Percent Error Calculator
Calculate percent error, percent yield and percent difference in one place. Enter your measured and accepted values to gauge accuracy, your actual and theoretical yield to find reaction efficiency, or any two measurements to compare them — with the formula, the signed error and a plain-English interpretation.
Percent error
| measured − accepted | ÷ | accepted | × 100
Result
The closer this is to 0%, the more accurate your measurement. Your measurement is lower than the accepted value (under-estimate).
About the Percent Error Calculator
Three of the most-used "percent" calculations in science labs share this one tool. Percent error measures accuracy: it tells you how far an experimental measurement falls from a known, accepted value, as a percentage of that accepted value — the smaller the percent error, the more accurate the result. Percent yield measures the efficiency of a chemical reaction: it compares the actual amount of product you obtained against the theoretical (maximum) amount that the balanced equation predicts. Unlike percent error, percent yield can legitimately go above 100% when the product is impure or still contains solvent, so this calculator never clamps it. Percent difference compares two measurements when neither is the "true" value — for example two readings of the same quantity, or results from two students — by dividing the size of the difference by the average of the two numbers. Each mode shows the formula in use, the result as a percentage, and (for percent error) the signed value so you can tell whether you over- or under-estimated. These calculations turn up constantly in chemistry titrations and synthesis, physics measurement labs, analytical method validation, and any report where you have to state how good a number is.
How to use this calculator
- 1 Choose a calculation: percent error, percent yield or percent difference.
- 2 Enter the two values it asks for — measured and accepted for error, actual and theoretical for yield, or value A and value B for difference.
- 3 Read the percentage result with its formula and a short interpretation; copy the answer, and for percent error see the signed value too.
The percent formulas
Each calculation uses a simple ratio expressed as a percentage: • Percent error = |measured − accepted| ÷ |accepted| × 100. The bars |…| mean absolute value, so the result is never negative. A signed version, (measured − accepted) ÷ |accepted| × 100, keeps the sign: positive means you over-estimated, negative means you under-estimated. • Percent yield = actual ÷ theoretical × 100. The theoretical yield is the maximum product a reaction can make according to its balanced equation and limiting reagent. Percent yield can exceed 100% if the product is impure or wet, so it is not capped. • Percent difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100. Because it divides by the average of the two values, it treats both symmetrically — neither is assumed to be the correct answer. For example, a measured gravity of 9.8 m/s² against the accepted 9.81 gives |9.8 − 9.81| ÷ 9.81 × 100 ≈ 0.10%. Obtaining 8 g of product when 10 g was possible gives 8 ÷ 10 × 100 = 80% yield. Comparing readings of 10 and 12 gives |10 − 12| ÷ 11 × 100 ≈ 18.18% difference.
Frequently asked questions
What is percent error?
Percent error tells you how far a measured (experimental) value is from a known, accepted value, expressed as a percentage of the accepted value. It is calculated as |measured − accepted| ÷ |accepted| × 100. A small percent error means the measurement is accurate; a large one means it is far from the true value. It is one of the most common ways to report the accuracy of an experiment in chemistry and physics.
What is the percent error formula?
Percent error = |measured − accepted| ÷ |accepted| × 100. The vertical bars mean absolute value, so the answer is always positive. If you want to know the direction of the error, use the signed form (measured − accepted) ÷ |accepted| × 100: a positive result means your measurement was too high (over-estimate) and a negative result means it was too low (under-estimate). For example, measuring 105 when the accepted value is 100 gives |105 − 100| ÷ 100 × 100 = 5%.
What is percent yield?
Percent yield measures how efficient a chemical reaction was by comparing the actual amount of product you collected to the theoretical yield — the maximum amount predicted by the balanced equation and the limiting reagent. The formula is actual ÷ theoretical × 100. Getting 8 g of product when 10 g was theoretically possible is an 80% yield. Yields above 100% are possible and usually mean the product is impure or still contains solvent, which is why this calculator does not cap the value at 100%.
What is the difference between percent error and percent difference?
Use percent error when one value is the accepted or true answer and you want to know how close your measurement came to it — it divides by the accepted value. Use percent difference when neither value is the "correct" one and you simply want to compare two measurements, such as two trials or two instruments — it divides by the average of the two values, treating them symmetrically. Percent error answers "how accurate?"; percent difference answers "how far apart?".
Related tools
Keep your lab math precise on UnitConv. Round answers correctly with the significant figures calculator, work out plain percentages with the percentage calculator, and explore more chemistry and physics with the molar mass, specific heat and half-life calculators.