About the Percentage Error Calculator
Comparing an experimental or measured value against a known true value is a core part of scientific method - percentage error quantifies exactly how far off a measurement was. Our Percentage Error Calculator finds it instantly.
How It Works
The calculator finds the absolute difference between your experimental and true values, divides by the absolute true value, and multiplies by 100 to express the discrepancy as a percentage.
Formula & Methodology
Dividing by the true value (rather than by the experimental value or an average of the two) makes percentage error a measure of how far off a measurement was relative to what it should have been - the reference point that defines correctness. Using absolute value ensures the result is always reported as a positive magnitude of error, since being too high or too low by the same amount represents an equally sized mistake, even though the direction of the error might separately matter for diagnosing its cause.
Step-by-Step: Calculating It By Hand
- 1Subtract the true value from the experimental (measured) value.
- 2Take the absolute value of that difference.
- 3Divide by the absolute value of the true value.
- 4Multiply by 100 to express the result as a percentage.
Examples
Small error
A measured value of 97 against a true value of 100 gives a 3% percentage error - a relatively small, often acceptable discrepancy depending on the context.
Larger error
A measured value of 85 against the same true value of 100 gives a 15% percentage error - significant enough to warrant investigating the source of the discrepancy.
Advantages
- Standardizes measurement discrepancies as a comparable percentage, regardless of the underlying units or scale
- Simple, widely used formula across all experimental sciences
- Fast way to evaluate the quality of a measurement or experimental result
- Useful for lab reports and coursework requiring error analysis
Common Mistakes
- Confusing percentage error with percentage difference, which uses a different (averaged) denominator
- Forgetting the formula uses absolute value, so error is always reported as a positive percentage
- Not investigating the source of a large percentage error, treating it only as a number to report rather than a signal to check methodology
- Comparing percentage errors across experiments with very different acceptable tolerance levels without context
Edge Cases to Watch For
- If the true value is zero, percentage error is undefined, since it requires dividing by zero.
- Percentage error is always reported as positive due to the absolute value - if the direction of error matters, that needs to be noted separately.
- Percentage difference (used when comparing two measured values with no known 'true' value) uses a different formula, typically dividing by the average of the two values instead.
- What counts as an 'acceptable' percentage error varies enormously by field and application - there's no universal threshold for what's considered a good or bad result.
Common Use Cases
- Lab report and coursework error analysis
- Evaluating the accuracy of experimental measurements
- Comparing measurement quality across different experimental trials
- Quality control and manufacturing tolerance checks