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

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.

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.

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.

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

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.

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.