![Featured](data:image/svg+xml,%3Csvg xmlns="http://www.w3.org/2000/svg" width="300" height="169" fill="%23333"%3E%3Crect width="300" height="169"/%3E%3Ctext x="50%25" y="50%25" dominant-baseline="middle" text-anchor="middle" fill="%23666" font-size="14"%3EFeatured Post%3C/text%3E%3C/svg%3E)
Percent Error Calculator
Calculate the percentage error between your experimental (measured) value and the theoretical (true) value instantly.
Calculate Percent Error
Enter your measured and true values below. Results update instantly.
Explore More Calculators
Need to calculate something else? Check out our other free tools.
Understanding Percent Error
What is Percent Error?
Percent error is a measure of accuracy. It shows how far off a measured (experimental) value is from the true (theoretical or accepted) value, expressed as a percentage. It is widely used in chemistry, physics, engineering, and manufacturing to assess the precision of measurements.
The Three Types of Error
- Absolute Error: The exact difference between the measured and true value, ignoring the sign. Formula:
|Measured − True| - Relative Error: The absolute error divided by the true value. It shows the size of the error relative to the size of the measurement. Formula:
Absolute Error / |True| - Percent Error: The relative error multiplied by 100 to express it as a percentage. Formula:
Relative Error × 100
Real-World Example
Imagine you are measuring the boiling point of water in a lab. The accepted (true) value is 100°C. Your thermometer reads 98°C.
- Absolute Error: |98 − 100| = 2°C
- Relative Error: 2 / 100 = 0.02
- Percent Error: 0.02 × 100 = 2%
A 2% error means your measurement was very close to the true value. In most scientific experiments, a percent error under 5% is considered acceptable.
Can Percent Error be Negative?
Strictly speaking, percent error is usually expressed as a positive value because we use the absolute value in the formula. However, in some scientific contexts, keeping the sign is useful to know if the measurement was an overestimate (positive) or an underestimate (negative).
Frequently Asked Questions
What is an acceptable percent error in experiments?
In most high school and introductory college labs, a percent error of less than 5% is considered acceptable. In more precise engineering or pharmaceutical contexts, the acceptable error might be 1% or even 0.1%.
What if the true value is zero?
If the true (theoretical) value is zero, percent error cannot be calculated because it would require dividing by zero. In this case, scientists usually report the absolute error instead.
What is the difference between percent error and percent difference?
Percent error compares a measured value to a known true value. Percent difference compares two experimental values to each other when neither is known to be "true", using their average as the reference.
How do I reduce percent error in my experiments?
Use more precise instruments, calibrate your equipment before use, take multiple measurements and calculate the average, and control environmental variables like temperature and humidity.
Is this calculator free to use?
Yes, 100% free with no limits, no signup required, and no hidden fees. Use it as many times as you need for school, lab work, or professional projects.
Calculate Your Error Margin
Get instant, accurate percent error calculations for your lab reports and experiments.
Open Calculator