Percent Error Calculator

Calculate the percentage difference between an observed value and a true value

Last updated: December 21, 2025

CreatorFrank Zhao

True Value

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Observed Value

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Percent Error

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1Percent Error

\% \text{ error} = \frac{V_{\text{observed}} - V_{\text{true}}}{V_{\text{true}}} \times 100

2Observed Value

V_{\text{observed}} = V_{\text{true}} \left(1 + \frac{\% \text{ error}}{100}\right)

3True Value

V_{\text{true}} = \frac{V_{\text{observed}}}{1 + \frac{\% \text{ error}}{100}}

V_{\text{true}}

Accepted Value

V_{\text{obs}}

Measured Value

\% \text{ Error}

Relative Error

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Overview

Percent error, also known as relative error, measures the accuracy of your measurement compared to the true value. Whether you're conducting a science experiment, quality control test, or validating a calculation, percent error helps you quantify how close you got to the target.

Key Point: A smaller percent error indicates a more accurate measurement.

Zero percent error means your measurement perfectly matches the true value.

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The Percent Error Formula

\% \text{ Error} = \frac{|V_{\text{observed}} - V_{\text{true}}|}{V_{\text{true}}} \times 100\%

Variable meanings

$V_{\text{true}}$ : The accepted, known, or theoretical value.
$V_{\text{observed}}$ : The measured or experimental value.
$| |$ : Absolute value - the result is always positive regardless of direction of error.

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Practical Example

Scenario: Boiling Point of Water

You measure the boiling point of water and get 99°C, but the true value is 100°C.

\% \text{ Error} = \frac{|100 - 99|}{100} \times 100\% = \frac{1}{100} \times 100\% = 1\%

Result: Your measurement has a 1% error, meaning you were very close to the true value.

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Calculation Modes

Find Percent Error

Given: True & Observed
Calculate: Percent Error

Find True Value

Given: Observed & Error
Calculate: True Value

Find Observed Value

Given: True & Error
Calculate: Observed Value

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Common Applications

🔬 Scientific Research

Compare experimental measurements with theoretical values in physics, chemistry, and biology.

⚙️ Quality Control

Assess manufacturing precision by measuring how actual product dimensions deviate from specifications.

📊 Data Analysis

Evaluate the accuracy of forecasts, predictions, and estimates against actual outcomes.

🎓 Academic Testing

Verify calculations and check the reliability of measurement instruments and techniques.

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Helpful Tips

Sign matters: Positive error means you overestimated, negative means you underestimated.
Absolute value: Many fields use absolute percent error, ignoring the sign.
Units: Always ensure True Value and Observed Value are in the same units.