Uncertainty & measurement

Percentage Error & Difference Calculator

Choose error when you have an accepted reference, or difference when neither measurement is the reference.

Your measurements

Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.

Percentage Error & Difference Calculator inputs

Calculated locally. No account or uploads.

Result & working

Example

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The formula

Error = |experimental − accepted| / |accepted| × 100%

Difference = |a − b| / [(|a| + |b|)/2] × 100%

Signed change = (new − initial) / |initial| × 100%

What the variables mean
SymbolMeaning
ExperimentalThe measured or experimental result.
AcceptedA non-zero reference value used for percentage error.
a, bTwo values with equal standing, used for percentage difference.

When to use this calculator

Percentage error measures how far an experimental result is from an accepted value; reversing the inputs usually changes the answer. Percentage difference is symmetric and measures separation relative to the average magnitude. Signed percentage change compares a new value with a non-zero initial value using its magnitude as the denominator; the sign indicates an increase or decrease.

With two measurements 10 and 12, percentage difference is 2/11 × 100 ≈ 18.18%. If 12 is the accepted reference, percentage error is 2/12 × 100 ≈ 16.67%. The formulas answer different questions.

Worked example

The calculator opens with these example values. All steps below are available even with JavaScript disabled.

  1. Percentage error = |experimental − accepted| / |accepted| × 100
  2. = |9.7 − (9.81)| / |9.81| × 100 = 1.121305%

1.121305%

Common mistakes

  • Do not call percentage difference a measurement uncertainty.
  • A zero accepted value makes percentage error undefined.
  • Both values zero make percentage difference undefined; opposite signs can give 200% under this convention.