Percent Error Calculator
Enter your measured value and the accepted value to get the percent error, with every step shown.
Quick answer: Percent error = |experimental − theoretical| ÷ |theoretical| × 100. For example, if you measure 2.85 g/cm³ and the accepted value is 2.70 g/cm³, the percent error is 0.15 ÷ 2.70 × 100 = 5.56%.
- Percent error shows how far your measurement is from the accepted value, as a percentage.
- Use absolute value so the answer is positive. Use the signed version to see if you measured too high or too low.
- The accepted (theoretical) value always goes on the bottom of the fraction.
How to Calculate Percent Error
- Subtract the theoretical value from the experimental value.
- Take the absolute value of the difference (drop any minus sign).
- Divide by the absolute theoretical value.
- Multiply by 100 to turn the decimal into a percentage.
It is the same idea as finding any percentage: a part divided by a whole, times 100. If you need a refresher, our percentage calculator and guide on how to calculate a percentage walk through the basics.
Worked Examples
Example 1: Density of aluminium
A student measures the density of an aluminium block as 2.85 g/cm³. The accepted value is 2.70 g/cm³.
- 2.85 − 2.70 = 0.15
- |0.15| = 0.15
- 0.15 ÷ 2.70 = 0.0556
- 0.0556 × 100 = 5.56% error (the measurement is 5.56% too high)
Example 2: Acceleration due to gravity
A pendulum experiment gives 9.62 m/s². The accepted value is 9.81 m/s².
- 9.62 − 9.81 = −0.19
- |−0.19| = 0.19
- 0.19 ÷ 9.81 = 0.0194
- 0.0194 × 100 = 1.94% error (the measurement is 1.94% too low)
Percent Error Quick-Reference Table
Here is how different measurements compare with an accepted value of 100 (any unit):
| Measured value | Difference | Percent error | Direction |
|---|---|---|---|
| 90 | −10 | 10% | Too low |
| 95 | −5 | 5% | Too low |
| 98 | −2 | 2% | Too low |
| 100 | 0 | 0% | Exact |
| 101 | +1 | 1% | Too high |
| 103 | +3 | 3% | Too high |
| 110 | +10 | 10% | Too high |
Percent Error vs. Percent Difference vs. Percent Yield
| Measure | Compares | Formula |
|---|---|---|
| Percent error | Measured value vs. accepted value | |E − T| ÷ |T| × 100 |
| Percent difference | Two measured values | |A − B| ÷ ((A + B) ÷ 2) × 100 |
| Percent yield | Actual product vs. maximum possible product | Actual ÷ Theoretical × 100 |
Tips for Lab Reports
- Show your working. Teachers usually award marks for the steps, not just the final percentage.
- Keep units consistent. Convert both values to the same unit before you subtract.
- Round at the end. Keep extra decimal places until the last step, then round to two decimals.
- Explain the error. Say whether your value was too high or too low and name a likely cause, such as heat loss or reaction time.
- Know what it’s worth. Lab reports often count toward your course grade. See how much a test or assignment is worth, or check your standing with the final grade calculator.
Frequently Asked Questions
What is percent error?
Percent error measures how far a measured (experimental) value is from the accepted (theoretical) value, as a percentage of the accepted value. A smaller percent error means your measurement was closer to the true value.
What is the percent error formula?
Percent error = |experimental − theoretical| ÷ |theoretical| × 100. Subtract the accepted value from your measured value, drop the minus sign, divide by the accepted value, then multiply by 100.
Can percent error be negative?
Percent error is normally reported as a positive number because the formula uses absolute value. Some teachers ask for the signed version, (experimental − theoretical) ÷ theoretical × 100, where a negative result means your value was too low. The calculator shows both.
What is a good percent error?
There is no universal cut-off. It depends on your equipment and the experiment: precise measurements are expected to have a much smaller error than quick classroom estimates. Check the standard your teacher or lab manual sets.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known accepted value. Percent difference compares two measured values when neither is the true value, using |A − B| ÷ ((A + B) ÷ 2) × 100.
Why do you divide by the theoretical value?
The accepted value is the reference point, so the error is expressed as a share of it. That makes results comparable: an error of 0.5 matters much more when the true value is 2 than when it is 200.
What if the theoretical value is zero?
Percent error cannot be calculated when the accepted value is 0, because you cannot divide by zero. Report the absolute error (the plain difference) instead.
How can I reduce percent error in a lab?
Calibrate instruments, take several readings and average them, read scales at eye level, and record values to the precision your equipment allows. Repeating a trial is one of the simplest ways to catch a mistake.
Is percent error the same as percent yield?
No. Percent yield compares the product you actually made with the maximum possible amount in a chemical reaction. Use our percent yield calculator for that.