Percent Error Calculator
Compare Measured Values vs. Theoretical Values
$$ \text{Error} = \left| \frac{\text{Approx} – \text{Exact}}{\text{Exact}} \right| \times 100\% $$
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By Prof. David Anderson
Science Professor | 20+ Years Lab Experience
“In my 20 years supervising University Chemistry and Physics labs, I’ve seen students perform perfect titrations only to fail the lab report because of one calculation: Percent Error. The most common mistake? Dividing by the experimental value instead of the theoretical one. Accuracy is the heart of science. Whether you are calculating the density of aluminum or the speed of sound, I designed this Percent Error Calculator to ensure your lab reports are flawless. Let’s analyze your data properly.”
Percent Error Calculator: Experimental vs. Theoretical
The Complete Guide to Error Analysis, Formulas & Chemistry Lab Accuracy
The Percent Error Calculator is an indispensable tool for science students, researchers, and engineers. In any scientific experiment, there is no such thing as “perfect measurement.” There is always a discrepancy between what you measured in the lab and what the true value should be.
Percentage Error quantifies this discrepancy. It tells you how accurate your experiment was. A low percent error (typically under 5%) indicates high accuracy, while a high error suggests issues with your equipment, technique, or assumptions.
1. The Percent Error Formula
⚠️ Professor’s Terminology Check
Textbooks use different names for the same variables. Don’t get confused!
• Theoretical Value: Also called Accepted Value, True Value, Actual Value, or Standard Value. (This is the “Book Value”).
• Experimental Value: Also called Measured Value, Observed Value, or Calculated Value. (This is what YOU found in the lab).
The calculation involves finding the absolute difference between your value and the true value, then dividing it by the true value. The absolute value bars ($|…|$) are crucial because error magnitude is usually positive.
Percent Error Formula
$$ \% \text{ Error} = \left| \frac{\text{Experimental} – \text{Theoretical}}{\text{Theoretical}} \right| \times 100\% $$
Note: Always divide by the Theoretical (True) Value, not the measured one!
2. How to Calculate Percent Error (Step-by-Step)
Using our percentage error calculator is fast, but you must know the manual method for your lab exams. Follow this strict protocol.
Step 1
Identify Values
Determine which number is the Theoretical Value (from the textbook) and which is the Experimental Value (from your experiment).
Step 2
Find the Difference
Subtract the Theoretical Value from the Experimental Value.
Exp – Theor = Error
Exp – Theor = Error
Step 3
Divide & Convert
Take the absolute value of the result from Step 2. Divide it by the Theoretical Value. Finally, multiply by 100 to get the percentage.
3. Professor’s Insight: The “Denominator Trap”
Why do students constantly lose points on this calculation? Because of the Denominator Trap.
Intuitively, some students want to divide by their own measured number. Do not do this. You must always compare your error against the standard of truth.
Correct: Divide by Theoretical Value ✅
Incorrect: Divide by Experimental Value ❌
Incorrect: Divide by Experimental Value ❌
Also, regarding the Absolute Value: In 95% of science classes, we only care about the magnitude of the error (how far off you were). We don’t usually care if you were high or low, just that you missed. If your calculator gives a negative number, drop the negative sign (unless your specific engineering context demands directional error).
4. Lab Examples: Chemistry & Physics
🧪 Chemistry Example: Specific Heat
Scenario: You measure the specific heat of Aluminum in a calorimetry lab.
• Accepted Value (Theoretical): $0.903 \text{ J/g}^{\circ}\text{C}$
• Your Result (Experimental): $0.880 \text{ J/g}^{\circ}\text{C}$
Calculation:
1. Difference: $0.880 – 0.903 = -0.023$
2. Absolute Value: $|-0.023| = 0.023$
3. Divide by True Value: $0.023 / 0.903 \approx 0.02547$
4. Percentage: $0.02547 \times 100 = \mathbf{2.55\%}$
*Result: High Accuracy (Under 5%). Great job!*
🚀 Physics Example: Gravity
Scenario: Determining acceleration due to gravity ($g$) using a pendulum.
• Accepted Value ($g$): $9.81 \text{ m/s}^2$
• Your Result: $10.5 \text{ m/s}^2$
Calculation:
1. Difference: $10.5 – 9.81 = 0.69$
2. Divide by True Value: $0.69 / 9.81 \approx 0.0703$
3. Percentage: $0.0703 \times 100 = \mathbf{7.03\%}$
*Result: Moderate Error. Check air resistance or timing errors.*
5. Critical Distinction: Percent Error vs. Percent Difference
This is the #1 confusion I see in lab reports. These two terms are not interchangeable.
| Feature | Percent Error | Percent Difference |
|---|---|---|
| When to use? | When you have ONE Accepted/True Value to compare against. | When comparing TWO Experimental Values to each other (no True Value known). |
| Denominator | The Theoretical Value. | The Average of the two values: $\frac{E_1 + E_2}{2}$. |
| Formula | $$ \frac{|E – T|}{T} \times 100 $$ | $$ \frac{|E_1 – E_2|}{(E_1 + E_2)/2} \times 100 $$ |
| Example | Comparing your gravity measurement to $9.81$. | Comparing Result A from Trial 1 vs Result B from Trial 2. |
6. Professor’s FAQ Corner
What is an “acceptable” Percent Error?
This depends entirely on the context.
• High School Labs: Under 5% is excellent, under 10% is good.
• Analytical Chemistry: Often requires under 0.1% or 0.01%.
• Biological Fieldwork: Due to natural variance, errors of 10-20% might be acceptable.
• High School Labs: Under 5% is excellent, under 10% is good.
• Analytical Chemistry: Often requires under 0.1% or 0.01%.
• Biological Fieldwork: Due to natural variance, errors of 10-20% might be acceptable.
Can Percent Error be over 100%?
Yes, but it’s bad news. An error > 100% means your experimental value was more than double the true value (or extremely far off). This usually indicates a fundamental calculation error, unit conversion mistake, or broken equipment.
What is “Relative Error”?
Relative Error is simply the decimal version of percent error, before you multiply by 100.
Relative Error = 0.05
Percent Error = 5%
Relative Error = 0.05
Percent Error = 5%
References
- Harris, D. C. (2010). Quantitative Chemical Analysis. W. H. Freeman. (Standard text for analytical error).
- Taylor, J. R. (1997). An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. University Science Books. (The definitive guide for Physics).
- NIST/SEMATECH e-Handbook of Statistical Methods. “Measurement Error.”
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