Scientific Audits

Percent Error Calculator

Find the percentage difference between your measured value and the true theoretical value.

Preparing Percent Error Calculator

Please wait ...

Input

Enter your measured (experimental) value and the true (theoretical) target value to calculate the relative error percentage instantly.

Input summary

Your calculator summary shows here.

Step by Step Calculation

Step by step calculation shows here

Calculate first and the full working will appear below automatically.

A Guide to Calculating Percent Error

In science, construction, and manufacturing, no measurement is completely perfect. There is always a small difference between the value you observe in the real world and the true, theoretical value that math, formulas, or science predicts. Percent error is the statistic that measures this discrepancy, expressing the difference as a percentage of the true value so you can evaluate the accuracy of your experimental methods. This helps researchers identify potential sources of systematic or random error in their calculations.

How the Formula Works

The formula for percent error is simple but specific. You subtract the true (theoretical) value from your measured (experimental) value. Next, take the absolute value of that result so it is always positive. Finally, divide that positive difference by the true value and multiply by one hundred to convert the ratio into a percentage.

Percent error measures accuracy, which is different from precision (how close multiple measurements are to each other). If you are looking to measure precision or see how scattered a set of numbers is, you should use our measuring dataset variation tool. For standard percent problems, check out our calculating standard percentages tool.

Where Error Metrics are Critical

Science Lab Reports: Chemistry and physics students calculate errors to see how closely their experiments matched natural laws.
Construction Materials: Architects check the difference between estimated brick counts and actual usage to refine planning.
Retail Inventory: Stores compare the expected stock count from computer logs against manual shelf audits. You can check discounts using our price markdown reductions tool.
Weather Forecasts: Meteorologists track the difference between predicted temperatures and actual temperatures to test weather models using a simple daily math checks tool.

Interpreting the Error Percentage

A lower percent error means your measurement is extremely close to the true target. For example, an error under 5% is generally considered highly accurate in high school physics labs. In commercial manufacturing, however, tolerances might be much tighter, requiring errors to stay below 0.1%.

Because these calculations often yield long, repeating decimals, it is common practice to round the final percentage. You can use our rounding decimal results tool to adjust the value to a clean number of decimal places.

Example of a Science Experiment

Suppose a chemistry student performs a lab to find the boiling point of water and records a temperature of 98.2°C, while the true boiling point is known to be 100.0°C.

To find the percent error, we subtract the true value from the measured value: 98.2 - 100.0 = -1.8. Taking the absolute value gives 1.8. We divide 1.8 by the true value (100.0) to get 0.018. Multiplying by 100 reveals a percent error of exactly 1.8%. This shows that the student's measurement was highly accurate.