Percent Error Calculator (Formula & Examples)

Q: Can percent error be negative?

The absolute percent error reported here is non-negative. The measured value may be above or below the accepted value; that direction is shown separately. Some assignments use a signed relative error, so follow the convention specified in your instructions.

Q: Can I enter a negative accepted or measured value?

Yes. Both inputs may be negative, but the accepted value must be nonzero. For measured −48 and accepted −50, the absolute gap is 2 and the accepted magnitude is 50, giving 4%. Make sure a percentage comparison is meaningful for your measurement scale.

Q: What happens if the accepted value is zero?

Percent error is undefined because the formula divides by the accepted magnitude. This also applies to measured zero and accepted zero. Report the absolute difference instead, and use the comparison method required by your assignment or procedure.

Q: Can percent error be greater than 100%?

Yes. Measured 25 compared with accepted 10 gives an absolute gap of 15 and a percent error of 150%. There is no 100% upper limit on this formula.

Q: Does 0% mean the measurement is perfectly accurate?

It means the entered measured and nonzero accepted values match numerically. It does not establish that the reference has no uncertainty or that the instrument is perfectly accurate. A small nonzero result below 0.005% is shown as less than 0.01%.

Q: Does swapping the two inputs change the percent error?

Usually, yes. The accepted value is the reference base. Measured 48 versus accepted 50 gives 4%, while measured 50 versus accepted 48 gives about 4.17%. Use percentage difference when neither value serves as the reference.

Q: What percent error is acceptable?

This calculator does not apply an acceptance threshold. Check the assignment, instrument specification, or applicable measurement procedure. Interpret the percentage alongside the absolute gap and the reliability of the reference value.

Q: How is the result rounded?

The percentage is normally displayed to two decimal places, with scientific notation for very large results. A positive result below 0.005% is displayed as less than 0.01%. Supporting amounts use up to six decimal places. Calculations use ordinary floating-point precision, so follow your own significant-figure rules when reporting.

What Is Percent Error?

Percent error tells you how far a measured or experimental value is from a known, accepted, or reference value. Instead of simply looking at the difference between the two numbers, percent error expresses that difference as a percentage.

This makes it easier to understand the size of an error relative to the value you are comparing it with. For example, an error of 2 units may be small when the true value is 100, but much more significant when the true value is 5.

A smaller percent error generally means the measured value is closer to the accepted value. A percent error of 0% means the two values are exactly the same.

Percent Error Formula

Percent Error = \frac{| Experimental Value - True Value |}{| True Value |} \times 100 %

The formula first finds the difference between the experimental value and the true value. That difference is then divided by the magnitude of the true value and multiplied by 100 to express the result as a percentage.

Notice the absolute value symbols around the difference. Together with the absolute value of the denominator, they make the percent error non-negative, whether your experimental value is higher or lower than the accepted value.

What the Values Mean

Each part of the formula has a specific purpose. Knowing what each value represents can help you avoid using the wrong number in the calculation.

Term	Meaning
Experimental value	The value you measured, calculated, or obtained from an experiment.
True value	The known, accepted, or reference value used as the basis for comparison.
Absolute difference	The size of the difference between the experimental and true values, without considering whether it is positive or negative.
Percent error	The difference expressed as a percentage of the magnitude of the true value.

How to Calculate Percent Error

You can calculate percent error by following a few simple steps. The most important thing is to make sure you know which value is the experimental result and which value is the accepted or reference value.

Identify the experimental or measured value.
Identify the true, accepted, or reference value.
Subtract the true value from the experimental value.
Take the absolute value of the difference so the error is non-negative.
Divide the absolute difference by the absolute true value.
Multiply the result by 100 to convert it into a percentage.

You do not need to perform these steps manually if you are using the calculator above. Enter the two values and press Calculate to apply the formula. Pressing Enter while you are in an input also submits the form.

Percent Error Example

Let's say you measure something and get an experimental value of 48. The accepted or true value is 50. We can use these two numbers to find the percent error.

