Percent Error Calculator

What is Percentage Error?

Percentage error measures the difference between an observed (measured) value and a true (expected or accepted) value. It’s commonly used to evaluate how accurate a measurement is when compared to a known standard or accepted value.

When collecting data—whether measuring the density of a material, the acceleration due to gravity, or any other physical quantity—the measured value often differs from the true value. These discrepancies can arise from human error, estimation, or limitations of measuring equipment. Percentage error helps quantify how much a measured value deviates from the true value.

A small percentage error indicates a close match between observed and true values, while a large percentage error may suggest mistakes or flaws in the method. For example, if your measured value differs from the true value by 90%, it’s a clear sign that something is wrong with the measurement or the technique used.

How to Calculate Percentage Error:

Formulas:

• Absolute Error = |Observed Value – True Value|
• Relative Error = (|Observed Value – True Value|) / (True Value)
• Percentage Error = (|Observed Value – True Value| / True Value) × 100%

Example:

If the observed value is 56.891 and the true value is 62.327:

Percentage Error = |56.891 − 62.327| / 62.327 × 100% = 8.722%

These formulas assume the true value is known. If it’s unknown, standard deviation can be used to estimate error instead.

Negative Percentage Error:

Typically, percentage error is expressed as a positive number because we focus on the size of the error, not its direction. However, it is possible to calculate a negative percentage error if we skip the absolute value. A negative result simply means the observed value is less than the true value.

Example:

Observed value = 7
True value = 9

Percentage Error = (7 − 9) / 9 × 100% = -22.22%

This negative result just shows the observed value is smaller than expected. A positive value would indicate the opposite.

The ideal scenario is a percentage error of 0%, meaning the observed and true values are identical.

Related Calculator:
Standard Deviation Calculator, Rounding Calculator, Log Calculator, Scientific Calculator

External Resources:

Percent Error Calculator on Calculator.net