Percent Error Calculator

Used in science and math labs worldwide, percent error measures how close an experimental measurement is to the true or theoretical value. This calculator gives you the error percentage and tells you whether your result was above or below the expected value.

How to Use This Calculator

1. Enter the experimental (measured) value — the value you obtained from your experiment or measurement.
2. Enter the theoretical (accepted) value — the true or expected value from a reference source.
3. Click Calculate to see the percent error, absolute error, and direction (positive or negative).

Percent Error Formula

% Error = |(Experimental − Theoretical)| ÷ |Theoretical| × 100

The absolute value (| |) ensures the result is always positive when you want magnitude only. Some applications report signed error (positive = over, negative = under) to show direction.

Example Calculation

You measured the boiling point of ethanol as 80.5°C. The accepted value is 78.37°C.

• Absolute error: |80.5 − 78.37| = 2.13
• % Error: 2.13 ÷ 78.37 × 100 = 2.72%
• Direction: Experimental > Theoretical (measured high)

What Is an Acceptable Percent Error?

• Under 5%: Generally acceptable in most lab settings.
• Under 1%: Excellent precision — typical in careful analytical chemistry.
• Above 10%: Indicates a significant systematic error that needs investigation.
• Context matters: 5% error in a rough field estimate is fine; 5% error in a pharmaceutical measurement is not.

Common Mistakes to Avoid

• Dividing by the experimental value instead of the theoretical value — Always use the accepted/theoretical value as the denominator.
• Not using absolute value — Whether you measured high or low, the magnitude of the error is what matters for most analyses.
• Confusing percent error with percent difference — Percent difference compares two measured values with no reference "true" value. Percent error requires a known theoretical value.

Frequently Asked Questions

What causes percent error in experiments?

Sources of error include: equipment limitations (instrument accuracy), human error (reading scales incorrectly), environmental factors (temperature, pressure), and procedural errors (contamination, timing).

What is systematic vs. random error?

Systematic error: consistent bias in one direction (e.g., a scale that always reads 2g too heavy). Random error: unpredictable variation around the true value. Systematic errors affect accuracy; random errors affect precision.

Is a negative percent error possible?

If you report signed error: yes. A negative error means your measurement was below the theoretical value. If you use the absolute value formula, percent error is always reported as positive.

Conclusion

Percent error is the standard way to evaluate experimental accuracy in science. Use this calculator for any lab report, measurement analysis, or quality control application — and investigate any error above 5% for systematic causes.

Related: Percent Calculator | Statistics Calculator | Standard Deviation Calculator