Percent Error Calculator
Calculate percent error between an experimental and an accepted value.
What Is the Percent Error Calculator?
Percent error measures how far a measured value sits from the value it was supposed to be. It is the standard way scientists, engineers and students report whether an experiment worked. You supply the accepted value, the true or textbook figure, and your own experimental measurement, and the result is the size of the gap as a percentage. Two details trip most people up. First, percent error is always positive, because a measurement can be too high or too low and the magnitude of the mistake is what matters. Second, an accepted value of zero makes percent error undefined, since the formula divides by that value. This calculator returns the percent error, the absolute error, the relative error as a decimal, and the signed error that tells you which direction you missed by, and it shows the full calculation rather than just the number.
Key Statistics
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1.55%
The accepted value of 9.80665 metres per second squared for standard gravity at sea level. This is the constant defined by international agreement in 1901 and re-evaluated in 1964, and it is the reference used to report percent error in any free fall or pendulum experiment.
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2.3 x 10 to the power of 10
The relative uncertainty in the measured value of the standard gravitational constant g from a 2018 quantum gravity experiment using atom interferometry, showing how experimental precision is actually expressed when reporting an error.
Source: Nature, Fixer and others, 2018
The Formula
Absolute error = |Experimental value minus Accepted value|. Relative error = Absolute error divided by |Accepted value|. Percent error = Relative error multiplied by 100. The signed percent error is (Experimental value minus Accepted value) divided by |Accepted value| multiplied by 100, and it carries a plus or minus sign showing the direction of the mistake.
Worked Examples
A laboratory expects a reaction yield of 50 grams and measures 53 grams. The absolute error is 53 minus 50, which is 3 grams. The relative error is 3 divided by 50, which is 0.06. The percent error is 0.06 multiplied by 100, which is 6 percent.
Percent error when the measurement is too high
- Take an accepted value of 50 and an experimental value of 53.
- Find the absolute error: the absolute value of 53 minus 50 is 3.
- Divide by the accepted value: 3 divided by 50 is 0.06.
- Multiply by 100: 0.06 times 100 is 6 percent.
Percent error: 6 percent, measured 3 units too high
Percent error when the measurement is too low
- Take an accepted value of 200 and an experimental value of 190.
- Find the absolute error: the absolute value of 190 minus 200 is 10.
- Divide by the accepted value: 10 divided by 200 is 0.05.
- Multiply by 100: 0.05 times 100 is 5 percent.
Percent error: 5 percent, measured 10 units too low
A physics laboratory example using standard gravity
- The accepted value for standard gravity is 9.80665 metres per second squared.
- Suppose your pendulum experiment measured 9.87.
- Absolute error: the absolute value of 9.87 minus 9.80665 is 0.06335.
- Relative error: 0.06335 divided by 9.80665 is about 0.00646.
- Multiply by 100 to get a percent error of about 0.646 percent.
Percent error: about 0.646 percent
Real World Use Cases
Chemistry and physics lab reports
Almost every lab write up asks for percent yield or percent error against a theoretical value. This is the exact calculation your write up needs, including the signed version showing whether you overshot or undershot.
Engineering tolerance checks
When a part is specified at 50 millimetres and your sample measures 53, the percent error says whether the deviation sits inside the allowed tolerance. Comparing percent error across different parts makes tolerances comparable in a way raw millimetres are not.
Verifying an instrument or a recipe
A scale or a process that should yield a known amount can be checked against that target. A percent error of zero means the process is exact, and a small steady percent error is usually easier to correct than a large erratic one.
Checking a quoted statistic
When a headline number is reported as an approximation, calculating the percent error against the exact source value shows how much rounding was involved. Large percent error on a supposedly precise figure is worth asking about.
Expert Tips
- ✓ Report percent error as a positive number. If the direction matters, state it in words or use the signed version so a high reading and a low reading are not confused.
- ✓ Keep the accepted value to enough significant figures for the calculation. An accepted value given to one decimal place cannot support a percent error quoted to four.
- ✓ Do not average percent errors across trials. Convert each trial back to an experimental value and average those, because the accepted value is the same denominator each time.
- ✓ A percent error above 10 percent usually points to a method problem rather than a rounding problem. Check units, calibration and the order of operations before quoting a number.
- ✓ Use percent difference, not percent error, when neither value is a known truth. Percent error needs something to be wrong against.
Frequently Asked Questions
What is the formula for percent error? ▼
Percent error equals the absolute difference between the experimental and accepted values, divided by the accepted value, multiplied by 100. The formula is: Percent error = (|Experimental - Accepted| / |Accepted|) x 100.
How do I calculate percent error? ▼
Subtract the accepted value from your experimental value and take the absolute value. Divide that by the absolute value of the accepted value. Multiply the result by 100. For an accepted 50 and experimental 53, that is 3 / 50 x 100, which is 6 percent.
Can percent error be negative? ▼
Not as normally defined. The absolute value makes it always positive because it measures the size of the mistake rather than its direction. If you need the direction, use the signed percent error, which this calculator also returns and labels as higher or lower than accepted.
What happens when the accepted value is zero? ▼
Percent error is undefined, because the formula divides by the accepted value and division by zero has no value. This is a property of the formula rather than a mistake in your entry. The absolute error is still meaningful, and percent difference is the right tool when you are comparing two measurements rather than checking against a known truth.
What is the difference between percent error and percent difference? ▼
Percent error compares a measurement against a known true value, so it needs an accepted value. Percent difference compares two measurements when neither is a true value, and it divides by the average of the two rather than by a known truth. Use error when you have a reference and difference when you do not.
How do I report percent error in a lab report? ▼
State the accepted value, the experimental value and the percent error, and quote the error to two or three significant figures rather than the full precision of your calculator. A result written as 6.00 percent reads better than 6.000000 percent and implies the same measurement quality.
What is an acceptable percent error for a science experiment? ▼
It depends entirely on the experiment and what you are measuring. Common undergraduate lab targets are under 5 percent, and anything under 1 percent is usually considered strong. Physics constants like standard gravity can often be measured to well under 1 percent, whereas reaction yields vary far more between runs.
What is relative error? ▼
Relative error is the absolute error divided by the accepted value, expressed as a decimal rather than a percentage. An absolute error of 3 against an accepted value of 50 gives a relative error of 0.06, which is the same figure as 6 percent before the final multiply by 100.
Why does my percent error differ from my partner's? ▼
The usual causes are rounding the accepted value differently, using more or fewer significant figures, or one of you dividing by the experimental value by mistake. Agreeing on the accepted value to a fixed number of decimal places before calculating removes most of the discrepancy.
Should I take the absolute value of the accepted number? ▼
Yes, and the calculator does it for you. When the accepted value is negative, dividing by it without the absolute value would flip the sign of your answer and produce a negative percent error, which is meaningless as a measure of error size.
Common Mistakes to Avoid
- ⚠ Dividing by the experimental value instead of the accepted value. The denominator is always the accepted value.
- ⚠ Forgetting to take the absolute value, which produces a negative percent error that then reads as if the answer is nonsense.
- ⚠ Omitting the final multiply by 100 and reporting a relative error of 0.06 as the percent error.
- ⚠ Trying to calculate percent error when the accepted value is zero, which is undefined rather than zero.
- ⚠ Rounding the accepted value before computing, which changes the answer at the precision you are trying to report.
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