Percent Error Calculator
Calculate percent error, absolute error, and relative error with step-by-step formulas. Includes reverse mode to find experimental value range.
About Percent Error Calculator
Calculate the absolute error, relative error, and percent error between an experimental measurement and a theoretical (accepted) value. Enter both values to see all three error measures with step-by-step formulas. A reverse mode finds the experimental value range for a given percent error tolerance.
Error Formulas
| Type | Formula | What It Measures |
|---|---|---|
| Absolute error | |Experimental - Theoretical| | The raw difference in the same units as the measurement |
| Relative error | |Experimental - Theoretical| / |Theoretical| | The error as a fraction of the true value |
| Percent error | (|Experimental - Theoretical| / |Theoretical|) x 100% | The error as a percentage of the true value |
Worked example: You measured the boiling point of water as 99.1°C. The accepted value is 100.0°C.
- Absolute error: |99.1 - 100.0| = 0.9°C
- Relative error: 0.9 / 100.0 = 0.009
- Percent error: 0.009 x 100% = 0.9%
What Is a "Good" Percent Error?
| Percent Error | Rating | Context |
|---|---|---|
| Under 1% | Excellent | Precision instruments, professional labs |
| 1 - 5% | Good | Student chemistry/physics labs with decent equipment |
| 5 - 10% | Acceptable | Student labs with basic equipment, field measurements |
| 10 - 20% | Poor | Rough estimates, low-precision instruments |
| Over 20% | High | Likely a systematic error or calculation mistake |
Percent Error vs Percent Difference
These are often confused but answer different questions:
| Percent Error | Percent Difference | |
|---|---|---|
| Compares | Measured value to a known true value | Two measured values to each other |
| Reference | The theoretical (accepted) value | The average of the two values |
| Formula | |exp - theo| / |theo| x 100% | |a - b| / ((a+b)/2) x 100% |
| Use when | There is a known correct answer | Both values are measurements with no "correct" one |
Sources of Error in Lab Measurements
- Systematic errors: Consistent bias in one direction. Examples: miscalibrated instrument, parallax reading, impure reagents. These cause percent error to be consistently positive or negative.
- Random errors: Unpredictable variation in both directions. Examples: temperature fluctuations, reading precision, timing reaction by hand. These cause scatter around the true value.
- Human errors: Mistakes like misreading a scale, spilling a solution, or using the wrong units. These are not true "errors" in the scientific sense and should be avoided rather than accounted for.
Reverse Mode: Finding the Acceptable Range
If you know the accepted value and the maximum acceptable percent error, you can find the range of experimental values that would pass:
Range = Theoretical ± (Percent Error / 100) x Theoretical
Example: Accepted density of aluminium = 2.70 g/cm³. Lab allows 5% error.
- Tolerance: 5% x 2.70 = 0.135 g/cm³
- Acceptable range: 2.70 ± 0.135 = 2.565 to 2.835 g/cm³
- Any measurement between 2.57 and 2.84 g/cm³ would be within 5%
Common Lab Values and Expected Errors
| Measurement | Accepted Value | Typical Student Result | Typical % Error |
|---|---|---|---|
| Boiling point of water | 100.0°C | 99-101°C | 0-1% |
| Density of water | 1.000 g/cm³ | 0.97-1.03 g/cm³ | 0-3% |
| Acceleration due to gravity | 9.81 m/s² | 9.5-10.1 m/s² | 0-3% |
| Speed of sound in air | 343 m/s | 330-355 m/s | 0-4% |
For handling the precision of your measurements correctly, the significant figures calculator counts and rounds to the right number of sig figs. For more complex calculations, the equation solver handles algebraic equations step by step.
All calculations run in your browser. No data is sent to any server.
Frequently Asked Questions
What is the percent error formula?
Percent error = |experimental - theoretical| / |theoretical| x 100%. It measures how far off your measured value is from the accepted or true value, expressed as a percentage.
What is the difference between percent error and percent difference?
Percent error compares a measured value to a known correct value. Percent difference compares two measured values to each other using their average as the reference. This tool calculates percent error.
What if the theoretical value is zero?
Percent error is undefined when the theoretical value is zero because the formula requires dividing by the theoretical value. The tool shows a clear message explaining this.
What does the reverse mode do?
Reverse mode works backwards. You enter a percent error and a theoretical value, and it tells you the range of experimental values that would produce that percent error. Useful for understanding measurement tolerances.
What counts as a good percent error?
It depends on the context. In a student lab, under 5% is generally considered good. In precision engineering, even 1% might be too much. The colour-coded bar gives a quick visual sense of accuracy.
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