statistics intuitive

  • Graphs
  • Basics
  • Hypothesis Testing
  • Regression
  • ANOVA
  • Probability
  • Time Series
  • Fun

Percent Error: Definition, Formula & Examples

By Jim Frost Leave a Comment

Percent error compares an estimate to a correct value and expresses the difference between them as a percentage. This statistic allows analysts to understand the size of the error relative to the true value. It is also known as percentage error and % error. It is a concept that relates to measurement error.

In this context, the estimate and correct values can be the following:

  • Estimate: A measurement, approximation, experimentally derived value, or a guess.
  • Correct Value: A quantity that has been proven or generally accepted as being valid. It can be a standard measurement for an item used in testing measurement systems. Or, a known value that is correct on a theoretical basis, such as the circumference of a circle.

Why Assess Percent Error?

Use percent error to assess the validity of your measurements.Percent error is a valuable statistic when your estimate targets a known, correct value. In general terms, use it to quantify how close an estimate is to that true value. Smaller errors occur when an approximate value is close to the correct value. As the estimates move further away from the actual value, the percent error increases.

The measurement instrument, estimation process, personnel, or a combination of factors can cause these errors. When the error becomes large enough, it can invalidate your estimates. At that point, you’ll need to take corrective measures. However, there is no standard cutoff point because it varies by subject area.

The purpose for calculating the percentage error depends on the context. In scientific studies and quality management projects, analysts use it to compare measured values to known values to assess the validity of their measurements. Alternatively, researchers use it to compare a value from an experiment to a theoretical or true value to understand the validity of their experimental calculations.

To calculate this type of measurement error, you must know the correct value. When you don’t know it, you’ll need to use another method, such as evaluating measurement variability.

After covering the formula, I’ll go over several examples of using it in different contexts.

Learn more about percentages in my posts, Percent Change and Relative Frequencies and Their Distributions.

Percent Error Formula

Finding the percent error involves three steps:

  1. Calculate the error, which is the Estimate – Correct Value.
  2. Divide by the Correct Value.
  3. Multiply by 100 to produce a percentage.

When calculating this statistic, some fields of study retain the plus or minus values to indicate whether the Estimate is above or below the Correct value. However, other areas use the absolute value of the error, which always produces positive values. In the percent error equations below, the bars (|) indicate using the absolute value.

When you don’t use the absolute value of the error, you’ll obtain positive percentages when the Estimate is greater than the Correct value and negative values when the Estimate is lower. However, the absolute value form always produces positive values. Check to see which version is the norm for your field!

Below are the percent error formulas:

Percent error formula.

Examples of Percent Error

For these percent error examples, I use the percent error formula that retains the positive and negative signs because it provides more information. Remove the negative signs to produce the absolute value form.

Guesses / Rough Estimations

Imagine you’re planning a party and estimate that 15 people will attend. In reality, 18 people attend.

Percent error example calculations.

Your guess was in error by -16.67%, meaning that it was too low.

Assessing Measurements

Measurements are inexact. They are approximations of the actual characteristic. Human error and device limitations can contribute to measurement error.

For example, quality control analysts are assessing the measurement system for their inspection process. They need to obtain valid measurements of part lengths. A standard part they use for testing has an agreed upon length of 5.0mm. An inspector measures this part and records 5.2mm.

Example calculations.

The inspector’s measurement contains 4% error and it was too high.

When you’re using percent error to compare measurements to a known standard item, smaller errors represent measurements that are close to the correct value. If your measurements have more significant errors, you might need to make adjustments to your measurement system.

Related posts: Accuracy vs. Precision and Random vs. Systematic Error.

Comparing Experimental Values to Known Values

In the third century BCE, Eratosthenes, a Greek librarian in Egypt, used the Sun’s positions at two locations at the same time to estimate the Earth’s circumference as being 43,075km. Currently, the Earth’s circumference has a known value of 40,096km.

Example calculations for percent error.

Eratosthenes’ experiment had an error of 7.4%. That’s on the high side, but it’s not too shabby for someone living in ancient Egypt!

Share this:

  • Tweet

Related

Filed Under: Basics Tagged With: conceptual, measurement error

Reader Interactions

Comments and QuestionsCancel reply

Primary Sidebar

Meet Jim

I’ll help you intuitively understand statistics by focusing on concepts and using plain English so you can concentrate on understanding your results.

Read More...

Buy My Introduction to Statistics Book!

Cover of my Introduction to Statistics: An Intuitive Guide ebook.

Buy My Hypothesis Testing Book!

Cover image of my Hypothesis Testing: An Intuitive Guide ebook.

Buy My Regression Book!

Cover for my ebook, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models.

Subscribe by Email

Enter your email address to receive notifications of new posts by email.

    I won't send you spam. Unsubscribe at any time.

    Top Posts

    • How to Interpret P-values and Coefficients in Regression Analysis
    • F-table
    • How To Interpret R-squared in Regression Analysis
    • Z-table
    • How to do t-Tests in Excel
    • How to Find the P value: Process and Calculations
    • Weighted Average: Formula & Calculation Examples
    • Cronbach’s Alpha: Definition, Calculations & Example
    • T-Distribution Table of Critical Values
    • Multicollinearity in Regression Analysis: Problems, Detection, and Solutions

    Recent Posts

    • Longitudinal Study: Overview, Examples & Benefits
    • Correlation vs Causation: Understanding the Differences
    • One Way ANOVA Overview & Example
    • Observational Study vs Experiment with Examples
    • Goodness of Fit: Definition & Tests
    • Binomial Distribution Formula: Probability, Standard Deviation & Mean

    Recent Comments

    • Jim Frost on Joint Probability: Definition, Formula & Examples
    • Harmeet on Joint Probability: Definition, Formula & Examples
    • kafia on Cronbach’s Alpha: Definition, Calculations & Example
    • Jim Frost on How to Interpret P-values and Coefficients in Regression Analysis
    • Jim Frost on Convenience Sampling: Definition & Examples

    Copyright © 2023 · Jim Frost · Privacy Policy