Percent Error Calculator - Calculate Measurement Accuracy

Free percent error calculator with step-by-step solutions. Calculate percent error, absolute error, and relative error for scientific measurements instantly.

Calculate Percent Error

Measured Value (Experimental)

True Value (Accepted/Theoretical)

Formula: Percent Error = (|Measured - True| / |True|) × 100

Example: If true value is 100 and measured is 95, percent error = 5%

Quick Guide

Formula

(|Measured - True| / |True|) × 100

Excellent

Less than 5% error

Good

5% to 10% error

Acceptable

10% to 20% error

Common Uses

•Chemistry lab experiments
•Physics measurements
•Engineering calculations
•Quality control testing
•Scientific research
•Manufacturing processes

Example

Chemistry Lab

True value: 10.0 g

Measured: 9.5 g

Error: 5%

What is Percent Error?

Percent error is a fundamental measurement in science and engineering that quantifies the accuracy of an experimental or measured value compared to a true, accepted, or theoretical value. It expresses the magnitude of error as a percentage, making it easy to understand and compare across different measurements and scales.

The percent error formula is: Percent Error = (|Measured Value - True Value| / |True Value|) × 100

This calculation uses absolute values to ensure the result is always positive, focusing on the magnitude of error rather than its direction. A lower percent error indicates higher accuracy, with values below 5% generally considered excellent in most scientific applications.

How to Calculate Percent Error

Step-by-Step Process

1
Find the Absolute Error: Subtract the true value from the measured value and take the absolute value: |Measured - True|
2
Calculate Relative Error: Divide the absolute error by the absolute value of the true value: Absolute Error / |True Value|
3
Convert to Percentage: Multiply the relative error by 100 to get the percent error

Example Calculation

True Value = 100 grams

Measured Value = 95 grams

Absolute Error = |95 - 100| = 5 grams

Relative Error = 5 / 100 = 0.05

Percent Error = 0.05 × 100 = 5%

Applications of Percent Error

Chemistry

• Comparing experimental yields with theoretical yields
• Evaluating titration accuracy
• Assessing spectroscopy measurements
• Quality control in pharmaceutical production

Physics

• Measuring gravitational acceleration
• Evaluating experimental constants
• Assessing equipment calibration
• Comparing theoretical predictions with results

Engineering

• Quality control in manufacturing
• Testing material properties
• Validating design specifications
• Calibrating measurement instruments

Research

• Validating experimental methods
• Comparing different measurement techniques
• Assessing data reliability
• Evaluating instrument precision

Frequently Asked Questions

Related Math Calculators

Percentage Calculator

Calculate percentages, increases, and decreases

Fraction Calculator

Add, subtract, multiply, and divide fractions

Scientific Calculator

Advanced mathematical calculations

Learn More About Percent Error

→Khan Academy - Statistics and Probability →NIST - Measurement Standards →American Chemical Society - Laboratory Techniques