Percent Error Calculator

Percent error measures how far an experimental (measured) value sits from the accepted (theoretical or true) value, expressed as a percentage of that true value. It answers a simple but important question: how accurate was my measurement? A small percent error means your result is close to the accepted answer; a large one signals that something — the instrument, the method, or the reading — pushed you off target. This calculator takes your experimental and theoretical values and returns the absolute percent error, the signed error (which shows whether you over- or under-estimated), and the raw difference between the two numbers.

The tool is built for students in physics, chemistry, and biology labs who have to report percent error alongside every measurement, but it is equally handy for engineers checking a part against its specification, quality-control staff comparing a sample to a standard, and anyone validating an estimate against a known figure. Because it shows the signed error as well as the absolute value, you can immediately tell the direction of the deviation, not just its size.

The formula

Percent error = |Experimental − Theoretical| / |Theoretical| × 100

The absolute-value bars make the headline result always positive, which is how percent error is conventionally reported. The denominator uses the magnitude of the theoretical value so the metric behaves sensibly even when the true value is negative (such as a temperature below zero). The signed version drops the outer absolute value: a positive signed error means your measurement was too high (an overestimate), and a negative signed error means it was too low (an underestimate). The theoretical value can never be zero — dividing by zero leaves percent error undefined — so the calculator flags that case instead of returning a meaningless number.

Step-by-step method

First, subtract the theoretical value from the experimental value to get the difference. Next, divide that difference by the absolute value of the theoretical value. Then multiply by 100 to convert the fraction into a percentage. To report the conventional positive figure, take the absolute value of the result. Keeping the sign through the calculation is useful because it tells you which way your experiment drifted, which often points straight at the cause.

Worked example

Suppose a student measures the acceleration due to gravity as 9.78 m/s² in a pendulum experiment, while the accepted value is 9.81 m/s². The difference is 9.78 − 9.81 = −0.03. Dividing by the true value gives −0.03 / 9.81 ≈ −0.003058, and multiplying by 100 gives a signed error of about −0.31%. The headline percent error is the absolute value, roughly 0.31%, and the negative sign tells us the measurement was a slight underestimate. For a contrasting case, measuring a 100 g mass as 102 g gives a difference of 2, a percent error of 2 / 100 × 100 = 2%, and a positive sign marking it an overestimate. A reading of 48 against a true 50 gives 4% error with a signed value of −4%.

Interpreting the result and useful tips

What counts as "good" depends entirely on the field. A school physics lab often accepts under 5%, a careful chemistry titration aims for under 1%, and precision engineering may demand a fraction of a percent. Always compare your figure to the tolerance expected for your specific task rather than to a universal threshold. If you take several readings, compute percent error from their average, and quote a sensible number of significant figures — reporting 0.305823% to six decimals implies a precision your apparatus almost certainly does not have. The signed error is your friend when troubleshooting: a consistent bias in one direction usually means a systematic problem (a mis-zeroed scale, parallax, a calibration offset) rather than random noise.

Common mistakes

The most common error is swapping the experimental and theoretical values — the accepted, known value always goes in the denominator, never your measurement. Another is confusing percent error with percent difference: percent difference compares two measurements of equal standing and divides by their average, whereas percent error compares a measurement to a trusted true value. People sometimes panic at a result above 100%, but that is perfectly valid and simply means the measurement was more than double the true value. Finally, forgetting that the denominator uses the absolute value of the theoretical figure leads to sign confusion whenever the true value is negative.