Percentage Error Calculator

What is Percentage Error?

Percentage error is a measure of the discrepancy between an observed or measured value and the true or accepted value. It expresses this difference as a percentage of the true value, providing a relative measure of accuracy.

Formula and Its Meaning

The formula for percentage error is:

\[\text{Percentage Error} = \left|\frac{\text{Observed Value} - \text{True Value}}{\text{True Value}}\right| \times 100\%\]

Where:

• Observed Value: The value measured or calculated in an experiment
• True Value: The accepted or known correct value
• The vertical bars || indicate the absolute value

This formula gives the magnitude of the error as a percentage, regardless of whether the observed value is higher or lower than the true value.

Calculation Steps

1. Subtract the true value from the observed value
2. Divide this difference by the true value
3. Take the absolute value of this ratio
4. Multiply by 100 to convert to a percentage

Example Calculation

Let's calculate the percentage error for an experiment where:

• Observed Value = 52 cm
• True Value = 50 cm

1. \(\text{Difference} = 52 - 50 = 2\text{ cm}\)
2. \(\text{Ratio} = \frac{2}{50} = 0.04\)
3. \(\text{Absolute Value} = |0.04| = 0.04\)
4. \(\text{Percentage} = 0.04 \times 100\% = 4\%\)

Therefore, the percentage error is 4%.

Visual Representation

This bar chart represents the example calculation. The blue bar shows the observed value (52 cm), while the green bar represents the true value (50 cm). The red line indicates the error between these two values.