MultiConvers

Percent Error Calculator

Compare a lab or classroom measurement with the accepted value and get an unsigned percent error — how far you were, not whether you were high or low.

How to use

  1. Enter the experimental (measured) value first.
  2. Enter the theoretical or accepted value from the textbook, certificate or data sheet.
  3. Read the unsigned percent. 9 vs 10 and 11 vs 10 both show 10%.
  4. Use percentage change if both numbers are just “old” and “new,” with no accepted truth.

How it works

Percent error is a lab statistic: |measured − accepted| ÷ |accepted| × 100. Against 10, a 9 and an 11 are the same 10% miss. The sign is dropped so a report can say “within 2%” without arguing direction. If you need “2% high,” that is a signed relative error and this page will not print the plus.

The denominator is the accepted value, not the measurement. Measuring 50 against 40 is 25% error, not 20%. Swapping the boxes is the usual homework mistake.

Accepted 0 is undefined. There is no finite “percent of nothing.” The tool refuses that case instead of printing Infinity.

This is not percentage change. Change compares two observations of the same kind of thing over time. Error compares a measurement to a standard. Density labs, titration titres and instrument checks belong here. Price history belongs on percentage change.

More than 100% is allowed. Measuring 3 against 1 is 200%. That is a relative gap, not a test score capped at 100.

Formula

Percent error = |experimental − theoretical| ÷ |theoretical| × 100

Worked examples

  • A lab density

    experimental 1.25, theoretical 1.20 → 4.1667%

  • Either side of 10

    9 vs 10, or 11 vs 10 → 10%

Useful notes

  • Unsigned: high and low misses of the same size match.
  • Divide by the accepted value, not the measurement.
  • Zero accepted value is rejected.

FAQ

What is the percent error formula?

Take the absolute difference between the experimental and theoretical values, divide by the absolute theoretical value, and multiply by 100.

Can percent error be more than 100%?

Yes. If you measure 3 against an accepted 1, the error is 200%. The figure is a relative gap, not a score that stops at 100.

Why is a theoretical value of 0 rejected?

You cannot divide by zero. There is no finite percent error against an accepted value of 0.

I measured 1.25 and the book says 1.20. What is the error?

|1.25 − 1.20| ÷ 1.20 × 100 ≈ 4.1667%.

Does this show if I was too high?

No. Both directions look the same. Subtract measured minus accepted yourself if you need the sign.

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