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Accuracy Calculator

Percent Error & Measurement Precision
The accepted or standard value.
The result from your experiment.
Accuracy 0%
Percent Error 0%
Absolute Error 0

What is Percent Error?

In science, engineering, and data analysis, no measurement is ever 100% perfect. There is always a slight difference between what you measured and what is true.

Percent Error quantifies this mistake. It tells you how far off you are, relative to the size of the thing you are measuring.

  • Being off by 1 inch when measuring a pencil is a HUGE error.
  • Being off by 1 inch when measuring a skyscraper is a tiny error.

The Formula

The standard formula for Percent Error uses the absolute value (bars) because error is always positive (you can't have negative error in this context).

% Error = (|Measured - True| / True) × 100
  • Measured (Observed) Value: The number you got from your experiment or tool.
  • True (Theoretical) Value: The scientifically accepted or correct number.

Accuracy Formula:
Once you have the Percent Error, Accuracy is simply the remainder:
Accuracy = 100% - Percent Error

Accuracy vs. Precision: The Target Analogy

These two words are often used interchangeably, but in science, they mean very different things.

1. Accuracy (Hiting the Bullseye)

Accuracy is how close your measurement is to the True Value. If you aim for the center and hit the center, you are accurate.

2. Precision (Grouping)

Precision is how consistent your measurements are. If you shoot 5 arrows and they all hit the exact same spot in the top-left corner, you are very precise (consistent), but not accurate (you missed the target).

Scenario Result
High Accuracy, High Precision Ideal. All shots hit the center.
High Accuracy, Low Precision Shots are scattered, but the average is the center.
Low Accuracy, High Precision Systematic Error. All shots hit the wrong spot consistently.
Low Accuracy, Low Precision Random noise. Shots are everywhere.

Types of Errors

Why do errors happen? They usually fall into two categories:

  • Systematic Error: Your tool is broken or calibrated wrong. (e.g., A scale that always reads 2 lbs too heavy). This leads to High Precision but Low Accuracy.
  • Random Error: Human error, wind, or environmental noise. (e.g., Your hand shaking while measuring). This leads to Low Precision.
Real World Example:
If GPS says your destination is 100 meters away, but your phone says 105 meters:
Error = |105 - 100| = 5.
Percent Error = (5 / 100) * 100 = 5% Error.
Accuracy = 95%.

Lab & Math Toolkit

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