Calculator How to Calculate Percent Error With Uncertainty

Percent Error Calculator with Uncertainty

Measured Value (M):

True Value (T):

Uncertainty (U):

 To calculate the percent error with uncertainty, you need to follow these steps:

1. Determine the measured value and the true value:

   • Measured value (M): The value you obtained from your measurement.
   • True value (T): The accepted or known true value.

2. Calculate the absolute error:

   • Absolute error (E) is the difference between the measured value and the true value.
   $$E = |M - T|$$

3. Calculate the percent error:

   • Percent error (PE) is the absolute error divided by the true value, multiplied by 100 to get a percentage.
   $$PE = \left(\frac{E}{T}\right) \times 100 = \left(\frac{|M - T|}{T}\right) \times 100$$

4. Determine the uncertainty in the measurement:

   • Uncertainty (U) represents the range within which the true value is expected to lie. It can be due to various factors like instrument precision, environmental conditions, etc.

5. Calculate the percent uncertainty:

   • Percent uncertainty (PU) is the uncertainty divided by the measured value, multiplied by 100 to get a percentage.
   $$PU = \left(\frac{U}{M}\right) \times 100$$

6. Combine the percent error and percent uncertainty:

   • To combine these values, consider the overall uncertainty in the measurement and the error in the context of how they might add or compound.

Here's a step-by-step example:

Example Calculation

Let's say you measured a value of 98 units, with an uncertainty of ±2 units. The true value is known to be 100 units.

1. Measured value (M): 98 units
2. True value (T): 100 units
3. Uncertainty (U): ±2 units

Step-by-step Calculation:

1. Calculate the absolute error (E):

   $$E = |M - T| = |98 - 100| = 2 \text{ units}$$

2. Calculate the percent error (PE):

   $$PE = \left(\frac{E}{T}\right) \times 100 = \left(\frac{2}{100}\right) \times 100 = 2\%$$

3. Calculate the percent uncertainty (PU):

   $$PU = \left(\frac{U}{M}\right) \times 100 = \left(\frac{2}{98}\right) \times 100 \approx 2.04\%$$

So, in this example, the percent error is 2%, and the percent uncertainty is approximately 2.04%.

Interpretation:

• The percent error tells you how far off your measurement is from the true value in percentage terms.
• The percent uncertainty gives you an idea of the reliability of your measurement.
• Together, they provide a comprehensive picture of your measurement's accuracy and precision. The combined consideration helps to understand the confidence in the measurement and its deviation from the true value.