Percent Error Calculator
Percent error: what it is
Percent error tells you how far a measured (experimental) value is from an accepted (true/theoretical) value, expressed as a percentage of the accepted value. It’s commonly used in science labs, engineering measurements, quality checks, and any situation where you’re comparing a measurement to a reference.
A smaller percent error generally indicates a measurement closer to the accepted value (higher accuracy). Because the result is scaled by the accepted value, percent error is easy to compare across different units and magnitudes (for example, comparing errors in grams vs kilograms).
Percent error formula (absolute vs signed)
Most textbooks and lab rubrics use the absolute percent error (always non‑negative). Some fields also report a signed percent error to show whether the measurement is above or below the accepted value.
Absolute percent error (most common)
Where:
- Vm = measured (experimental) value
- Vt = true/accepted/theoretical value
Note that this calculator divides by |Vt| (the magnitude of the accepted value) so the percentage scale behaves sensibly even when the accepted value is negative (a case that occurs in some physics/finance contexts).
Signed percent error (directional)
If the signed percent error is positive, the measurement is above the accepted value. If it’s negative, the measurement is below the accepted value.
How to use the calculator
- Enter the True/Accepted value (the reference value from a datasheet, textbook constant, calibration standard, etc.).
- Enter the Measured value (your experimental result).
- Select whether you want absolute or signed percent error (optional).
- Click Calculate. The tool shows the percent error and also the underlying absolute and signed differences so you can sanity‑check your inputs.
Worked example (step by step)
Example: You measured the boiling point of a liquid as 97.2 °C. The accepted value is 100.0 °C.
- Difference (measured − accepted): 97.2 − 100.0 = −2.8
- Absolute difference: |−2.8| = 2.8
- Divide by accepted value: 2.8 / 100.0 = 0.028
- Convert to percent: 0.028 × 100% = 2.8%
Interpretation: Your measurement is off by 2.8% relative to the accepted value. Using the signed version would show −2.8%, indicating the measurement is below the accepted value.
Interpreting results
- 0% means the measured value matches the accepted value exactly.
- 1–5% is often considered “close” in many classroom labs, but acceptable thresholds depend on your instrument precision and context.
- Large percent error can indicate systematic error (calibration issue), procedural mistakes, unit conversion problems, or that the “accepted value” isn’t appropriate for your conditions.
Percent error vs. related measures
| Measure | What it compares | Formula (concept) | Typical use |
|---|---|---|---|
| Absolute error | Measured vs accepted | |measured − accepted| | Raw deviation in original units |
| Signed error | Measured vs accepted | measured − accepted | Direction of bias (high/low) |
| Percent error | Measured vs accepted | |measured − accepted| / |accepted| × 100% | Scaled deviation for cross‑scale comparison |
| Percent difference | Two measured values | |A − B| / average(A,B) × 100% | Comparing two experiments when neither is “true” |
Assumptions, limitations, and edge cases
- Accepted value cannot be 0: percent error is undefined when the true/accepted value is zero (division by zero). In that case, use absolute error (measured − accepted) or another domain‑specific metric.
- Units must match: both inputs must be in the same units (e.g., both in meters, not meters vs centimeters).
- Negative accepted values: this tool uses |accepted| in the denominator for the absolute percent error so the magnitude behaves consistently. For the signed percent error, the sign depends on the accepted value; interpret carefully if your accepted value is negative.
- Rounding: results are rounded for display. For reporting, match the significant figures to your lab requirements (often limited by instrument precision).
- Not a substitute for uncertainty analysis: percent error compares to a single accepted value. It does not incorporate measurement uncertainty, confidence intervals, repeatability, or propagation of error.
FAQ
Can percent error be negative?
The absolute percent error is never negative. A signed percent error can be negative when the measured value is below the accepted value.
What if my accepted value is zero?
Percent error is undefined when the accepted value is 0. Use absolute error (difference in units) or a metric appropriate to your field.
What’s the difference between percent error and percent difference?
Percent error compares a measurement to a known/accepted value. Percent difference compares two measured values when neither is treated as the “true” value (it typically divides by the average of the two values).