Last updated: 2026-07-01

Percent error in the chemistry lab

Almost every quantitative chemistry experiment ends with a measured number — a density, a molar mass, a concentration, an enthalpy of reaction — that can be checked against a value the textbook or the literature already accepts. Percent error is the standard way to report how close the measurement landed. It expresses the gap between the experimental result and the accepted value as a percentage of that accepted value, so results measured on completely different scales can be compared on the same footing.

Here $x_{\text{exp}}$ is the value obtained from the experiment and $x_{\text{acc}}$ is the accepted (theoretical) value. A smaller percent error means a more accurate measurement.

Why the absolute values

The vertical bars make percent error non-negative. A titration that overshoots the accepted concentration and one that falls short by the same amount are equally inaccurate, and percent error treats them the same way. The sign of the deviation still carries useful information — it tells you whether a systematic effect is pushing readings high or low — so this calculator also reports the absolute error, $x_{\text{exp}} - x_{\text{acc}}$, with its sign kept intact.

Worked example: density of a metal

A student measures the density of an aluminium sample and gets 2.64 g/mL. The accepted density of aluminium is 2.70 g/mL.

1. Absolute error: $2.64 - 2.70 = -0.06$ g/mL. The negative sign shows the measurement came out low.
2. Divide by the accepted value: $\dfrac{|-0.06|}{2.70} = 0.0222$.
3. Multiply by 100: $0.0222 \times 100 = 2.22\%$.

The measurement is about 2.2% below the accepted density — a reasonable result for a benchtop determination, and a hint that the measured volume or mass was slightly off.

What counts as a good percent error

There is no universal cutoff, because acceptable accuracy depends on the technique. A gravimetric determination performed carefully might be expected within a fraction of a percent, while a quick volumetric estimate could reasonably land within a few percent. When percent error is much larger than the technique should allow, it usually points to a specific cause rather than ordinary scatter.

Accuracy versus precision

Percent error measures accuracy — how close a result is to the accepted value. It says nothing about precision, the repeatability of a set of measurements. A method can be precise yet inaccurate (tightly clustered readings that all sit off the true value because of a calibration error), or accurate on average yet imprecise. When you repeat a measurement several times, average the replicates first and compute the percent error of that mean; report the spread of the individual values separately to describe precision.

Percent error is not percent yield

The two are easy to confuse because both produce a percentage in chemistry. Percent error compares a measured quantity with an accepted reference and gauges accuracy. Percent yield compares the product actually obtained in a reaction with the theoretical maximum and gauges efficiency, and it is not wrapped in an absolute value. Use percent error to judge how good a measurement is, and percent yield to judge how well a synthesis ran.

Related calculations

A general percent-error tool covers the same arithmetic outside a chemistry context. Rounding a result to a sensible number of figures keeps the percent error from implying more precision than the data support, and scientific notation helps when the accepted value spans many orders of magnitude.