Percent Error = |48 − 50| ÷ 50 × 100

= 2 ÷ 50 × 100

= 4%

The difference between 48 and 50 is 2. When that difference is compared with the true value of 50, it represents 4% of the true value. Therefore, the percent error is 4%.

How to Use the Percent Error Calculator

The calculator is designed to give you the result without having to work through the formula yourself. You only need the experimental value and the true or accepted value.

Enter the experimental or measured value.
Enter the true, accepted, or reference value.
Click Calculate.
Read the percent error, absolute difference, and whether the measured value is above or below the reference.

Make sure both values use the same unit before calculating. For example, if the experimental value is measured in centimeters, the reference value should also be in centimeters.

The true value cannot be zero because the formula requires division by its magnitude. Blank inputs are incomplete entries, not zeros. Changing either value clears the old answer; press Calculate again after editing. Reset restores the illustrative values 48 and 50 and their 4% result.

Percent Error Examples

Here are several examples showing how different experimental and true values produce different percent errors. The calculation is always based on the true value in the denominator.

Experimental	True	Percent Error
48	50	4%
102	100	2%
9.5	10	5%
75	80	6.25%
3.2	3.0	6.67%

Notice that the experimental value does not have to be lower than the true value. For example, 102 compared with 100 gives a 2% error, while 9.5 compared with 10 gives a 5% error. The absolute value in the formula means the standard percent error describes the size of the difference rather than its direction.

Percent Error in Science

Percent error is often used in science classes and laboratory experiments when a measured result needs to be compared with an accepted or reference value. It gives students and researchers a simple way to describe how close an experimental result is to the value being used for comparison.

For example, a student may measure the length of an object, determine its mass, measure its volume, or calculate the density of a material. The experimental result can then be compared with an accepted or reference value to find the percent error.

Percent error can also be useful when checking the accuracy of a measurement or experiment. A larger percentage indicates a larger difference relative to the reference value, while a smaller percentage indicates that the result is closer to the reference.

What If the Experimental Value Is Higher or Lower?

The experimental value can be either higher or lower than the true value. In the standard percent error formula, the absolute value removes the negative sign, so the final percent error is normally positive or zero.

Situation	Signed Difference
Experimental > True	Positive
Experimental < True	Negative
Experimental = True	Zero

If you want to know the direction of the error rather than just its size, you can look at the signed difference: Experimental Value − True Value.

For example, an experimental value of 48 compared with a true value of 50 gives a signed difference of −2. An experimental value of 52 compared with 50 gives a signed difference of +2. Both have a standard percent error of 4%.

Percent Error vs Percent Difference

Percent error and percent difference are similar because both express a difference as a percentage, but they are used in different situations. The main question is whether one of the values is considered the known or accepted value.

Use percent error when you have an experimental value and a true, accepted, or reference value. Percent difference is generally used when comparing two values without treating either one as the true value.

Calculation	Formula
Percent Error	\|Experimental − True\| ÷ \|True\| × 100
Percent Difference	\|Value 1 − Value 2\| ÷ Average × 100

For percent difference, the average of the two values is used as the reference in the denominator. This is different from percent error, where the true or accepted value is used.

Percent Error vs Percent Change

Percent change is used when you want to measure how much a value has increased or decreased from an original value. It is commonly used when comparing a value before and after a change.

Percent error has a different purpose. It compares an experimental result with a known, accepted, or reference value to show how far the result is from that value.

Percent Change

(New Value − Original Value) ÷ |Original Value| × 100

So, if you are comparing an old value with a new value, percent change is usually the calculation you need. If you are comparing a measurement with an accepted value, percent error is the better choice.

Quick Reference

Use this table as a quick check when working through a percent error calculation. Remember that the true value is used as the denominator.

