# Percent error calculator

> Percent error tells you how far a measurement is from the accepted value, expressed as a percentage. Enter both values and get the result instantly.

Calculate percent error between a measured (experimental) value and the accepted (theoretical) value. Also shows absolute and relative error.

**Interactive version:** https://onlinecalculator.me/math/percent-error/
**Category:** Math

## Formula

```
Percent error = |measured − theoretical| / |theoretical| × 100
```

All variables defined:

- **measured**: the value you obtained from an experiment or measurement
- **theoretical**: the accepted, true, or expected value
- **Absolute error**: |measured − theoretical|
- **Relative error**: |measured − theoretical| / |theoretical|

## Worked example

Gravitational acceleration experiment:

- Measured: 9.8 m/s²
- Theoretical (accepted): 9.81 m/s²
- Absolute error: |9.8 − 9.81| = 0.01
- Percent error: 0.01 / 9.81 × 100 ≈ **0.102%**

## Frequently asked questions

### What is percent error?

Percent error = |measured − theoretical| / |theoretical| × 100. It measures how close a measurement is to the true value, always expressed as a non-negative percentage.

### What is the difference between absolute and relative error?

Absolute error is the raw difference |measured − theoretical|. Relative error is that difference divided by the true value (a ratio, not a percentage). Percent error is relative error × 100.

### Why is percent error always positive?

By convention, percent error uses the absolute value of the difference so it is always non-negative. The signed error field in this calculator shows whether you measured over or under.

### What does it mean when theoretical is zero?

Percent error is undefined when the theoretical value is zero because dividing by zero is not allowed. The calculator shows "undefined" in that case.

### How do I share my calculation?

Click "Share with my numbers" to copy a URL that restores your measured and theoretical values.

## Sources

- [Approximation error (relative and percent error)](https://en.wikipedia.org/wiki/Approximation_error) — Wikipedia
- [Percentage Error](https://mathworld.wolfram.com/PercentageError.html) — Wolfram MathWorld

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