Percent Error Calculator

How it works

Percent error measures how far off an estimated or experimental value is from the true accepted value, expressed as a percentage. A lower percent error means a more accurate result. The absolute value is used so the result is always positive regardless of whether the estimate was too high or too low.

The formula

Why this works: The numerator gives the size of the error in absolute terms. Dividing by the actual value scales the error relative to the size of what was being measured, so a 5-unit error means something very different when the actual value is 10 versus 10,000. Multiplying by 100 expresses that scaled error as a percentage.

Worked examples

When to use this

Percent error is the right tool when you have a known or accepted reference value and want to quantify how far a measurement or estimate deviates from it.

• GCSE and A-Level science practicals. When measuring the acceleration due to gravity in a physics practical, students compare their result (say 9.6 m/s²) to the accepted value of 9.81 m/s² and calculate percent error as part of their evaluation. Under 5% is typically acceptable; under 1% indicates a well-controlled experiment.
• Chemistry yield calculations. A student predicts a theoretical yield of 3.6 g from a synthesis reaction but obtains only 3.2 g. The percent error of 11.1% reveals how much was lost to side reactions, incomplete transfer, or measurement imprecision.
• Manufacturing quality control. A specification calls for a component to weigh 250 g. A batch weighs an average of 247 g. The 1.2% error is within tolerance, so the batch passes. A result above the tolerance threshold triggers a review.
• Business and financial forecasting. A company forecast Q3 profit at £480,000 but actual profit came in at £510,000. The 5.9% error helps finance teams calibrate their models and justify how accurate or conservative their forecasting methodology is.
• Engineering and construction. A structural engineer estimates the load on a beam at 18 kN but measured deflection implies 19.2 kN. A 6.25% error is flagged for review, as engineering tolerances in safety-critical applications are typically tighter than those in laboratory work.

Understanding the result

The percent error result is always a positive number because the formula uses the absolute value of the difference. Whether your estimate was too high or too low, the result tells you the magnitude of the deviation without indicating direction. If direction matters, note whether the estimate exceeded or fell short of the actual value separately.

In school science, a percent error below 5% is generally considered acceptable for GCSE practicals and below 1-2% for A-Level work, though this varies by subject and examiner. A large percent error does not automatically mean the experiment was poorly designed; it may reflect the inherent limitations of the equipment being used. Identifying and explaining sources of error is as important as the number itself.

There is an important distinction between random errors (which scatter results above and below the true value) and systematic errors (which consistently push results in one direction). Percent error captures the overall deviation but does not distinguish between the two. A series of percent error calculations across multiple trials, combined with the average, gives a clearer picture of measurement quality.

Related concepts

• ➡ calculate the percentage deviation of any reading from a reference value
• ➡ compare two experimental readings without designating either as the reference
• ➡ find the mean percent error across a series of experimental trials

How to do this in Excel

In Microsoft Excel or Google Sheets, put the estimated value in cell A1 and the actual (accepted) value in cell B1, then enter this formula in C1:

The ABS function ensures the result is always positive. To run percent error across multiple experiments, put each estimated value in column A and each actual value in column B, then copy the formula down column C. You can then average column C with =AVERAGE(C1:C10) to get the mean percent error across the trial set.

How to do this without a calculator

Find the difference between your estimated and actual values, ignoring any minus sign. Divide that difference by the actual value. Then multiply by 100 to convert to a percentage.

For example, if you measured 9.6 m/s² and the accepted value is 9.81 m/s²: the difference is 0.21. Divide 0.21 by 9.81. This is approximately 0.21 / 10 = 0.021 (using 10 as a rough estimate), so about 2.1%. The precise answer is 2.14%, so the estimate is close enough for a quick check.

When the actual value is a round number, the mental arithmetic is straightforward. If the actual value is 50 and the difference is 2, then 2 / 50 = 4/100 = 4% without needing a calculator. If the actual is 20 and the difference is 2, that is 10%.

Real world uses

• Assessing accuracy of lab measurements in GCSE and A-Level science practicals.
• Evaluating the precision of instruments or methods in quality control and manufacturing.
• Comparing a business forecast to an actual outcome to gauge forecasting reliability.
• Checking how closely a scale model or architectural plan corresponds to real-world dimensions.
• Benchmarking the accuracy of an algorithm's predictions against verified reference outputs.

Common mistakes

Related calculators