Experimental	True	Error
48	50	4%
102	100	2%
9.5	10	5%
75	80	6.25%
3.2	3.0	6.67%

Common Mistakes

Percent error is a simple calculation, but it is easy to get a different answer by using the wrong value or missing one of the steps. Here are some common mistakes to watch for:

Using the experimental value as the denominator. The true or accepted value is used as the denominator in the standard formula.
Forgetting the absolute value. Standard percent error describes the size of the error, so the difference is normally made positive.
Forgetting to multiply by 100. Dividing the difference by the true value gives a decimal. Multiplying by 100 converts it to a percentage.
Confusing percent error with percent difference. Percent error uses a true or accepted value, while percent difference compares two values without designating one as the true value.
Using zero as the true value. Division by zero is undefined, so percent error cannot be calculated when the true value is zero.
Using different units. Convert the values to the same unit before calculating percent error.
Rounding too early. Keep additional decimal places during the calculation and round the final answer when appropriate.

When to Use Percent Error

Use percent error when you have a measured or experimental result and want to see how far it is from a known, accepted, or reference value. It is especially helpful when the size of the difference is more useful as a percentage than as a raw number.

You may encounter percent error in laboratory experiments, science assignments, engineering measurements, research, and other situations where an experimental result is compared with a reference value.

For example, if your measurement is 2 units away from the accepted value, the number 2 alone does not tell you whether that difference is large or small. Percent error puts the difference into context by comparing it with the size of the true value.

Zero, negative, and very small reference values

A measured value of zero is allowed when the reference is nonzero. For example, 0 compared with 50 has a gap of 50, so its percent error is 100%. A reference of zero is different: dividing by zero is undefined, even when the measured value is also zero. In that case, report the difference in the original unit rather than inventing a percentage or replacing the reference with a convenient small number.

Negative inputs are accepted by the declared magnitude-based formula. For example, measured −48 and accepted −50 give an absolute gap of 2 and a percent error of 2 ÷ 50 × 100 = 4%. The measured value is above the reference because −48 is greater than −50. Its direction and its percent error describe different things; the percentage itself remains non-negative.

When the accepted magnitude is very small, a modest absolute gap can produce a large percent error. Measured 0.02 compared with accepted 0.01 gives 100%, although the gap is only 0.01 in the original unit. Check both the percentage and the absolute difference before deciding what the result means. Do not interpret a large percentage alone as proof that a measurement procedure is unusable.

Rounding and choosing a meaningful comparison

The calculator keeps the available precision through the calculation and normally displays the percentage to two decimal places. A positive error below 0.005% appears as less than 0.01%, so a small mismatch is not presented as exact equality. Supporting amounts use up to six decimal places and scientific notation for very large or small values. Apply your assignment’s significant-figure or reporting rules when copying the result.

A display of 0.00% means the entered values match numerically. It does not prove that either value is perfectly accurate, that the instrument has no uncertainty, or that repeated measurements agree. Enter the recorded values without adding digits the instrument did not measure. Ordinary number precision also limits how many significant digits can be distinguished.

A percentage comparison needs a meaningful zero and a consistent basis. Converting both lengths from centimeters to meters preserves this percentage because both numbers are multiplied by the same factor. Adding an offset to a scale does not preserve it. For example, 18°C compared with 20°C gives 10% by this arithmetic, while 291.15 K compared with 293.15 K gives about 0.68%. Follow the required physical scale or report the temperature difference instead of treating these percentages as interchangeable.

There is no acceptance threshold built into this tool. A classroom exercise, instrument check, or laboratory method may have its own comparison rules. Use the relevant instructions and reference data; this calculation alone does not label a result acceptable or identify the cause of the discrepancy.

Before you report the result

Identify the accepted value from the appropriate reference, rather than choosing the value that gives the smaller error.
Use matching units, conditions, and a meaningful comparison scale.
Check the nonzero reference and keep the recorded signs of negative quantities.
Read the absolute difference and direction beside the percentage.
State the reference, rounding, and applicable reporting requirements when sharing the answer.

Calculation basis

OpenStax’s explanation of absolute and relative error distinguishes the size of a discrepancy from its size relative to the reference. This calculator applies that magnitude-based relationship to your entered values and multiplies by 100. It reports the absolute percent error; signed-error conventions used in a particular course or method should be stated separately.

Frequently asked questions

Can percent error be negative?