Percent error calculator

Absolute error is the size of the gap between your measurement and the true value, in the same units as the measurement:

absolute error = |measured − true|

Percent error expresses that gap as a share of the true value:

percent error = |measured − true| / |true| × 100

Because it is relative, percent error lets you compare the quality of measurements of very different sizes. Being off by 1 mm on a 10 cm block is a 1% error; being off by 1 mm on a 10 m hallway is 0.01%.

Some teachers and textbooks drop the absolute value bars and keep the sign, so that a measurement below the true value gives a negative percent error. The calculator shows both: the usual unsigned percent error as the main result, and the signed error, with a note saying whether your value was high or low.

In a pendulum lab you get 9.6 m/s² for the acceleration due to gravity. The accepted value is 9.81 m/s².

1. Absolute error: |9.6 − 9.81| = 0.21 m/s².
2. Divide by the true value: 0.21 / 9.81 = 0.021407.
3. Multiply by 100: 2.14%.

Your value is below the accepted one, so the signed error is −2.14%. For a high school or intro college lab that is a good result. Timing a few swings by hand with a stopwatch, measuring the string length to the wrong point on the bob and swinging at a large angle each add a little error.

You transfer exactly 2.50 mL from a calibrated pipette into a graduated cylinder and read 2.48 mL.

• Absolute error: 0.02 mL.
• Percent error: 0.02 / 2.50 × 100 = 0.8%.

In a lab report, give both numbers. The absolute error relates to the instrument's resolution (the cylinder's smallest division), while the percent error tells the reader how good the measurement is overall.

If the true value is zero, percent error is undefined because you can't divide by zero. In that case report the absolute error only.

The two words are often used interchangeably, but in science they mean different things:

• Accuracy is how close a measurement is to the true value. Percent error measures accuracy.
• Precision is how close repeated measurements are to each other. It is described with the standard deviation, or with the percentage difference between two trials.

A set of measurements can be precise but not accurate. If a balance isn't zeroed, every reading is off by the same amount: the readings agree with each other, but they are all wrong. Repeating the measurement won't fix this kind of systematic error; only calibrating the instrument will. Random errors, on the other hand, shrink when you average several readings. If you took multiple trials, average them first and enter the average as your measured value.

When a result is calculated from several measured quantities, their errors combine. The simple worst-case rules taught in most intro courses:

• Sums and differences: absolute errors add.
• Products and quotients: percent errors add.
• Powers: the percent error is multiplied by the exponent (the error in r² is twice the error in r).

For example, if the length of a rectangle has a 1% error and the width a 2% error, the area has an error of up to 3%. In more advanced courses independent errors are combined in quadrature (the square root of the sum of squares), which gives a smaller, more realistic figure: about 2.24% here. This calculator checks the final result against an accepted value; it doesn't propagate errors for you.

There is no universal cutoff. It depends on the experiment and the equipment:

• In many high school and intro college labs, a percent error under about 5% is considered good, and under 10% acceptable.
• In analytical chemistry, results are often expected within a fraction of a percent.
• In engineering, the acceptable error is set by the specification or tolerance of the part.

The most useful comparison is with your instrument's stated accuracy. If your percent error is much larger than what the instrument can achieve, look for a problem in the procedure. Results are shown to four decimal places; round to two significant figures (2.1%) for most reports. The Share button copies a link with your values, so lab partners can check the same calculation.

With the measured value in A2 and the accepted value in B2, the Excel or Google Sheets formula is =ABS(A2-B2)/ABS(B2)*100. Remove the ABS around the difference, =(A2-B2)/ABS(B2)*100, if your course wants the signed version. Fill it down to grade a whole table of trials at once.