Every physics and chemistry practical asks how close your result is to the accepted value. Enter your measured value and the true value to get the absolute, relative and percentage error.
Enter your measured value.
Enter the accepted true value.
Read the percentage error.
Percentage error: |measured − true| ÷ |true| × 100
Percentage error tells you how far a measured or experimental value is from the true or accepted value, as a share of the true value. This calculator takes both values and returns the absolute error |measured − true|, the relative error, which is absolute error ÷ |true|, and the percentage error, which is the relative error × 100.
Every physics and chemistry practical in Classes 11 and 12 asks for it: measuring g with a pendulum, the focal length of a lens, the density of a solid or the concentration of a solution by titration. It is also used in manufacturing to see whether a part is within tolerance, in surveying and in checking whether a weighing scale or meter is accurate. Because it is a percentage, it lets you compare the quality of measurements of very different sizes.
1. Write down the measured value and the true or accepted value, in the same unit.
2. Find the absolute error: |measured − true|.
3. Divide by the magnitude of the true value to get the relative error: |measured − true| ÷ |true|.
4. Multiply by 100 to get the percentage error.
5. If your course keeps the sign, use (measured − true) ÷ true × 100, so a positive answer means your value was too high.
6. If the true value is zero, report the absolute error instead, because percentage error is undefined.
Absolute error is in the same unit as the measurement, such as 0.05 cm. It does not tell you whether the error is large or small without context. An error of 1 cm matters a lot for a 5 cm length but hardly at all for a 100 m track. Relative error divides by the true value to remove the unit and give a pure ratio, and percentage error simply multiplies that by 100. The calculator divides by the absolute value of the true value, so negative quantities give a sensible positive error.
Percentage error measures accuracy: how close you are to the true value. Precision is different: it is how close repeated measurements are to each other. A student can be precise but inaccurate if the instrument has a zero error that shifts every reading, and a single lucky reading can be accurate without being precise. Systematic errors, from faulty instruments or method, push results in one direction. Random errors scatter them and can be reduced by averaging many readings.
Percentage error needs a known true value to compare against. When you compare two experimental results with no accepted value, such as two students' readings, use percentage difference instead: |A − B| divided by their average, times 100. Percentage error is also related to, but distinct from, the percentage uncertainty that comes from an instrument's least count. In error propagation for a product or quotient, percentage uncertainties add, which is why a squared quantity doubles its percentage uncertainty.
In a Class 11 practical, Tanya measured the period of a pendulum designed to swing with a 2 second period, and her average reading was 2.03 s.
Absolute error: |2.03 − 2| = 0.03
Percentage error: 0.03 ÷ |2| × 100 = 1.5%
Answer: Percentage error 1.5%; Absolute error 0.03; Relative error 0.015
Dividing by the measured value instead of the true value.
Swapping the two inputs, which changes the result because the denominator changes.
Forgetting to multiply by 100 and reporting a relative error of 0.015 as a percentage.
Comparing values in different units, such as cm with m.
Using percentage error when there is no accepted value, where percentage difference is the right measure.
Writing the error analysis section of physics and chemistry practical records.
Checking a weighing scale, thermometer or meter against a standard.
Quality control of manufactured parts against their specified dimensions.
Comparing a forecast or estimate with the actual outcome.
Evaluating how well a model or approximation matches known values.
Can percentage error be negative?
With the absolute-value formula it is always positive. Some courses keep the sign to show whether the result was high or low.
What if the true value is zero?
Percentage error is undefined; report the absolute error instead.