Percent Error Calculator

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

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

Notice the absolute value symbols around the difference. They make the standard percent error positive, 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.

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.

1. 1. Identify the experimental or measured value.
2. 2. Identify the true, accepted, or reference value.
3. 3. Subtract the true value from the experimental value.
4. 4. Take the absolute value of the difference so the error is non-negative.
5. 5. Divide the absolute difference by the absolute true value.
6. 6. 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. Simply enter the two values and the calculator will apply the formula for you.

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.

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.

1. Enter the experimental or measured value.
2. Enter the true, accepted, or reference value.
3. Click Calculate.
4. Read the percent error shown in the result.

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 the true value, and division by zero is undefined.

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.

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 a temperature, 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.

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.

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.

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.

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.

Frequently Asked Questions