How the Percent Error Calculator works.
percent error = |experimental − accepted| ÷ |accepted| × 100E is the experimental value and A is the non-zero accepted reference value.
Worked example
An experiment of 9.5 against accepted 10 has 5% error.
What the result means
Percent error reports distance from a reference, not whether a method is biased.
Edge cases
An accepted value of zero makes the relative comparison undefined.
Formula and accepted-value reference
Percent error measures the absolute difference between an experimental value E and a nonzero accepted or reference value A, relative to the magnitude of A: |E − A| ÷ |A| × 100. The absolute values make the reported error size nonnegative. The accepted value is the denominator and therefore sets the comparison scale; swapping the two entries can change the result, so place the measured result and reference in their labelled fields deliberately.
Worked experimental example
For an experimental value of 9.5 and an accepted value of 10, the absolute difference is |9.5 − 10| = 0.5. Divide by the accepted magnitude: 0.5 ÷ |10| = 0.05. Multiply by 100 to obtain 5%. A quick reverse check is that 5% of the accepted value 10 equals the 0.5 absolute difference. Keep unrounded source values through the calculation and round only the reported result.
Signs, units and absolute magnitude
Both inputs may be positive or negative when the underlying quantity legitimately uses signed values. The denominator uses |A|, so an experimental value of −9.5 compared with an accepted value of −10 also gives 5%. The two values must describe the same quantity in compatible units and on the same scale. Convert units before calculating; comparing 950 centimetres directly with 10 metres would produce a mathematically valid but meaningless result.
Zero, equality and input boundaries
An accepted value of zero is rejected because division by |A| would be undefined. If both values are equal and the accepted value is nonzero, the percent error is exactly 0%. Zero is allowed as the experimental value when the accepted value is nonzero, producing 100% error. Blank, non-finite and values outside the supported numeric range are rejected rather than producing a result that looks precise. Check signs and decimal placement before interpreting a very large percentage.
Percent error versus other comparisons
Percent error is appropriate when one value is treated as the accepted reference. Percent difference commonly compares two peer measurements by dividing their absolute difference by an average magnitude; percent change uses an original value as its baseline; percentage-point difference subtracts two percentages directly. Those methods answer different questions and can return different numbers. Do not relabel this calculator’s accepted value merely to force a preferred denominator or use the result as a symmetric comparison.
Measurement uncertainty and reporting limits
A small percent error means the entered experimental value is close to the entered accepted value on this relative scale, but it does not establish accuracy, precision, repeatability, calibration quality, statistical significance or freedom from bias. The accepted value may itself have uncertainty, tolerances or revisions. For laboratory, engineering, quality-control or regulated reporting, retain units, significant figures, instrument resolution, uncertainty information and the authoritative reference alongside the calculated percentage.
What this calculator does not include.
Measurement uncertainty, significant figures, and calibration are outside this formula.
Percent Error Calculator questions.
How is percent error calculated?
Subtract the accepted value from the experimental value, take the absolute difference, divide by the absolute accepted value, and multiply by 100. The absolute values make the reported error magnitude nonnegative.
Why can the accepted value not be zero?
The accepted value is the formula denominator. Dividing by an accepted magnitude of zero is undefined, so the calculator rejects zero instead of displaying infinity or an exact-looking percentage.
Can experimental and accepted values be negative?
Yes, when negative values are meaningful for the quantity. The calculator uses the signed difference and divides by the absolute accepted magnitude. For example, −9.5 compared with −10 produces 5% error.
What does a zero or 100% result mean?
Zero percent means the two entered values are equal and the accepted value is nonzero. An experimental value of zero compared with any nonzero accepted value produces 100% error because the absolute difference equals the accepted magnitude.
Is percent error the same as percent difference or percentage-point difference?
No. Percent error uses a designated accepted value as its denominator. Percent difference usually treats two measurements as peers and uses an average magnitude, while percentage-point difference directly subtracts two percentages.
Does a small percent error prove a measurement is accurate?
No. It shows only that the entered experimental value is close to the entered accepted value on this formula. It does not account for reference uncertainty, instrument resolution, repeatability, calibration, bias, sample quality or statistical significance.