Percent Error Calculator

What Is a Percent Error Calculator?

A percent error calculator compares an experimental value with an accepted value and shows the size of the error as a percentage of the accepted value.

The accepted value is the value considered correct, true, or theoretically expected. The experimental value is the value you actually measured or observed.

For example, if the accepted value is 16 but your experiment produces 18, there is a difference of 2. However, the difference alone does not show how large the error is relative to the accepted value. Percent error solves this problem by expressing that difference as a percentage.

This percentage error calculator also helps you understand related measurements, including absolute error and relative error.

How to Use the Percent Error Calculator

You only need two values to calculate percent error with this calculator.

Step 1: Enter the Accepted Value

Enter the correct, true, or theoretical value in the Accepted Value (true/theoretical) field.

For example, enter 16 if 16 is the accepted value you want to use as your reference.

Step 2: Enter the Experimental Value

Enter your measured or observed result in the Experimental Value (measured) field.

For example, enter 18 if that is the value obtained from your experiment or measurement.

Step 3: Click Calculate

Select Calculate to compare the two values.

The calculator displays:

• Percent Error (Magnitude)

• Absolute Error

• Relative Error

• Accuracy interpretation

• Calculation steps

It also indicates whether your measured value is above or below the accepted value.

Step 4: Review the Calculation Steps

The Steps section shows how the values were used to determine the result. This can be especially useful when learning how to calculate percent error manually or checking your own work.

To perform another calculation, select Clear and enter new values.

Percent Error Formula

The standard percent error formula measures the absolute difference between the experimental and accepted values relative to the accepted value.

$\text{Percent Error} = \frac{|\text{Experimental Value}-\text{Accepted Value}|} {|\text{Accepted Value}|} \times 100$

Where:

• Experimental Value is the measured or observed result.

• Accepted Value is the true, theoretical, or reference value.

• The vertical bars represent absolute value, which makes the magnitude of the difference nonnegative.

• Multiplying by 100 converts the relative error into a percentage.

Using absolute value is common when the goal is to report the magnitude of percent error rather than its direction.

Absolute Error Formula

Absolute error tells you the size of the difference between the experimental and accepted values.

$\text{Absolute Error} = |\text{Experimental Value}-\text{Accepted Value}|$

For example, if the experimental value is 18 and the accepted value is 16:

$|18-16|=2$
The absolute error is 2.

Unlike percent error, absolute error is expressed in the same units as the original values when those values represent a measured quantity.

Relative Error Formula

Relative error compares the absolute error with the accepted value.

$\text{Relative Error} = \frac{|\text{Experimental Value}-\text{Accepted Value}|} {|\text{Accepted Value}|}$

Relative error is a ratio. Multiply this value by 100 to express the error as a percentage.

$\text{Percent Error}=\text{Relative Error}\times100$

This relationship explains why relative error and percent error describe the same proportional difference in different forms.

How to Calculate Percent Error

If you want to know how to find percent error manually, subtract the accepted value from the experimental value, take the absolute value of the difference, divide it by the absolute accepted value, and multiply the result by 100.

Suppose:

Accepted Value = 16
Experimental Value = 18

First, find the difference:

$|18-16|=2$

Next, divide the difference by the accepted value:

$\frac{2}{16}=0.125$

Then convert the relative error to a percentage:

$0.125\times100=12.5$

Therefore:

• Absolute Error: 2

• Relative Error: 0.125

• Percent Error: 12.5%

Because the experimental value of 18 is greater than the accepted value of 16, the measurement overestimates the accepted value by 2.

The reported percent-error magnitude remains 12.5%.

How to Interpret Percent Error Results

A percent error tells you how large the measurement error is relative to the accepted value.

In general, a smaller percent error means the experimental value is closer to the accepted value, while a larger percent error means there is a greater relative difference.

What Does 0% Percent Error Mean?

A percent error of 0% means the experimental value exactly matches the accepted value.

For example:

$\frac{|50-50|}{50}\times100=0$

This indicates no difference between the two values for that comparison.

Is a Lower Percent Error Better?

When the goal is to reproduce an accepted value accurately, a lower percent error generally indicates closer agreement.

However, there is no universal percentage that counts as a “good” percent error. An acceptable error depends on the field, experiment, measuring equipment, method, and required tolerance.

A 5% error might be acceptable in one situation but too large in another.

Can Percent Error Be Negative?

This depends on how percent error is defined.

When percent error is reported as a magnitude, the absolute value of the difference is used, so the final percentage is nonnegative.

A signed calculation can instead preserve direction:

$\frac{\text{Experimental Value}-\text{Accepted Value}} {\text{Accepted Value}}\times100$

A positive or negative sign can then indicate whether the measurement is above or below the accepted value.

This percent error calculator reports the percent error magnitude while separately helping you understand the direction of the difference. This avoids confusing the size of the error with whether the experimental value is an overestimate or underestimate.

Percent Error vs. Absolute Error vs. Relative Error

Although these terms are closely related, they describe measurement error in different ways.

Absolute Error

Absolute error is the numerical difference between the experimental and accepted values.

For accepted value 16 and experimental value 18, the absolute error is 2.

It answers:

“How far apart are these two values?”

Relative Error

Relative error compares the absolute error with the accepted value.

