Free percent error calculator
Calculate percent error between experimental and theoretical values — enter both values to see the percentage difference, updated live, as you type.
On this page10 sections
|experimental − theoretical| ÷ |theoretical| × 100. Always non-negative. Source: NIST.
Results are estimates. Consult a professional.
How the percent error calculator works
Percent error measures how far an experimental or measured value deviates from the accepted (theoretical) value, expressed as a percentage. The absolute value in the numerator ensures the result is always non-negative unless you specifically need directional error.
Worked example: density measurement
A student measures the density of a liquid and records 1.24 g/mL. The accepted value from the literature is 1.30 g/mL.
Typical acceptable percent error by measurement type
Acceptable error thresholds vary by discipline and instrument precision. The table below shows common benchmarks.
| Measurement type | Typical acceptable % error | Notes |
|---|---|---|
| Analytical balance (mass) | < 0.1% | High-precision lab instrument |
| Volumetric glassware | 0.1 – 0.5% | Burette, pipette, volumetric flask |
| General chemistry lab | 1 – 5% | Common student experiments |
| Physics experiments | 1 – 10% | Depends on equipment quality |
| Industrial measurements | 0.5 – 2% | Process control environments |
| GPS positioning | < 3 m (~0.0003%) | Relative to Earth's circumference |
Source: adapted from general laboratory practice guidelines
Tips for minimising and interpreting percent error
A low percent error confirms your method and equipment are working correctly. Here is how to get the most from this metric.
- Always use the accepted value as the denominator — dividing by the experimental value gives a different (and less standard) metric called percent difference.
- Repeat measurements reduce random error — take multiple readings and average them before calculating percent error to filter out noise.
- Systematic errors won't average out — if your instrument is mis-calibrated, repeating the measurement won't help; recalibrate first.
- Sign matters for bias detection — if your signed error is consistently positive (or negative) across repeated trials, your instrument has a directional bias.
- Compare to the measurement uncertainty — a percent error smaller than your instrument's stated uncertainty is effectively zero; don't over-interpret it.
Accuracy and limitations
The percent error formula is undefined when the theoretical value is zero — division by zero has no mathematical meaning. In practice, if the accepted value is zero or very close to zero, report the absolute error instead. This calculator evaluates to full double-precision floating point (15 significant digits). For extremely small differences (e.g. < 10⁻¹²), results may be affected by floating-point rounding; use specialised scientific software for sub-picogram or sub-nanometre precision work.
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About this calculator
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