# What is the percent error?

Computes the percent error between an experimental (measured) value and the theoretical (true) value, or either value from the other and the percent error.

- Page: https://www.acalculator.org/math/percent-error-calculator
- JSON spec: https://www.acalculator.org/math/percent-error-calculator.json
- Version: 8daba471f55b

## Default answer

Example with the default inputs (Theoretical value 100, Experimental value 105): The percent error between 100 and 105 is 5%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| theoretical | Theoretical value | The true or accepted value. It cannot be 0. |
| experimental | Experimental value | The measured or observed value. |
| percentError | Percent error | The size of the difference as a percent of the true value, never negative. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| theoretical | Theoretical value | The true or accepted value. It cannot be 0. |
| experimental | Experimental value | The measured or observed value. |
| error | Percent error | The size of the difference as a percent of the true value, never negative. |
| signed | Signed error | The difference with its sign, (E − T) ÷ \|T\| × 100: positive when the measurement is too high. |
| difference | Difference | The experimental value minus the theoretical value, E − T. |

## Method

δ = |E − T| ÷ |T| × 100, where E is the experimental value and T the theoretical value.

## Assumptions

- The theoretical (true) value is not 0.
- The percent error is never negative; the signed error shows whether the measurement is high or low.
- Finding the experimental value from the true value and the error has two answers, one below and one above. Finding the true value from the measurement and the error also has two, E ÷ (1 + δ/100) and E ÷ (1 − δ/100), except at 100% where only the first exists.

## Worked examples

1. theoretical = 100, experimental = 105 gives percentError = 5%, signed = 5%, difference = 5. Source: Percent error: CK-12 Introductory Chemistry, section 3.13 "Percent Error" (Chemistry LibreTexts). https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/03:_Measurements/3.13:_Percent_Error.
2. theoretical = 9.81, experimental = 9.6 gives percentError = 2.140673%, signed = -2.140673%. Source: Percent error: CK-12 Introductory Chemistry, section 3.13 "Percent Error" (Chemistry LibreTexts). https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/03:_Measurements/3.13:_Percent_Error.
3. theoretical = -10, experimental = -12 gives percentError = 20%, signed = -20%. Source: Percent error: CK-12 Introductory Chemistry, section 3.13 "Percent Error" (Chemistry LibreTexts). https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/03:_Measurements/3.13:_Percent_Error.
4. theoretical = 100, percentError = 5% gives experimental = 95. Source: Percent error: CK-12 Introductory Chemistry, section 3.13 "Percent Error" (Chemistry LibreTexts). https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/03:_Measurements/3.13:_Percent_Error.
5. experimental = 105, percentError = 5% gives theoretical = 110.526316. Source: Percent error: CK-12 Introductory Chemistry, section 3.13 "Percent Error" (Chemistry LibreTexts). https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/03:_Measurements/3.13:_Percent_Error.

## FAQ

### What is percent error?

Percent error is a measure of the accuracy of a measurement or calculation compared to the true or accepted value. It's calculated as the absolute difference between the observed value and the true value, divided by the true value, multiplied by 100.

### How do you calculate percent error?

The formula for percent error is: |Observed Value - True Value| ÷ |True Value| × 100. This gives you the size of the difference between your measurement and the accepted value, as a percentage.

### What does a positive signed error mean?

The percent error itself is never negative. The signed error keeps the sign of the difference: a positive signed error means your observed value is higher than the true value (overestimation). For example, if you measured 105 when the true value is 100, the percent error is 5% and the signed error is +5%.

### What does a negative signed error mean?

A negative signed error means your observed value is lower than the true value (underestimation). For example, if you measured 95 when the true value is 100, the percent error is 5% and the signed error is −5%.

### When is percent error used?

Percent error is commonly used in scientific experiments, quality control, engineering measurements, and any situation where you need to assess the accuracy of measurements or calculations compared to known standards.

### What is a good percent error?

A good percent error depends on the context: the instrument, the method, and what the result is used for. Many teaching labs treat a few percent as acceptable, but there is no single standard, so check what your field or course expects.

### How is percent error different from percent difference?

Percent error compares a measured value to a known true value, while percent difference compares two experimental values to each other. Percent error is used when you have a reference standard, while percent difference is used when comparing two measurements.

### Can percent error be more than 100%?

Yes, percent error can exceed 100%. This happens when the observed value is more than double the true value. For example, if the true value is 50 and you measure 150, the percent error is 200%.

### How do I interpret percent error in experiments?

In experiments, percent error helps you evaluate the accuracy of your measurements. Lower percent errors indicate more accurate measurements. Consider factors like instrument precision, human error, and systematic biases when interpreting results.

### What are common sources of percent error?

Common sources include measurement instrument limitations, human reading errors, environmental factors, systematic biases, and random variations. Understanding these sources helps improve measurement accuracy.

### Why do I get two answers?

A percent error says how far off a measurement is, not in which direction. So a true value of 100 and a 5% error fit a measurement of 95 or 105, and the calculator shows both.

## Sources

- Percent error: CK-12 Introductory Chemistry, section 3.13 "Percent Error" (Chemistry LibreTexts). https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/03:_Measurements/3.13:_Percent_Error