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Absolute Error vs Relative Error vs Percent Error

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Direct answer

Absolute error retains the measurement unit. Relative error scales that error by the reference magnitude. Percent error is relative error expressed per hundred.

Formula and method

Absolute error = |m−r|; relative error = |m−r|/|r|; percent error = relative error × 100

This page must show the formula exactly as the calculator or worked method uses it. Inputs remain unrounded during the calculation; rounding applies only to the displayed answer unless a domain-specific rule requires otherwise.

Step-by-step calculation

  1. Find the absolute gap in the original unit.
  2. Divide by the reference magnitude for a dimensionless ratio.
  3. Multiply by 100 for percent error.
  4. Report the measure that fits the decision.

Worked examples

Length

Measured 49.5 cm vs 50.0 cm: absolute error 0.5 cm; relative error 0.01; percent error 1%.

Scale matters

An error of 0.5 cm is 10% against 5 cm but 0.1% against 500 cm.

Zero

With reference 0, absolute error remains available but relative and percent error do not.

Interpretation and edge cases

  • Relative error is dimensionless; absolute error is not.
  • Percent error does not contain uncertainty by itself.
  • Use a validated tolerance when deciding pass/fail.

Frequently asked questions

Which error has units?

Absolute error.

Is relative error already a percentage?

It is a ratio; multiply by 100 or apply percent formatting to express it as a percentage.

Which is best?

It depends on whether physical magnitude or scale-normalized comparison matters.

Sources and transparency

The formulas and examples were evidence-checked on 2026-09-10. This is educational mathematical content. It does not replace a field-specific standard, accounting policy, laboratory method, contractual definition or professional judgment. CalculatorGeek should display a named human reviewer only after a real reviewer has completed and documented that review.

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