Percent Error Calculator

At a glance:Percent error is the standard metric in experimental science for 'how accurate a measurement is' — it expresses, as a percentage, the relative magnitude by which a measured value deviates from the theoretical (accepted or true) value. The formula is %error = |experimental − theoretical| / |theoretical| × 100%, where the 'experimental value' is the number you actually measured in the lab, and the 'theoretical value' is the value from a textbook formula, an accepted standard, or a standard method. The numerator |experimental − theoretical| is the 'absolute error', the gap between the measurement and the true value; dividing it by the absolute theoretical value gives the 'relative error', then × 100% makes a percentage. We usually take the absolute value throughout, so percent error is always positive, reflecting only the 'size' of the deviation, not its direction; to know whether the measurement is high or low, keep the sign (positive = high, negative = low). Using this tool's default: measured 9.7, theoretical 9.8, %error = |9.7 − 9.8| / 9.8 × 100% = 0.1 / 9.8 × 100% ≈ 1.02%, a very small error meaning the measurement is quite accurate. Percent error is more useful than 'absolute error' because it is 'relative': a difference of 0.1 is only about 1% against a true value of 9.8 (very accurate) but 50% against a true value of 0.2 (very inaccurate). Relative percentage is the fair way to compare accuracy across different magnitudes. Distinguish two easily confused concepts: 'accuracy' is how close a measurement is to the true value, reflected by percent error — smaller is more accurate; 'precision' is how close repeated measurements are to each other, reflected by standard deviation or percent deviation — unrelated to closeness to truth. A data set can be precise (always 9.5) yet inaccurate (true value 9.8), usually due to systematic error. Error sources split into two: (1) systematic error — from uncalibrated instruments, method flaws, environment; always biased the same way; removable by calibration or method improvement; (2) random error — from uncontrollable fluctuations; can be positive or negative; reducible by averaging many measurements. Percent error is used widely in chemistry experiments (comparing measured molar mass, concentration, reaction heat against theory), physics experiments (measuring g, speed of light), analytical method validation, and anywhere reliability must be assessed. Good experiments usually keep percent error within a few percent (< 5%), but the acceptable range depends on the experiment and instrument precision. Notes: first, the theoretical value cannot be 0, or the denominator is zero and percent error is undefined (this tool returns 0). Second, experimental and theoretical values must be the same physical quantity and unit. Third, this tool outputs the absolute (positive) error; for a signed error, judge yourself whether the experiment is high or low. Fourth, small percent error means 'accurate', not 'precise' — assess separately.