Understanding accuracy in experimental science and statistics is crucial. A percentage error calculator (often called an error percentage calculator) helps you determine the precision of your measurements relative to the actual, correct value. This guide walks you through the math, explains what is percent error, and details how to apply the error formula manually.
Experimental vs. Theoretical Values: What is the Difference?
Before you run a percent error calculation, you must understand the two inputs required by the percent error calculator:
- Experimental Value (Observed Value): This is the score or quantity measured during an experiment, calculated in a lab, or estimated in a forecast.
- Theoretical Value (True Value): This is the exact, accepted scientific standard value, or the known exact quantity established by mathematics or physics.
The Percent Error Formula and Percent Error Equation
To manually perform an error calculation, you apply the standard percentage error formula. The percent error equation divides the absolute error by the true value and multiplies by 100 to yield a percentage:
Percentage Error Formula = [ |Experimental Value - Theoretical Value| / Theoretical Value ] × 100
By using the absolute value, the formula of percentage error ensures that the final result represents the size of the deviation, regardless of whether it is an overestimate or an underestimate.
How to Find Percent Error: A Step-by-Step Guide
If you want to know how to do percent error or how to calculate percent error manually in your lab reports, follow these steps:
- Subtract the theoretical value from the experimental value to find the deviation.
- Take the absolute value of that result (ignore any negative sign) to get the absolute error.
- Divide the absolute error by the theoretical value.
- Multiply the resulting decimal fraction by 100. This is how to find percent error.
For example, if your experiment measures a substance's boiling point at 95°C (Experimental) but the literature states it is 100°C (Theoretical), the absolute difference is |95 - 100| = 5. Dividing 5 by 100 yields 0.05. Multiplying by 100 gives a 5% result.
Can Percent Error Be Negative?
Strictly speaking, the percent error formula uses the absolute difference, so the result is typically expressed as a positive percentage. A negative value in a calculation just indicates the experimental value is lower than the theoretical one, but it should be reported as an absolute value for the final percentage error.