Percentage error calculator

A measured value of 9.8 against an accepted value of 10 has a percentage error of 2%. Enter your measurement and the true or accepted reference to see the absolute percentage error, signed error, working and a comparison chart.

What this calculator does

Percentage error expresses the distance between a measurement and its accepted reference as a percentage of the reference magnitude. It helps science and lab students compare errors across measurements with different sizes. The main result is never negative, while the signed breakdown shows whether the measurement is numerically above or below the accepted value.

Use this calculation when you have a designated reference, such as a stated mass, standard solution concentration or expected experimental result. The accepted value is not necessarily known without uncertainty. This tool calculates the arithmetic comparison; it does not establish the accuracy of the reference, diagnose equipment faults or replace the uncertainty analysis required for a laboratory report.

Formula

Percentage error = |measured − accepted| ÷ |accepted| × 100

Or in one step: 100 × absolute error ÷ accepted magnitude

In plain English, subtract the accepted value from the measured value, take the size of that difference, divide by the size of the accepted value and multiply by 100. Absolute-value bars turn negative quantities into positive magnitudes. The accepted value cannot be zero because it is the denominator.

Worked example

A sample is measured as 9.8 g against an accepted mass of 10 g. The signed error is 9.8 − 10 = −0.2 g. Its absolute size is 0.2 g. Divide 0.2 by 10 and multiply by 100: the percentage error is 2%, with the measurement below the reference.

Worked example: volume error and a tolerance limit

A measured volume is 51.2 ml and the accepted volume is 50 ml. The signed error is +1.2 ml, so the measurement is over the accepted value. Divide 1.2 by 50 and multiply by 100 to get 2.4% error. The sign indicates direction, while the percentage describes the size of the discrepancy.

If a task specifies a tolerance of ±2% around 50 ml, the numerical permitted range is 49 ml to 51 ml. A reading of 51.2 ml is outside that range. The calculator supplies the error, not an automatic certification decision: use the stated tolerance, measurement uncertainty and any required decision rule for your particular task.

Worked example: a resistor within a stated tolerance

A resistor has an accepted nominal value of 100 ohms and measures 104.7 ohms. Its signed error is +4.7 ohms. The absolute percentage error is 4.7 ÷ 100 × 100 = 4.7%. Against a simple ±5% nominal tolerance, the numerical range is 95 to 105 ohms, so this reading falls inside that range.

Record the conditions and instrument resolution alongside the result. Rounding the displayed measurement too early can move a borderline reading across a tolerance boundary. For repeated measurements, do not assume that a small error in their average means every individual reading was close to the reference; spread and systematic bias are different issues.

Percentage error in Excel and Google Sheets

Put the measured value in A1 and the accepted value in B1. Use =ABS(A1-B1)/ABS(B1)*100 to get percentage error as an ordinary number. For the signed relative error, use =(A1-B1)/ABS(B1)*100. Both Excel and Google Sheets support these formulas, and both require a non-zero accepted value.

If you want the result in a percentage-formatted cell, omit the final *100 and apply percentage formatting instead. Keep the signed difference in another cell with =A1-B1, labelled with the measurement unit. Convert unlike units before doing any of these calculations, and round the final reported answer rather than the intermediate difference.

Everyday examples

Example	Answer	Try it
Mass: measured 9.8 g, accepted 10 g	2%
Volume: measured 51.2 ml, accepted 50 ml	2.4%
Resistance: measured 104.7 ohms, accepted 100 ohms	4.7%
Length: measured 24.5 cm, accepted 25 cm	2%

Common mistakes

Dividing by the measured value instead of the accepted value. The reference determines the denominator in a percentage error calculation.
Reporting a negative absolute percentage error. Preserve the sign separately to show over or under, then use absolute values for the main result.
Mixing units before subtracting. Convert both measurements to the same unit, such as grams, before entering the numbers.
Treating a small percentage error as proof of reliable technique. Repeated readings, calibration and uncertainty still matter, even when one result happens to be close.

Common questions

What is the percentage error formula?

Subtract the accepted value from the measured value, take the absolute difference, divide by the absolute accepted value and multiply by 100. For 9.8 measured against 10 accepted, this gives |9.8 − 10| ÷ |10| × 100 = 2%.

Can percentage error be negative?

The absolute percentage error used here cannot be negative. A signed relative error can be negative when the measurement is below the accepted value. The breakdown includes both the signed difference in the original units and the signed relative error, separately from the non-negative main result.

Why can the accepted value not be zero?

The accepted value is the base of the relative comparison. Dividing by its magnitude would mean dividing by zero. You can still calculate an absolute difference from zero, but an ordinary percentage error is undefined, so the calculator asks for a non-zero reference.

Can the measured value be zero?

Yes. If the accepted value is non-zero, a zero measurement has 100% error because the absolute difference equals the accepted magnitude. For example, measured 0 against accepted 10 gives |0 − 10| ÷ 10 × 100 = 100%.

Can percentage error be greater than 100%?

Yes. A measurement of 25 against an accepted value of 10 has an absolute difference of 15, giving 150% error. This is mathematically valid. Check the units, transcription, reference value and experimental method before interpreting such a large discrepancy.

What is the difference between percentage error and percentage difference?

Percentage error uses a designated accepted value as its reference. Percentage difference compares two positive values on equal terms, using their average as the denominator. Swapping measured and accepted values can change percentage error, whereas swapping the two values does not change percentage difference.

Can I use a negative accepted value?

Yes, provided it is not zero. The denominator uses its absolute magnitude. Signed over or under refers to numerical position, not magnitude. Be careful with offset scales such as Celsius: a relative percentage may not have the intended physical meaning, even though the arithmetic can be performed.

Last reviewed 8 November 2026. Results use exact decimal arithmetic and are rounded once for display.