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.

How to Use the Percent Error Calculator

This calculator works out percent error between a value you measured and the value it should have been, and shows every step so you can quote the working in a lab report or assignment.

Step-by-Step Instructions

1 Enter the accepted value in the first box. This is the true or textbook figure you are measuring against.
2 Enter your experimental value in the second box. This is your own measurement.
3 Read the percent error, absolute error, relative error and signed error together. The signed figure tells you whether you measured high or low.
4 Check the How this is worked out panel to copy the arithmetic into your write up.
5 If neither value is a known truth, tick the percent difference option and compare the two measurements against each other instead.

Understanding the Inputs

Accepted value

The accepted value, also called the theoretical, true, reference or literature value. This is the denominator of the whole calculation, so its precision directly limits how precise your percent error can be.

How to find it: Your textbook value, a reference table such as NIST, or the theoretical yield predicted by the reaction equations. Common physics constants such as standard gravity at 9.80665 come from these tables.

Why it matters: Percent error is meaningless without something to be wrong against. Supplying the accepted value converts a raw difference into a comparable measure of how large the mistake is.

Type: number · Default: 50

Experimental value

Your own measured value. It can be higher or lower than the accepted value, and the calculator reports both the magnitude of the error and its direction.

How to find it: Whatever your instrument, balance or reaction produced. Enter it exactly as measured, without rounding first, and let the calculator do the rounding at the end.

Why it matters: The gap between this and the accepted value is the raw material of the calculation. Rounding it before it gets here changes the answer at the precision you are trying to report.

Type: number · Default: 53

Tips & Best Practices

✓ Quote your final answer to two or three significant figures, not the full precision shown.
✓ Keep more decimal places on the accepted value than you plan to report on the answer.
✓ If the accepted value is zero, switch to percent difference rather than forcing a result.
✓ For multiple trials, average the experimental values first and then run a single percent error.

Try the Percent Error Calculator

by CalculatorPro Tools · Updated 10-12-2026