Percent Error Calculator
Calculate the percent error between an experimental value and a theoretical value. A fundamental calculation in science to determine the accuracy of a measurement.
Bookmark this Calculator!
Understanding the Percent Error Calculator
The Percent Error Calculator is a vital tool for scientists, engineers, and students to quantify the difference between an experimental (or measured) value and a theoretical (or known) value. It expresses this difference as a percentage, which provides a clear indication of the accuracy of a measurement. A smaller percent error signifies that the experimental value is very close to the true value.
How to Use the Calculator
- Enter the Observed/Experimental Value: This is the value you measured or obtained through your experiment.
- Enter the True/Accepted Value: This is the known, theoretical, or generally accepted value for the quantity you are measuring.
- Calculate: The calculator will instantly compute the absolute error and the percent error.
The Percent Error Formula
The calculation is a two-step process:
1. Find the Absolute Error
First, calculate the absolute difference between the observed and true values. This gives you the magnitude of the error.
Absolute Error = |Observed Value - True Value|
2. Calculate the Percent Error
Next, divide the absolute error by the absolute value of the true value and multiply by 100 to express it as a percentage.
Percent Error = (Absolute Error / |True Value|) × 100%
Practical Example
Imagine you are conducting a chemistry experiment to determine the boiling point of water. The accepted theoretical value is 100°C. Your experimental measurement is 98.5°C.
- Observed Value: 98.5°C
- True Value: 100°C
- Absolute Error: |98.5 - 100| = |-1.5| = 1.5
- Percent Error: (1.5 / |100|) × 100% = 1.5%
Your measurement has a percent error of 1.5%, indicating it was quite close to the true value.
Frequently Asked Questions (FAQ)
- Can percent error be negative?
- While the difference (Observed - True) can be negative, the standard formula for percent error uses the absolute value of this difference. This means percent error is almost always expressed as a positive value, as it represents the magnitude of the error, not its direction.
- What is considered a "good" percent error?
- This depends heavily on the context. In high-precision fields like pharmaceuticals or aerospace, a percent error below 1% might be required. In other fields like biology or environmental science, a percent error of 5-10% might be acceptable due to natural variability.
- What's the difference between percent error and percent difference?
- Percent error compares an experimental value to a known "true" value. Percent difference, on the other hand, compares two experimental values to each other when there is no known true value, expressing their discrepancy relative to their average.
Similar Calculators
Quickly calculate the average (mean) of a set of numbers. Simply enter your numbers to find their central tendency.
Calculate the confidence interval for a sample mean or proportion. Determine the range in which the true population parameter is likely to fall.
Calculate the Mean Absolute Deviation (MAD) of a data set, which measures the average distance between each data point and the mean. A simple measure of variability.
Calculate the mean, median, mode, and range for any set of numbers. A fundamental tool for understanding the central tendency and spread of data.
Calculate probabilities and Z-scores for a normal distribution (bell curve). A powerful statistical tool for analyzing continuous data.
Calculate the p-value from a Z-score, t-score, or other statistical test. Determine the statistical significance of your results in hypothesis testing.
Calculate permutations (nPr) and combinations (nCr) for a set of items. An essential tool for probability, statistics, and combinatorics.
Determine the minimum sample size needed for a survey or experiment. Calculate the sample size for a given population, confidence level, and margin of error.
Explore Other Calculators
Quickly calculate the date that is 100 days from a starting date. Perfect for tracking 100-day challenges or project milestones.
Estimate your self-employment taxes as a freelancer or independent contractor. Helps you plan for quarterly tax payments and avoid surprises.
Find the date that is 120 days from any given start date. Useful for planning timelines, loan terms, and long-term projects.
Calculate the date that is 180 days (about six months) from a specific start date. Ideal for setting semi-annual goals or deadlines.
A simple tool to find the date that is exactly 30 days from a given start date. Commonly used for trial periods and monthly planning.
Quickly add or subtract 30 minutes from any given time. A handy tool for scheduling meetings, breaks, or appointments.
Project the growth of your 401(k) retirement savings over time. See how contributions, employer match, and investment returns can impact your nest egg.
Find the date that is 45 days from a specific start date. Useful for tracking mid-quarter deadlines and other short-term goals.