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The value you measured or calculated
The known or accepted true value
Show direction (over/under the theoretical value)
Error Visualization
Step-by-Step Solution
Step 1: Find the absolute error
|Experimental - Theoretical| = |47.5 - 50| = 2.500000
Step 2: Divide by the absolute theoretical value
2.500000 / |50| = 0.050000
Step 3: Multiply by 100 to get percentage
0.050000 x 100 = 5.000%
Percent Error = 5.000% (Good accuracy!)
Error Interpretation Guide
| Percent Error | Interpretation | Typical Applications |
|---|---|---|
| 0-1% | Excellent | Precision instruments, physics |
| 1-5% | Good | Most lab experiments |
| 5-10% | Acceptable | General measurements, surveys |
| >10% | Poor - Review needed | May indicate systematic error |
Common Sources of Error
Systematic Errors
- Calibration issues
- Consistent measurement technique errors
- Environmental factors
- Equipment limitations
Random Errors
- Reading scale imprecision
- Reaction time variations
- Environmental fluctuations
- Sample variations
Related Error Formulas
Percent Error (Absolute)
= |Experimental - Theoretical| / |Theoretical| x 100%
Signed Percent Error
= (Experimental - Theoretical) / |Theoretical| x 100%
Percent Difference
= |Value1 - Value2| / ((Value1 + Value2) / 2) x 100%
Relative Error
= |Experimental - Theoretical| / |Theoretical|
Absolute Error
= |Experimental - Theoretical|
Error Analysis
Percent Error
5.000%
Common Percent Error Examples
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Practice Problems
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?How Do You Calculate Percent Error?
Percent error measures how far an experimental value is from the theoretical (accepted) value. Formula: |Experimental - Theoretical| / |Theoretical| * 100%. For example, if you measured 9.8 m/s^2 for gravity (theoretical 9.81): |9.8 - 9.81| / 9.81 * 100% = 0.102% error. Lower is better.
What is Percent Error?
Percent error (or percentage error) is a measure of how inaccurate a measurement is, expressed as a percentage of the true value. It compares an experimental or measured value to a known theoretical or accepted value, showing how far off the measurement is. Percent error is essential in science, engineering, and quality control.
Key Facts About Percent Error
- Formula: |Experimental - Theoretical| / |Theoretical| * 100%
- Always expressed as a positive percentage
- Lower percent error = more accurate measurement
- Absolute error = |Experimental - Theoretical|
- Relative error = Absolute error / Theoretical value
- Used to evaluate accuracy of experiments and measurements
- 0% error means perfect accuracy (rare in practice)
- Systematic vs random errors affect percent error differently
Quick Answer
Percent error measures how far an experimental value is from the theoretical (accepted) value. Formula: |Experimental - Theoretical| / |Theoretical| * 100%. For example, if you measured 9.8 m/s^2 for gravity (theoretical 9.81): |9.8 - 9.81| / 9.81 * 100% = 0.102% error. Lower is better.
Frequently Asked Questions
What is percent error?
Percent error measures the difference between an experimental (measured) value and a theoretical (accepted/true) value, expressed as a percentage. It shows how accurate your measurement or calculation is compared to the accepted value.
What is the percent error formula?
Percent Error = |Experimental - Theoretical| / |Theoretical| x 100%. The absolute value ensures the result is always positive. Some contexts use signed error to show direction (over or under).
What is an acceptable percent error?
Acceptable error depends on the field. In chemistry labs, 5-10% is often acceptable. Physics experiments may require <1%. Manufacturing tolerances vary by product. Generally, lower is better, but context determines what's acceptable.
What is the difference between percent error and percent difference?
Percent error compares to a known/accepted value (theoretical). Percent difference compares two measured values where neither is "correct." Error uses: |exp-theo|/|theo|. Difference uses: |v1-v2|/((v1+v2)/2).
Can percent error be negative?
Standard percent error uses absolute values, so it's always positive or zero. However, "signed percent error" (without absolute values) can be negative, indicating the experimental value is less than the theoretical value.
What is signed percent error?
Signed percent error keeps the direction of the error. A positive signed error means you measured higher than expected (overestimate). A negative signed error means you measured lower (underestimate). Formula: (Experimental - Theoretical) / |Theoretical| x 100%.
Last updated: 2026-01-15
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How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
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