Calculate percent error between experimental and theoretical values. Find absolute error, relative error, signed error, and measurement accuracy with tolerance analysis.
Percent Error
5.000%
The value you measured or calculated
The known or accepted true value
Show direction (over/under the theoretical value)
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!)
| 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 |
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|
Percent Error
5.000%
Quick-start with common scenarios
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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.
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.
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.
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.
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).
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.
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).
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.
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: 2025-01-15
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Percent Error
5.000%