Percent Error Calculator

| Added in Math & Numbers

What is Percent Error?

Percent error is a calculation that compares your experimental value to a known true value, expressing the difference as a percentage. It provides a standardized way to assess the accuracy of measurements regardless of scale.

How to Calculate Percent Error

The percent error formula is:

[\text{Percent Error} = \left( \frac{|\text{True Value} - \text{Observed Value}|}{|\text{True Value}|} \right) \times 100]

Where:

  • True Value is the accepted or known value in the scientific community
  • Observed Value is the value you measured or found in your experiment

Calculation Example

Suppose you're measuring the weight of an element that should weigh exactly 20kg. Your scale reads 19.95kg.

Using the formula:

[\text{Percent Error} = \left( \frac{|20 - 19.95|}{20} \right) \times 100 = 0.25%]

A 0.25% error indicates a highly accurate measurement.

Importance of Percent Error

  • Enhances Reliability: Quantifies how much results deviate from expected values
  • Facilitates Comparisons: Provides a standardized method to compare accuracy across different measurements
  • Identifies Systematic Errors: High percent errors may indicate problems with measurement processes

Applications

Medicine and Healthcare

Percent error ensures medication dosages are accurate and diagnostic equipment is properly calibrated.

Engineering and Construction

Engineers use percent error to verify material estimates, ensure structural integrity, and maintain quality control.

Frequently Asked Questions

Percent error is used to measure the accuracy of experimental results by comparing them to known or accepted values. It is commonly used in science, engineering, and quality control.

When using the absolute value formula, percent error is always positive. However, some calculations omit the absolute value to show whether the measurement was above or below the true value.

A good percent error depends on the context. In many scientific experiments, less than 5% is considered acceptable, though precision requirements vary by field.

Absolute error is simply the difference between measured and true values. Percent error expresses this difference as a percentage of the true value, making it easier to compare across different scales.