What is percent error in simple terms?

Percent error shows how far a measured value is from the true value as a percentage of the true value. It is a relative measure of accuracy, so it helps you compare errors across different scales. The smaller the percentage, the closer the measurement is to the reference.

What is the formula for percent error?

The standard formula is absolute value of measured value minus true value, divided by absolute value of true value, times 100%. Written symbolically, it is |measured − true| / |true| × 100%. The absolute value keeps the result non-negative.

What is absolute error?

Absolute error is the plain difference between the measured value and the true value, written as |measured − true|. It stays in the original units, so it tells you how many units off the measurement was. Percent error converts that difference into a percentage of the true value.

Why is the true value used in the denominator?

The true value is the reference point, so the error is measured relative to it. Using the measured value would change the meaning of the result and no longer match the standard percent error definition. This is one of the most common mistakes people make.

Can percent error be negative?

Standard percent error is usually not negative because the formula uses absolute value. If you remove the absolute value, you can show direction, but that is not the usual percent error formula. For most uses, the magnitude of the error is what matters.

What if the true value is zero?

Percent error is not defined when the true value is zero because you would be dividing by zero. In that case, percent error does not work well as a measure. Use absolute error or another comparison method instead.

Is percent error the same as percentage change?

No. Percent change compares a new value with an old value, while percent error compares a measured value with a true value. They may look similar, but they answer different questions. If you need change over time or between two states, use a percentage change calculation instead.

Percent Error Calculator

Percent error tells you how far a measured value is from the true value, expressed as a percentage of the true value. It is a standard way to judge accuracy when you have a measured result and a known reference value.

You may also see absolute error, which is the plain difference between the two values. Percent error answers “how big is the error relative to the true value?” while absolute error answers “how many units off was the measurement?” For a quick refresher on percentage terms, see Percentage, and for a broader look at how percentages compare changes, Percentage Change Calculator can help.

What percent error means

Percent error is used when you want to compare an observed or measured value against a trusted true value. Common uses include lab work, manufacturing checks, classroom problems, and any situation where the size of the error needs to be standardized.

The key idea is that the true value is the reference point. That means the same absolute difference can produce different percent errors depending on what the true value is. An error of 2 units is small if the true value is 1,000, but large if the true value is 10.

A calculator page like this one helps you turn that comparison into a clear percentage. If you are curious about the general idea of a calculator as a tool, the Wikipedia article on calculators gives a basic overview.

The formulas behind the calculation

The usual percent error formula is:

Percent error = |measured value − true value| / |true value| × 100%

In words:

Subtract the true value from the measured value.
Take the absolute value so the result is always non-negative.
Divide by the absolute true value.
Multiply by 100 to convert to a percentage.

Absolute error is simpler:

Absolute error = |measured value − true value|

So if the measured value is 48 and the true value is 50, the absolute error is the difference in units, and the percent error shows that difference as a share of 50.

This matters because percent error is not the same as percentage change. Percent change compares a new value to an old value; percent error compares a measured value to a true value. If you need the change-between-values version instead, use Percentage Change Calculator.

How to interpret the result

A smaller percent error means the measured value is closer to the true value. A larger percent error means the measurement is less accurate relative to the reference.

The sign is usually not the main point in a percent error result. Because the formula uses absolute values, the answer is normally non-negative. That makes it useful when you want size of error, not direction.

Direction can still matter in some contexts:

If measured value is greater than the true value, the measurement is high.
If measured value is less than the true value, the measurement is low.

If you need both the size and direction, look at the raw difference first, then use percent error for the relative size. Absolute error is helpful when you care about units rather than percentages, such as grams, inches, or dollars.

Worked examples

Here are a few hypothetical examples. The calculator uses the standard formula above.

Example 1: simple measurement

Suppose the true value is 100 and the measured value is 95.

Absolute error:

Percent error:

This means the measurement is 5 units away from the true value, or 5% off.

Example 2: measured value above the true value

Suppose the true value is 250 and the measured value is 260.

Absolute error:

Percent error:

Even though the measured value is too high, the percent error is still reported as a non-negative percentage because of the absolute value in the formula.

Example 3: small true value

Suppose the true value is 8 and the measured value is 10.

Absolute error:

Percent error:

This shows why percent error can look large when the true value is small. A difference of 2 units is much more significant when the reference value is only 8.

When you should use absolute error instead

Percent error is useful when comparisons need to be normalized, but absolute error is better when the raw size of the mistake is what matters.

Use absolute error when:

You want the error in the original units.
You are comparing measurements with the same scale and precision.
The true value is very small, making percent error less intuitive.

Use percent error when:

You want a relative measure of accuracy.
You need to compare errors across different scales.
You need a standard classroom or lab-style error report.

A future value calculator or other finance tool may use percentages in a different way, but percent error itself is specifically about comparing a result to a reference value.

Common mistakes and limits

A few mistakes show up often with percent error.

Using the wrong reference value

The denominator should be the true value, not the measured value. Swapping them changes the meaning of the result and gives the wrong percentage.

Forgetting the absolute value

Without absolute value, the result can be negative when the measured value is below the true value. That may be useful in some settings, but it is not the standard percent error formula.

Confusing error with percent change

Percent error is not a growth or decline calculation. It does not describe movement over time. It compares a measurement to a reference point.

Treating a very small true value casually

When the true value is near zero, percent error can become very large or undefined. In those cases, absolute error may be more useful, or you may need a different metric.

Assuming percent error tells the full story

Percent error shows size relative to the true value, but not why the error happened. It does not tell you whether the issue came from rounding, instrument limits, or a flawed method.

How to use the calculator well

To get a meaningful result, first decide which number is the true value and which one is the measured value. Then compare the percentage error and absolute error together.

A practical reading method is:

Check the absolute error to see the difference in units.
Check the percent error to judge the size of that difference relative to the true value.
Decide whether the result is acceptable for your purpose.

If you are using the calculator for homework, lab work, or quality checks, write both the measured and true values clearly before calculating. That reduces the chance of mixing up the reference value.

Frequently asked questions

What is percent error in simple terms?: Percent error shows how far a measured value is from the true value as a percentage of the true value. It is a relative measure of accuracy, so it helps you compare errors across different scales. The smaller the percentage, the closer the measurement is to the reference.
What is the formula for percent error?: The standard formula is absolute value of measured value minus true value, divided by absolute value of true value, times 100%. Written symbolically, it is |measured − true| / |true| × 100%. The absolute value keeps the result non-negative.
What is absolute error?: Absolute error is the plain difference between the measured value and the true value, written as |measured − true|. It stays in the original units, so it tells you how many units off the measurement was. Percent error converts that difference into a percentage of the true value.
Why is the true value used in the denominator?: The true value is the reference point, so the error is measured relative to it. Using the measured value would change the meaning of the result and no longer match the standard percent error definition. This is one of the most common mistakes people make.
Can percent error be negative?: Standard percent error is usually not negative because the formula uses absolute value. If you remove the absolute value, you can show direction, but that is not the usual percent error formula. For most uses, the magnitude of the error is what matters.
What if the true value is zero?: Percent error is not defined when the true value is zero because you would be dividing by zero. In that case, percent error does not work well as a measure. Use absolute error or another comparison method instead.
Is percent error the same as percentage change?: No. Percent change compares a new value with an old value, while percent error compares a measured value with a true value. They may look similar, but they answer different questions. If you need change over time or between two states, use a percentage change calculation instead.

About this article

Written by Yahav Atia, WSO – the digital agency (wso.co.il) that owns and founded this site, with the help of AI, and passed automated quality checks before publication. Numbers in the worked examples were computed in code, not estimated.