Percent error is a useful measure that tells us how accurate a measured or estimated value is compared to the true or accepted value. It expresses the error as a percentage relative to the actual value, allowing easy interpretation of the level of accuracy or deviation.

What is Percent Error Calculator ?

Percent error quantifies the difference between an estimated or measured value and the true value, expressed as a percentage of the true value. It helps highlight how large the error is in relation to the accepted value. A smaller percent error means the estimate is closer to the true value, while a larger percent error indicates a bigger deviation.

Why Percent Error Calculator ?

Percent error is frequently used in scientific experiments, engineering, and mathematics to:

• Assess measurement accuracy
• Compare estimated results with actual values
• Understand limitations due to human error or instrument precision
• Improve experimental methods or calculations

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The Percent Error Formula

The formula to calculate percent error is:Percent Error=∣Measured Value−True ValueTrue Value∣×100%Percent Error=True ValueMeasured Value−True Value×100%

Key points:

• Use the absolute value (ignoring any negative sign) so the error is always expressed as a positive percentage.
• The “Measured Value” is the value obtained from your experiment, estimation, or calculation.
• The “True Value” is the exact, accepted, or theoretical value that you compare against.

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Step-by-Step Calculation of Percent Error

1. Identify the true (accepted) value and the measured (experimental) value.
2. Find the difference between the measured and true values:Error=Measured Value−True ValueError=Measured Value−True Value
3. Take the absolute value of this difference:Absolute Error=∣Error∣Absolute Error=∣Error∣
4. Divide the absolute error by the true value:Relative Error=Absolute ErrorTrue ValueRelative Error=True ValueAbsolute Error
5. Multiply by 100 to convert to a percentage:Percent Error=Relative Error×100%Percent Error=Relative Error×100%

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Example Calculation

Suppose you measure the length of a rope and find it to be 48 cm. The actual length is 50 cm. What is the percent error?

• Measured Value = 48 cm
• True Value = 50 cm

Steps:

1. Calculate the difference: 48−50=−248−50=−2
2. Take absolute value: ∣−2∣=2∣−2∣=2
3. Divide by true value: 250=0.04502=0.04
4. Convert to percentage: 0.04×100=4%0.04×100=4%

So, the percent error is 4%, indicating your measurement is very close to the actual length.

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Summary

• Percent error provides a standardized way to communicate accuracy of measurements.
• Always base the calculation on the true value to gauge how much your estimate deviates.
• Use absolute values so the sign of the difference doesn’t affect the error magnitude.
• Multiply by 100 to express the error as a percentage for easy understanding.

By following these steps and using the formula, you can calculate percent error accurately to assess and improve your measurements and experiments.