Percent Error Calculator

Percent error quantifies how far a measured or experimental value falls from an accepted theoretical value, expressed as a percentage of the theoretical magnitude. Scientists, engineers, and lab students use it to judge measurement quality without losing scale — a 0.5 cm error on a 10 cm object (5%) is far more significant than the same absolute error on a 10 m beam (0.05%). The standard formula is percent error = |experimental − theoretical| / |theoretical| × 100%, which always returns a non-negative percentage regardless of whether the measurement is high or low.

Worked example from physics: you measure gravitational acceleration as 9.8 m/s² while the accepted value is 10.0 m/s². Absolute error = |9.8 − 10.0| = 0.2. Relative error = 0.2 / 10.0 = 0.02. Percent error = 0.02 × 100 = 2%. A 2% deviation might be acceptable for a classroom pendulum experiment but unacceptable for a calibrated instrument without documented uncertainty. Always report both absolute and percent error so readers can judge practical impact.

Percent error differs from percent difference, which compares two peer values without labeling one as "correct." Percent difference = |A − B| / ((A + B)/2) × 100%, using the average as the denominator so neither value dominates. Use it when comparing duplicate trials, two instruments, or survey responses where no gold standard exists. Percent change = (new − old) / |old| × 100% tracks growth or decline over time — revenue, population, or stock price — and preserves sign so increases and decreases are distinguishable.

The theoretical value must be non-zero for percent error; dividing by zero is undefined. Near-zero denominators inflate percentages dramatically, so cite absolute error alongside percent figures in those edge cases. Significant figures matter in lab reports: if your balance reads to 0.01 g, quoting percent error to six decimals misrepresents precision. Round final percentages sensibly with the rounding calculator and keep raw data in full precision until the last step.

Percent error connects to statistics via the standard deviation calculator when repeated trials form a distribution, and to the percentage calculator for complementary fraction-decimal-percent conversions. In quality control, specifications often state maximum allowable percent error; in chemistry, percent yield compares actual product mass to stoichiometric prediction using the same absolute-over-reference structure.

Choose the mode that matches your question: percent error when one value is authoritative theory, percent difference when comparing two measurements of equal standing, percent change when tracking temporal shift. Enter values with consistent units, verify the reference value is correct, and use the step-by-step breakdown below each result to document homework or lab notebooks transparently.