Percentage Error Calculator
Calculate the percent error between an exact (theoretical) value and a measured (experimental) value. Supports step-by-step solutions for science, math, and engineering experiments.
Experimental Error Solver
Calculate accuracy and error margins instantly
The accepted, known, or theoretical value of the measurement
The value you obtained from your experiment or measurement
View the complete step-by-step calculation process
Your Error Analysis
Percentage error, absolute error, and steps
Enter your exact and measured values, then click Calculate Error to see the full error analysis.
Percentage Error Interpretation Guide
General guidelines for evaluating the accuracy of experimental measurements based on the calculated percentage error.
| Error Range | Accuracy Level | Typical Context |
|---|---|---|
| 0% | Perfect | Theoretical / Mathematical proofs |
| < 1% | Extremely High | Advanced scientific research |
| 1% – 5% | High / Excellent | Standard physics/chemistry labs |
| 5% – 10% | Acceptable | High school experiments, field studies |
| > 10% | Poor / Needs Review | Significant experimental flaws present |
Percentage Error FAQ
Everything you need to know about calculating error, accuracy, and experimental measurements.
Percentage error is a measure of how inaccurate a measurement is, relative to the true or exact value. It is expressed as a percentage and is commonly used in science and engineering to quantify the difference between an experimental (measured) value and a theoretical (exact) value.
The formula for percentage error is: Percentage Error = (|Measured – Exact| / |Exact|) × 100%. You subtract the exact value from the measured value, take the absolute value of that difference (absolute error), divide it by the absolute value of the exact value, and multiply by 100 to get the percentage.
In most scientific applications, percentage error is expressed as a positive value (absolute percentage error) because we are interested in the magnitude of the error, not the direction. However, if you need to know whether the measurement was an overestimate or underestimate, you can omit the absolute value bars to get a signed percentage error.
Absolute error is the actual physical difference between the measured value and the exact value (Measured – Exact). It has the same units as the measurement. Percentage error, on the other hand, is the absolute error divided by the exact value, expressed as a percentage. It is a relative measure that allows you to compare the accuracy of measurements across different scales.
What constitutes a ‘good’ percentage error depends entirely on the context and the difficulty of the measurement. In high school physics or chemistry, a percentage error of less than 5% is generally considered excellent. In complex engineering or advanced research, an error of less than 1% might be required. For rough estimates, 10-15% might be acceptable.
Relative error is very similar to percentage error, but it is expressed as a decimal or fraction rather than a percentage. The formula is: Relative Error = |Measured – Exact| / |Exact|. To convert relative error to percentage error, simply multiply by 100%.
Percentage error is crucial in science because it provides a standardized way to evaluate the accuracy of experimental results. Since measurements can involve vastly different scales (e.g., measuring the mass of an atom vs. the mass of a planet), absolute error isn’t always useful for comparison. Percentage error normalizes the error, allowing scientists to assess the reliability of their methods and equipment.
Accuracy refers to how close a measurement is to the true or exact value (which is what percentage error measures). Precision refers to how close multiple measurements of the same item are to each other, regardless of whether they are close to the true value. A measurement can be precise but not accurate (e.g., a scale that consistently reads 5g too heavy).