Percent Deviation Calculator

| Added in Statistics

What is Percent Deviation?

Percent Deviation measures how much a measured or experimental value differs from a known true or accepted value. It is expressed as a percentage and can be positive (overestimate) or negative (underestimate), providing insight into both the magnitude and direction of measurement error.

How to Calculate Percent Deviation

The formula for calculating percent deviation is:

[\text{Percent Deviation} = \frac{X_m - X_t}{X_t} \times 100]

Where:

  • Percent Deviation is the deviation expressed as a percentage
  • Xₘ is the measured or experimental value
  • Xₜ is the true or accepted value

Calculation Example

Suppose you measured a length as 102.5 cm when the true value is 100 cm.

Step 1: Identify the values:

  • True Value (Xₜ): 100 cm
  • Measured Value (Xₘ): 102.5 cm

Step 2: Apply the formula:

[\text{Percent Deviation} = \frac{102.5 - 100}{100} \times 100]

Step 3: Calculate:

[\text{Percent Deviation} = \frac{2.5}{100} \times 100 = 2.5%]

The measurement shows a positive 2.5% deviation, meaning it overestimates the true value by 2.5%.

Interpretation Guide

Percent Deviation Meaning
Positive (+) Measured value is higher than true value
Negative (-) Measured value is lower than true value
0% Perfect accuracy
±1% Excellent accuracy
±5% Good accuracy
> ±10% Consider recalibration

Frequently Asked Questions

Percent deviation measures how much a measured or experimental value differs from a known true value, expressed as a percentage of the true value.

A negative percent deviation indicates the measured value is less than the true value. A positive deviation means the measured value exceeds the true value.

Percent error typically uses the absolute difference, always giving a positive result. Percent deviation can be positive or negative, showing the direction of the error.

This depends on the application. Scientific experiments often aim for less than 5% deviation. Industrial processes may have different tolerances based on quality requirements.