For the same example:

$\frac{2}{16}=0.125$

It answers:

“How large is the error relative to the accepted value?”

Percent Error

Percent error expresses relative error as a percentage.

$0.125\times100=12.5$

It answers:

“What percentage of the accepted value does this error represent?”

Percent error is often easier to compare across measurements of different sizes because it describes the error proportionally rather than only showing the raw numerical difference.

Percent Error vs. Percent Difference

Percent error and percent difference are related calculations, but they are used in different situations.

Percent error is used when one value is considered the accepted, true, or theoretical value. You compare your experimental value against that reference value.

Percent difference is generally used when comparing two experimental or measured values and neither one is considered the accepted value.

The percent difference formula is:

$\text{Percent Difference} = \frac{|A-B|} {\frac{|A|+|B|}{2}} \times100$

The key difference is the denominator. Percent error uses the accepted value as the reference, while percent difference typically uses the average magnitude of the two values.

If you have a known accepted value, a percent error calculation is usually the appropriate comparison.

When and Where Is Percent Error Used?

Percent error is useful whenever you need to compare a measured or experimental result with an established reference value.

Science and Laboratory Experiments

Students and researchers can compare experimental measurements with accepted or theoretical values. This helps show how closely an experiment agrees with the expected result.

Physics and Chemistry

Percent error is commonly used when working with measured quantities such as mass, volume, density, temperature, acceleration, and other experimental results.

Engineering and Manufacturing

Engineers and technicians may compare measured dimensions, test results, or performance values against specifications or reference values.

Instrument Testing and Calibration

Measurements from an instrument can be compared with a known reference to help evaluate measurement error. A percent error alone, however, does not replace a complete calibration or uncertainty analysis.

Research and Data Analysis

Researchers can use relative and percentage errors to describe the size of a discrepancy relative to a reference value, when that reference is appropriate for the comparison.

Common Mistakes When Calculating Percent Error

Even though the percent error equation is straightforward, small mistakes can produce an incorrect result.

Using the Wrong Value in the Denominator

For standard percent error, divide the error by the accepted value, not the experimental value.

For example:

$\frac{|\text{Experimental}-\text{Accepted}|} {|\text{Accepted}|}$

Using the experimental value in the denominator changes the calculation.

Confusing the Accepted and Experimental Values

The accepted value is the true, theoretical, or established reference value. The experimental value is the value you measured or observed.

Identify these correctly before performing the calculation.

Forgetting the Absolute Value

When calculating percent-error magnitude, use the absolute difference between the experimental and accepted values.

This keeps the reported magnitude nonnegative. The direction of the difference can be described separately as an overestimate or underestimate.

Forgetting to Multiply by 100

Relative error is expressed as a ratio. To convert it into percent error, multiply by 100.

For example:

$0.125\times100=12.5$

Using Different Units

Both values must represent the same quantity in compatible units.

For example, do not directly compare a measurement in centimeters with an accepted value in meters without first converting one of them.

Rounding Too Early

Rounding intermediate values can affect the final result, especially when working with small differences. Keep sufficient decimal places during the calculation and round the final result appropriately.

Confusing Percent Error With Percent Difference

Use percent error when you have an accepted reference value. If neither value is considered the accepted value, percent difference may be more appropriate.

What Happens If the Accepted Value Is Zero?

The standard percentage error formula divides by the magnitude of the accepted value:

$\text{Percent Error} = \frac{|\text{Experimental}-\text{Accepted}|} {|\text{Accepted}|} \times100$

If the accepted value is zero, the denominator is zero. Division by zero is undefined, so the standard percent error cannot be calculated.

In this situation, you may still be able to report the absolute error, but another comparison method may be needed to describe the relative difference.

How to Get More Reliable Percent Error Results

The percent error calculator performs the arithmetic based on the numbers you provide, so reliable results depend on using appropriate input values.

• Verify the accepted value: Use a reliable theoretical, reference, or established value for the comparison.

• Use the same units: Convert both values to compatible units before comparing them.

• Enter precise measurements: Avoid unnecessary rounding before calculating.

• Check measuring instruments: Properly maintained and calibrated equipment can reduce measurement problems.

• Repeat measurements when appropriate: Multiple observations can help identify variation and unusual results.

• Review the calculation context: A small percent error does not automatically prove that an experiment or measurement method is valid.

Percent Error and Measurement Accuracy

Percent error is often used as an indicator of how closely an experimental value agrees with an accepted value.

If the percent error is small, the measured value is relatively close to the reference value. If it is large, there is a greater relative difference.

However, accuracy and precision are not the same thing.

Accuracy describes closeness to an accepted or reference value. Precision describes how closely repeated measurements agree with one another.

A single percent error calculation can help evaluate agreement with a reference value, but it cannot by itself tell you how precise a set of repeated measurements is.

Conclusion

A percent error calculator makes it easy to compare an experimental or measured value with an accepted value. By calculating percent error, absolute error, and relative error, you can better understand both the size of a measurement difference and how large that difference is relative to the reference value.

Enter the accepted and experimental values to calculate the result instantly, then review the calculation steps to understand how the percentage was determined.

Helpful Resources

• Percent Error Explained (Khan Academy)

Pro Tips

• Absolute error is the simple difference regardless of sign.

• Relative error helps put the error in perspective relative to the total value.

• Low percent error indicates high experimental accuracy.